![15
Genetic Algorithm
factors such as competition, territory and environmental situations. An individual
with poor fitness value may have chance to produce excellent features in conjunction
with genes of other individuals. Hence by not discarding poor solutions, a chance is
given to the poor individuals so that good features remain.
Since the range of values changes and is problem dependent, normalization of
values is very important. One of the issues that surround the roulette wheel is that it
fails in handling the negative values. Therefore the negative values must be mapped
to positive ones through fitness scaling as negative values may impact during the
cumulative sum process.
Some of the other selection operators (Genlin, 2004) besides roulette wheel are:
steady-state reproduction (Syswerda, 1989), proportional selection (Grefenstette,
1989), fuzzy selection (Ishibuchi and Yamamoto, 2004), truncation selection
(Blickle and Thiele, 1996), rank selection (Kumar, 2012), Boltzmann selec-
tion (Goldberg, 1990), linear rank selection (Grefenstette, 1989), fitness uniform
selection (Hutter, 2002), local selection (Collins and Jefferson, 1991), steady-state
selection (Syswerda, 1991) and tournament selection (Miller and Goldberg, 1995).
The natural selection process aids in selection of individuals for the crossover
step and are treated as parents. This allows for gene exchange between individu-
als to produce new solutions. Literature suggests a number of different methods of
crossover. The chromosome is divided into two or three pieces in case of the easiest
of the methods (Shenoy et al., 2005). The genes between the chromosomes are then
exchanged. This can be visualized in Figure 2.2 clearly.
The chromosomes of two parent solutions are swapped with each other in the
single
-point crossover and therefore there is one crossover point. However, in case
of
double-point crossover, there are two crossover points i.e., the chromosomes of
the
parent solutions swap between these points. The other techniques of cross-
over as
mentioned in different literatures are: uniform crossover (Semenkin and
Semenkina, 2012), three parents crossover (Tsutsui et al., 1999), cycle crossover (Smith
and Holland, 1987), position-based crossover (Fonseca and Fleming, 1995), masked
crossover (Louis and Rawlins, 1991), half-uniform crossover (Hu and Di Paolo, 2009),
partially matched crossover (Bäck et al., 2018), order crossover (Davis, 1985), heuristic
crossover (Fogel and Atma, 1990) and multi-point crossover (Eshelman et al., 1989).
The overall objective of the crossover step is to ensure that genes are exchanged
and the children inherit the genes from the parent solutions. The main mechanism of
exploration in GA is the crossover step. There can be crossover using random points
and hence the GA is trying to check and search for different combinations of genes
coming from parents. This step therefore aids in exploration of possible solutions
without the introduction of new genes.
Probability of the crossover i.e., Pc is an important parameter in GA that identifies
the probability of accepting a new child. This parameter is a solution in the interval 0
and 1. For each child a random number is generated in the interval [0,1]. The child is
propagated to the subsequent generation if the random number generated is less than
the probability of crossover. If this is not the case then parent is propagated. This is
also true with the nature wherein all the offspring don’t survive.
The main issue associated with the crossover is the lack of introduction of new
genes. If all the solutions become poor, the crossover mechanism will not result in](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-35-320.jpg)
![25
PSO Algorithm
It is common practice to set up upper limit for the velocity parameter. To restrict
the particles flying out of the search space, velocity clamping has been used (Shahzad,
2014). Constriction coefficient is another method that was proposed by Clerc and
Kennedy (2002).
Inertia is represented in the first part of Equation (3.2) and provides the necessary
momentum for the particles to roam across the search space. The second part of the
Equation (3.2) represents the cognitive component and is significant of individual
thinking of particle. This component is a motivational factor for the particles to prog-
ress toward their own best position. Cooperation component is the third part of the
Equation (3.2) and reflects the collaborative efforts of the particles. This component
aids the particle to search for the global optimal solution (Zhang et al., 2014).
Position and velocities are adjusted at each time step, and the optimization
function is then evaluated for the new coordinates. The particle stores the coordi-
nates in the vector pbest id as and when the particle discovers a pattern that is better
than the previously identified one. The difference between the current individual
point and the best point identified by a particular agent is added to the current veloc-
ity stochastically and therefore the trajectory of the particle as such is caused to
oscillate around the point. Furthermore, each particle is defined within the realm of
topological neighborhood that comprises the particle itself and other particles in the
population. Also the particle velocity gets updated through the addition of weighted
difference between the global best and neighborhood best to its current velocity. This
addition is also stochastic and hence the velocity is adjusted for the next time step.
3.2.2 Some Definitions
Particle (X): This is candidate solution and is represented by d dimensional vector.
The dimension of vector is defined by the number of optimized parameters. Particle
at any time t can be depicted as Xi(t)=[Xi1(t), Xi2(t),…,Xid(t)], where the optimized
parameters are represented by X’s and Xid(t) reflects the position of ith particle w.r.t.
to the value of the dth optimized parameter in the ith candidate solution.
Population X(t): The set of particles is reflected in population and is represented
by X(t)=[X1(t), X2(t)…Xn(t)].
Swarm: The disorganized population of moving particles is represented by swarm.
In a swarm the particles tend to cluster with one another wherein each particle moves
in a random direction.
Particle velocity V(t): The velocity of moving particles is represented by d dimen-
sional vector. The velocity of a particle at any time t can be obtained using Equation
(3.2). It is represented by Vi(t)=[Vi1(t), Vi2(t)…Vid(t)] where the velocity of the ith
particle with respect to the dth dimension. The value of Vid(t) fluctuates between the
range −Vmin and −Vmax and is therefore referred to as velocity clamping.
Inertia weight (w): The exploitation and exploration of the search space are
controlled by the inertia weight. It dynamically adjusts the velocity. The effect on
current velocities of the previous velocity is controlled using the inertia weight.
A compromise between the global and local exploration abilities of the swarm is
exhibited. Global exploration is facilitated through a large inertia weight wherein
the local exploration is facilitated by a small weight. Therefore the inertia weight](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-45-320.jpg)
![27
PSO Algorithm
The feasibility of all the generated solutions are ensured through a check on all
the imposed constraints. If in case any of the inequality constraint is violated by any
element, then the position of the individual is fixed to its maximum or minimum
operating point. Archive is also updated that stores the non-dominated solution.
Memory update: The particle’s best position as well as the global best solutions
are updated using the following equations.
1 1 if 1
1 1 if 1
best best
best best
p t p t f p t f p t
g t p t f p t f g t
[ ]
[ ]
[ ]
[ ]
( ) ( ) ( )
( ) ( ) ( )
( )
( )
+ = + +
+ = + +
(3.5)
where, f(X) is the objective function that requires to be minimized.
The fitness evaluation of particles are compared with particles pbest. If current
value is better than pbest(t), then pbest(t+1) is set as the new current value for subse-
quent iteration in the d dimensional space. The fitness evaluation is compared with
the population’s overall previous best. If the current global position gbest(t+1) is better
than gbest(t) then the global best is set to gbest(t+1).
Examination of termination criteria: The algorithm repeats the aforementioned
steps until and unless a sufficient good fitness value is achieved or maximum number
of iterations have been achieved. The algorithm, on termination, will generate the
output points gbest(t) and hence f(gbest(t)).
The optimal parameters that have been considered usually to yield optimal
solutions are as follows: population size considered is 50, number of iterations as
100, c1 and c2 are set to 2, inertia weight w can range between 1.4 and 0.4.
3.4
SOME MODIFIED PSO ALGORITHMS
3.4.1
Quantum-Behaved PSO
The concept of quantum-behaved PSO (QPSO) stemmed from quantum mechanics.
A modified QPSO was proposed by Jau et al. (2013) that aided in elimination of
the associated drawbacks of basic PSO. The proposed algorithm employed a high-
breakdown regression estimator as well as least-trimmed square method. QPSO with
differential mutation operator was employed by Jamalipour et al. (2013) for optimiza-
tion of WWER-1000 core fuel management. It was revealed that QPSO-Differential
mutations(QPSO-DMs)performsbetterthanthebasicPSOalgorithm.QPSOwasused
by Bagheri et al. (2014) for foreign exchange market. An improved QPSO algorithm
was proposed by Tang et al. (2014) for continuous nonlinear large-scale problems
which was based on memory mechanism and memetic algorithm. The memetic algo-
rithm aided the particles to gain some experience through the local search phase and
then utilize this experience for the subsequent evolutionary process. On the other
hand the memory mechanism led to the introduction of bird kingdom and therefore
improving the global search ability of the QPSO algorithm. A new hybrid approach
encompassing QPSO and simplex algorithms was proposed by Davoodi et al. (2014)
wherein QPSO was the main optimizer and simplex algorithm was used to fine-tune
the solution obtained from QPSO. Artificial fish swarm algorithm was integrated](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-47-320.jpg)
![So far we have been concerned with the tendency in dreams to
objectify portions of the body by constructing out of them new
personalities. But precisely the same process goes on in sleep with
regard to our thoughts and feelings. We split off portions of these
also and construct other personalities out of them, and sometimes
even endow the persons thus formed with thoughts and feelings
more native to our own normal personality than those which we
reserve for ourselves. Thus a lady who dreamed that when walking
with a friend she discovered a species of animal fruit, a kind of
damson containing a snail, expressed her delight at finding a
combination so admirably adapted to culinary purposes; it was the
friend who, retaining the attitude of her own waking moments,
uttered an exclamation of disgust. Most of the dreams in which there
is any dramatic element are due to this splitting up of personality; in
our dreams we may experience shame or confusion from the
rebukes or the arguments of other persons, but the persons who
administer the rebuke or apply the argument are still ourselves.[167]
Some writers on dreaming have marvelled greatly at this tendency of
the sleeping mind to objectify portions of itself, and so to create
imaginary personalities and evolve dramatic situations. It has
seemed to them quite unaccountable except as the outcome of a
special gift of imagination appertaining to sleep. Yet, remarkable as
it is, this process is simply the inevitable outcome of the conditions
under which psychic life exists during sleep. If we realise that a
more or less pronounced degree of dissociation of the contents of
the mind occurs during sleep, and if we also realise that, sleeping
fully as much as waking, mind is a thing that instinctively reasons,
and cannot refrain from building up hypotheses, then we may easily
see how the personages and situations of dreams develop. Much the
same process might, under some circumstances, occur in waking
life. If, for instance, we heard an unknown voice speaking behind a
curtain, we could not fail to build up an imaginary person in
connection with that voice, the characteristics of the imaginary
person being largely determined by the nature of the voice and of
the things it uttered: it would, further, be quite easy to enter into](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-52-320.jpg)
![conversation with the person we had thus constructed. That is what
seems to occur in dreams. We hear a voice behind the curtain of
darkness, and to fit that voice and the things it utters we
instinctively form a picture which, in virtue of the hallucinatory
aptitude of sleep, is thrown against the curtain; it is then quite easy
to enter into conversation with the person we have thus constructed.
It no more occurs to us during sleep to suppose that the voice we
hear is only a voice and nothing more, than it would occur to us
awake to suppose that the voice behind the curtain is only a voice
and nothing more. The process is the same; the difference is that in
dreams we are, without knowing it, living among what from the
waking point of view are called hallucinations.
This process by which dreams are formed in sleeping consciousness
through the splitting of the dreamer's personality for the
construction of other personalities has been recognised ever since
dreams began to be seriously studied. Maury referred to the scission
of personality in dreams.[168] Delboeuf dealt with what he termed
the altruising by the dreamer of part of his representations.[169]
Foucault terms the same process personalisation.[170] Giessler
attempts elaborately to explain the enigma of self-diremption—the
formation of a secondary self—in dreams; if, he argues, a touch or
other sensation exceeds the dream-body's capacity of adaptation—
i.e., if the state of stimulus is above the apperceptive threshold—
only one part of the perception is referred to the dream-body and
the other is transferred to a secondary self.[171] This explanation,
while it very fairly covers the presentative class of dreams, directly
connected with sensory stimuli, cannot so easily be applied to the
dramatisation of our representative dreams, which are not obviously
traceable to direct bodily stimulation.
The splitting up of personality is indeed a very pronounced and
widely extended tendency of the mind, and has, during recent years,
been elaborately studied. We thus have the basis of that psychic
phenomenon which is variously termed secondary personality,
double personality, duplex personality, multiple personality,](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-53-320.jpg)
![alternation of personality, etc.,[172] and in earlier ages was regarded
as due to possession by demons. Such conditions seem to be usually
associated with hysteria. The essential fact about hysteria is,
according to Janet, its lack of synthetising power, which is at the
same time a lack of attention and of apperception, and has as its
result a disintegration of the field of consciousness into mutually
exclusive parts; that is to say, there is a process of dissociation. Now
that is a condition resembling, as we have seen, the condition found
in dreaming. It is not, therefore, difficult to accept the view of Sollier
and others, that hysteria is a condition allied to sleep, a condition of
vigilambulism in which the patients are often unable to obtain
normal sleep, simply because they are all the time in a state of
abnormal sleep; as one said to Sollier: 'I cannot sleep because I am
asleep all the time.' It may thus be the case that hysterical multiple
personalities[173] furnish a pathological analogue of that tendency to
the dramatic objectivation of portions of our personality which is
normal and healthy in dreams.
Similarly in insanity we have an even more constant and pronounced
tendency for the subject to attribute his own sensations to imaginary
individuals, and to create personalities out of portions of the real
personality. All the illusions, delusions, and hallucinations of the
insane are merely the manifold manifestations of this tendency.
Without it the insanity would not exist. It is not because he is
subjected to unusual sensations—visionary, auditory, tactile,
olfactory, visceral, etc.—that a man is insane. It is because he
creates imaginary personalities to account for these sensations; if his
food tastes strange some one has given him poison if he hears a
strange voice it is some one communicating with him by telephones
or microphones or hypnotism; if he feels a strange internal sensation
it is perhaps because he has another person inside him. The case
has even been recorded of a man who attributed any feeling he
experienced, even the most normal sensations of hunger and thirst,
to the people around him. It is exactly the same process as goes on
in our dreams. The sane man, the normal waking man, may](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-54-320.jpg)
![experience all these strange sensations, but he recognises that they
are the spontaneous outcome of his own organisation.
We may, however, advance a step beyond this position. This self-
objectivation, this dramatisation of our experiences, is not confined
to sleep and to pathological conditions which resemble sleep. It is
natural and primitive in a far wider sense. The infant will gaze
inquisitively at its own feet, watch their movements, play with them,
'punish' them; consciousness has not absorbed them as part of the
self.[174] The infant really acts and feels towards the remote parts of
his own body as the adult acts and feels in dreaming. We are
reminded of the generalisation of Giessler that dream consciousness
corresponds to the normal psychic state in childhood, while sleeping
subconsciousness corresponds to the embryonic psychic state; so
that the dream state represents the renascence of the ego
disentangling itself from the impersonal sensations and indistinct
images of the embryonic stage of life. That sleeping consciousness is
the primitive embryonic consciousness is, indeed, indicated, it has
often seemed to me, by the fact that in many animals the embryonic
position is the position of rest and sleep. Ducklings and chicks in the
shell have their heads beneath their wing. The dog lies with his feet
together, head flexed, and hind-quarters drawn up. Man, alike in the
womb and asleep, tends to be curled up, with the flexors
predominating over the extensors.
The savage has gone beyond the infant in ability to assimilate the
impressions of his own limbs, but on the psychic side he still
constantly tends to objectify his own feelings and ideas, re-creating
them as external beings. Primitive man has done so from the first,
and this impulse has struck its roots into all our most fundamental
human traditions even as they survive in civilisation to-day. The man
of the early world moves, like the dreamer, among a sea of emotions
and ideas which he cannot recognise the origin of, and, like the
dreamer, he instinctively dramatises them. But, unlike the dreamer,
he gives stability to the images he has thus created and in good faith
mistaken for independent beings. Thus we have the animistic stages](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-55-320.jpg)
![of culture, and early man peoples his world with gods and spirits and
demons and fairies and ghosts which enter into the traditions of his
race, and are more or less accepted even by a later race which no
longer creates them for itself.
In our more advanced civilisations we are still struggling with later
forms of that Protean tendency to objectify the self and to animate
the things and even the people around us with our own spirit. The
impatient and imperfectly bred child, or even man, kicks viciously
the object he stumbles against, animate or inanimate, in order to
revenge a wrong which exists only in himself. On a slightly higher
plane, the men of mediæval times brought actions in the law courts
against offending animals and solemnly pronounced sentence
against them as 'criminals,'[175] while even to-day society still
'punishes' the human criminal because it has imaginatively re-
created him in the image of an ordinary normal person, and lacks
the intelligence to perceive that he has been moulded by the laws of
his nature and environment into a creature which we do well to
protect ourselves against, but have no right to 'punish.'[176]
Everywhere we still see around us the surviving relics of this
primitive tendency of men to project their own personalities into
external objects. A fine civilisation lies largely in the due
subordination of this tendency, in the realisation and control of our
own emotional possibilities, and in the resultant growth of personal
responsibility.
It is thus impossible to over-estimate the immense importance of the
primitive symbolic tendency to objectify the subjective. Men have
taken out of their own hearts their best feelings and their worst
feelings, and have personalised and dramatised them, bowed down
to them or stamped on them, unable to hear the voice with which
each of their images spoke: 'I am thyself.' Our conceptions of
religion, of morals, of many of the mightiest phenomena of life,
especially the more exceptional phenomena, have grown up under
this influence, which still serves to support many movements of to-
day by some people imagined to be modern.](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-56-320.jpg)
![CHAPTER VIII
DREAMS OF THE DEAD
Mental Dissociation during Sleep—Illustrated by the Dream of
Returning to School Life—The Typical Dream of a Dead Friend—
Examples—Early Records of this Type of Dream—Analysis of
such Dreams—Atypical Forms—The Consolation sometimes
afforded by Dreams of the Dead—Ancient Legends of this
Dream Type—The Influence of Dreams on the Belief of Primitive
Man in the Survival of the Dead.
Our memories tend to fall into groups or systems. We all possess a
great number of such systematised groups of impressions. Every
period of life, every subject we have occupied ourselves with, every
intimate friend we have had, each represents a more or less
separate mass of ideas and feelings. Within each system one idea or
feeling easily calls up another belonging to the same system.
Moreover, in full and alert waking life, each system is in touch with
the systems related to it. If there crowd into the field of
consciousness the memories belonging to one period of life, or one
country we have lived in, we can control and criticise those
memories by reference to others belonging to another period or
another country. If we are overwhelmed by the thoughts and
emotions associated with the memory of one friend we can restore
our mental balance by evoking the thoughts and emotions
associated with another friend. The various systems are in this way
co-ordinated in apperception.[177]
In sleep, however, these groups are not usually so firmly held
together by the cords along which we can move in our waking
moments from one to the other. They are, as it were, loosened from](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-58-320.jpg)
![their moorings, and on the sea of sleeping consciousness they drift
apart or jostle together in new and what seem to be random
associations. This is that process of dissociation which we find so
marked in dreaming, and in all those psychic phenomena—
hallucinations, hysteria, multiple personality, insanity—which are
allied to dreaming.
A simple illustration of the clash and confusion of two opposing
systems of memories in dreams, when due apperceptive control is
lacking, is supplied by a common and well-recognised type of dream,
the dream of returning to the school of youth.[178] Many people are
occasionally liable to this dream, which is often vivid and disturbing.
We may have left the schoolroom thirty years or more ago, and
never seen it since; it may have vanished from our waking thoughts.
Yet from time to time we find ourselves there in our dreams, and
called upon to take our old place, always with a sense of conflict, a
vague discomfort, a feeling of something incongruous and
humiliating, for we realise that we are now too old. Here is a dream
in illustration: I find myself back at my old school, but my old
schoolmaster is not there; he is away ill, as I am told by his
substitute, whose face somehow seems familiar, though I cannot
recall where I have seen it. I do not know any of the boys; I am
returning after an absence of some months. I realise that I am to
take my old place again, and yet I feel a profound repulsion to do
so, a sense that it is somehow incongruous. This latter feeling seems
to prevail, for I finally assume the part of a visitor, and remark,
insincerely, to the master that it is pleasant to see the old place
again.
In such a case as this it seems that a picture from an ancient system
of memories floats across the field of sleeping consciousness, and
the dreamer is naturally drawn into that system and begins to adapt
himself to its demands. But, as he does so, the influence of other
later and incompatible systems of memories begins unconsciously to
affect the dreamer.[179] The cords of connection, however, which
when awake would enable him to adjust critically the opposing](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-59-320.jpg)
![systems, are not acting; apperception is defective. Yet the opposing
systems are there, outside the immediate field of consciousness, and
jostling the ancient system which has come into the central focus.
Finally this jostling of the ancient system by more recent systems
causes a harmonising modification in consciousness. The dreamer
ceases to be a boy in his old school, and assumes the part of a
visitor.
Dreams of our recently dead friends furnish a type of dream which is
formed in exactly the same way as these dreams of a return to
school life. The only difference is that they often present it in a more
vivid, pronounced, and poignantly emotional shape. This is so, partly
from the very subject of such dreams, and partly because the fact of
death definitely divides our impressions of our dead friends into two
groups, which are intimately allied to each other by their subject,
and yet absolutely opposed by the fact that in the one group the
friend is alive, and in the other dead.
I proceed to present two series of dreams—one in a man, the other
in a woman—illustrating this type of dream.[180]
Observation I.—Mr. C., age about twenty-eight, a man of scientific
training and aptitudes. Shortly after his mother's death he
repeatedly dreamed that she had come to life again. She had been
buried, but it was somehow found out that she was not really dead.
Mr. C. describes the painful intellectual struggles that went on in
these dreams, the arguments in favour of death from the
impossibility of prolonged life in the grave, and how these doubts
were finally swallowed up in a sense of wonder and joy because his
mother was actually there, alive, in his dream.
These dreams became less frequent as time went on, but some
years later occurred an isolated dream which clearly shows a further
stage in the same process. Mr. C. dreamed that his father had just
returned home, and that he (the dreamer) was puzzled to make out
where his mother was. After puzzling a long time he asked his sister,
but at the very moment he asked it flashed upon him—more, he](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-60-320.jpg)
![thinks, with a feeling of relief at the solution of a painful difficulty
than with grief—that his mother was dead.
Observation II.—Mrs. F., age about thirty, highly intelligent but of
somewhat emotional temperament. A week after the death of a
lifelong friend to whom she was greatly attached, Mrs. F. dreamed
for the first time of her friend, finding that she was alive, and then in
the course of the dream discovering that she had been buried alive.
A second dream occurred on the following night. Mrs. F. imagined
that she went to see her friend, whom she found in bed, and to
whom she told the strange things that she had heard (i.e., that the
friend was dead). Her friend then gave Mrs. F. a few things as
souvenirs. But on leaving the room Mrs. F. was told that her friend
was really dead, and had spoken to her after death.
In a fourth dream, at a subsequent date, Mrs. F. imagined that her
friend came to her, saying that she had returned to earth for a few
minutes to give her messages and to assure her that she was happy
in another world and in the enjoyment of the fullest life.
Another dream occurred more than a year later. Some one brought
to Mrs. F., in her dream, the news that her friend was still alive; she
was taken to her and found her as in life. The friend said she had
been away, but did not explain where or why she had been
supposed dead. Mrs. F. asked no questions and felt no curiosity,
being absorbed in the joy of finding her friend still alive, and they
proceeded to talk over the things that had happened since they last
met. It was a very vivid, natural, and detailed dream, and on
awaking Mrs. F. felt somewhat exhausted. Although not
superstitious, the dream gave her a feeling of consolation.
The next series has been observed more recently. I include all the
dreams and the intervals at which they occurred. The somewhat
unexpected news reached me of the death of a near and lifelong
friend when I was myself recovering from an attack of influenza. No
dream which could be connected with this event occurred until about
a fortnight later[181] (16th January). I then dreamed that I was with](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-61-320.jpg)
![for I saw their names on the title-page of a number of it which was
put in my hands. It surprised me that, though alive and well, he
should have ceased to edit the journal; the theory by which I
satisfactorily accounted to myself for his appearance was that,
though he had been so near death that his life was despaired of, he
had not actually died; his death had been prematurely reported. It
flashed across my dream consciousness, indeed, that I had read
obituaries of my friend in the papers, but this reminiscence merely
suggested the reflection that some one had been guilty of a grave
indiscretion.[182]
Although no attempt had been made to analyse this type of dream
before 1895, the dream itself had often been noted down, as from
its poignant and affecting character it could not fail to be. An early
example is furnished by the philosopher Gassendi, who states that
he dreamed he met a friend, that he greeted him as one returned
from the dead, and that then, saying to himself in his dream that
this was impossible, he concluded that he must be dreaming.[183]
Pepys, again, in his Diary, on the 29th June 1667, a few months
after his mother's death, dreamed that 'my mother told me she
lacked a pair of gloves, and I remembered a pair of my wife's in my
chamber, and resolved she should have them, but then recollected
[reflected] how my mother came to be here when I was in mourning
for her, and so thinking it to be a mistake in our thinking her all this
while dead, I did contrive that it should be said to any that inquired
that it was my mother-in-law, my wife's mother, that was dead, and
we in mourning for.' This dream, Pepys adds, 'did trouble me
mightily.' Edmond de Goncourt, in his Journal (27th July 1870), well
describes how in the first dream of the dead brother to whom he
was so tenderly attached, the two streams of memories appeared.
He dreamed he was walking with his brother, but at the same time
he knew he was in mourning for him, and friends were coming up to
offer condolences; the emotions caused by the conflict of these two
certainties—his brother's life affirmed by his presence and his death
affirmed by all the other circumstances of the dream—was
profoundly distressing. A few years earlier Renan, when his dearly](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-63-320.jpg)
![loved sister Henrietta died by his side in the Lebanon, also had
dreams of this type, which deeply affected even his cautious and
sceptical nature. She had died of Syrian fever, from which he also
was suffering, and shortly afterwards he wrote in a letter that 'in
feverish dreams a terrible doubt has risen up before me; I have
fancied I heard her voice calling to me from the vault where she was
laid.' He comforted himself, however, with the thought that this
horrible supposition was unjustified, since French doctors had been
present at her death. Maury[184] also mentions that he had often
had dreams of this type in which the dead appeared as living,
though the sight of them always produced astonishment and doubt
which the sleeping brain endeavoured to allay by some kind of
explanation. Beaunis also describes how he has dreamed with
surprise of meeting a friend whom even in his dream he knew to be
dead.[185]
It is not difficult, in the light of all that we have been able to learn
regarding the psychology of the world of dreams, to account for the
process here described, for its frequency, and for its poignant
emotional effects. This dream type is only a special variety of the
commonest species of dream, in which two or more groups of
reminiscences flow together and form a single bizarre congruity, a
confusion in the strict sense of the word. The death of a friend sets
up a barrier which cuts into two the stream of impressions
concerning that friend. Thus, two streams of images flow into
sleeping consciousness, one representing the friend as alive, the
other as dead. The first stream comes from older and richer sources;
the second is more poignant, but also more recent and more easily
exhausted. The two streams break against each other in restless
conflict, both, from the inevitable conditions of dream life, being
accepted as true, and they eventually mix to form an absurd
harmony, in which the older and stronger images (in accordance
with that recognised tendency for old psychic impressions generally
to be most stable) predominate over those that are more recent.
Thus, in the first observation the dreamer seems to have begun his
dream by imagining that his mother was alive as of old; then his](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-64-320.jpg)
![Sometimes atypical dreams of the dead occur in which even from
the first there appears little clash or doubt. When the vision can thus
easily be accepted, it is sometimes a source of consolation, joy, and
even religious faith which may still persist in the waking state.
Chabaneix has, for instance, recorded the dream experiences of a
poet and philosopher who had been deeply attached to a woman
with whom his relations were both passionate and intellectual. From
the night after her death onwards, at intervals, he had dreams of the
beloved woman, at first appearing as a floating vision, later as a
vividly seen and tangible person; these dreams caused refreshment
and mental invigoration, and seemed to bring the dreamer into
renewed communication with his dead friend.[186]
I am indebted to a clergyman for the record of a somewhat similar
experience. 'A close friendship,' he writes, 'once existed between
myself and a lady, somewhat older, and of a religious temperament.
We often discussed the life beyond the grave, and agreed that if she
died first, and this appeared more than probable, as she was the
victim of a mortal disease, she would appear to me. I may add that
she was of a highly-strung and nervous nature, and though purely
English had many of the psychic characteristics of the Celt. After her
death, I looked for some appearance or manifestation, and about
three days after dreamed that she had come back to me, and was
discussing with me a matter which I much wished to speak about
before her death, but was unable to, owing to her weakness and the
presence of strangers. In the dream it was perfectly clear to me that
she was a dead woman back from another sphere of existence. For
some weeks after this I had similar experiences. They were never
dreams of the old life and friendship before death, but always
reappearances from the other world. Of course it may be said of this
experience of mine, that it was merely the result of expectation. But
I have found that the things most on my mind are rarely the subject
of my dreams. Moreover, these dreams formed a series, lasting for
weeks, and all of the same character, though the conversations
differed.'](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-66-320.jpg)
![When a dreamer awakes in an emotional state which corresponds to
a dream he has just experienced, it is usually a safe assumption that
the dream was the result, and not the cause, of the emotional state.
That is by no means always the case, however, and in the type of
dream we are here concerned with it is rarely the case. Even though
it may be quite true that an emotional state evoked the dream, it is
equally true that in its turn the dream itself may arouse an emotional
state. The dream of encountering a celestial visitant, especially if the
visitant is a beloved friend, cannot fail to produce an especial effect
of this kind. It is noteworthy that the emotional influence may be
present even when the fact of dreaming has not been recalled. Thus
a lady who, on waking in the morning could not remember having
dreamed, realised during the day that she was feeling as she was
accustomed to feel after dreaming of a beloved friend, and was
ultimately able to recall fragments of the dream.[187] A man of so
great an intellect as Goethe has borne witness to the consoling
influence of dreams. 'I have had times in my life,' he said, in old age,
to Eckermann, 'when I have fallen asleep in tears, but in my dreams
the loveliest figures come to give me comfort and happiness, and I
awake next morning once more fresh and cheerful.'[188]
If we take a wide sweep we shall find in many parts of the world
stories and legends concerning the relationship of the living with the
dead which have a singular resemblance with the typical dream of
the dead here investigated. Thus, in Japan, it appears that stories of
the returning of the dead are very common. Lafcadio Hearn
reproduces one, as told by a Japanese, which closely resembles
some of the dreams we have met with. 'A lover resolved to commit
suicide on the grave of his sweetheart. He found her tomb and knelt
before it, and prayed and wept, and whispered to her that which he
was about to do. And suddenly he heard her voice cry to him
Anata! and felt her hand upon his hand: and he turned and saw
her kneeling beside him, smiling and beautiful as he remembered
her, only a little pale. Then his heart leaped so that he could not
speak for the wonder and the doubt and the joy of that moment. But
she said, Do not doubt; it is really I. I am not dead. It was all a](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-67-320.jpg)
![mistake. I was buried because my parents thought me dead—buried
too soon. Yet you see I am not dead, not a ghost. It is I; do not
doubt it!' It is perhaps worth mentioning that the incident told in
the Fourth Gospel (xx. 11-18) as occurring to Mary Magdalene when
at the tomb of Jesus, recalls the dream process of fusion of images.
She turns and sees, as she thinks, the gardener, but in the course of
conversation it flashes on her that he is Jesus, risen from the tomb.
In quite another part of the world the Salish Indians of British
Columbia have a story of a man who goes back to the spirit-world to
reclaim his lost wife; this can only be done under special conditions,
and for some time refraining to touch her; if he breaks these
conditions she vanishes in his arms, and he is left alone.[189] That
story, again, cannot fail to remind us of the almost identical Greek
legend of the return of Orpheus to the under-world to reclaim his
dead wife Eurydice. If these myths and legends were not directly
based on the dream-process, it can only be on the ground, alleged
with some force by Freud's school, that myths and legends
themselves develop by means of the same mechanism as dreams.
The probable influence of dreams in originating or confirming the
primitive belief of men in a spirit world has often been set forth.
Herbert Spencer attached great importance to this factor in the
constitution of the belief in another world, in spirits and in gods.[190]
Wundt even considers that such dreams furnish the whole origin of
animism. Other writers, less closely associated with anthropological
psychology, have argued in the same sense.[191]
But while these thinkers have in some cases specifically referred to
dreams of the dead, and not merely to the widespread belief of
savages that in sleep the soul leaves the body to wander over the
earth, they have never realised that there is a special mechanism in
the typical dream of a dead friend, due to mental dissociation during
sleep, which powerfully suggests to us that death sets up no fatal
barrier to the return of the dead. In dreams the dead are thus
rendered indestructible; they cannot be finally killed, but rather tend
to reappear in ever more clearly affirmed vitality. Dreams of this sort](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-68-320.jpg)
![time of a great number of combined memories. Stories were told of
people who, when awakened by sounds or contacts which must
have aroused them almost immediately, had yet experienced
elaborate visions which could only have been excited by the stimulus
which caused the awakening. The dream of Maury—who, when
awakened by a portion of the bed cornice falling on his neck,
imagined that he was living in the days of the Reign of Terror, and,
after many adventures, was being guillotined—has become famous.
[192]
It is unquestionably true that dreams are sometimes evoked by
sensory stimuli which almost immediately awake the dreamer. But
the supposition that this fairly common fact involves an extraordinary
acceleration of the rapidity with which mental images are formed is
due to a failure to comprehend the conditions under which psychic
activity in sleep takes place. If the sleeper were wide awake, and
were suddenly startled by a mysterious voice at the window or the
door, he would arrive at a theory of the sound, and even form a plan
of action, with at least as much rapidity as when the stimulus occurs
during sleep. The difference is that in sleep the ordinary mental
associations are more or less in abeyance, and the way is therefore
easily open to new associations. These new associations, when we
look back at them from the standpoint of waking life, seem to us so
bizarre, so far-fetched, that we think it must have required a long
time to imagine them. We fail to realise that, under the conditions of
dream thought, they have come about as automatically and as
instantaneously as the ordinary psychic concomitants of external
stimulation in waking life. It must also be remembered that in all the
cases in which the rapidity of the dream process has seemed so
extraordinary, it has merely been a question of visual imagery, and it
is obviously quite easy to see in an instant an elaborate picture or
series of pictures which would take a long time to describe.[193] At
the most the dreamer has merely seen a kind of cinematographic
drama which has been condensed and run together in very much the
way practised by the cinematographic artist, so that although the
whole story seems to be shown in constant movement, in reality the](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-71-320.jpg)
![necessary and constant result of the form assumed by psychic life
during sleep.[194]
If this peculiarity of memory in dreaming is not difficult to explain as
a natural illusion, there are other and rarer characteristics of dream
memory which are much more puzzling.
In attempting to unravel these, it is probable that, as in explaining
the illusion of rapidity, we must always bear in mind the tendency of
memory-groups in dreams to fall apart from their waking links of
association, so well as the complementary tendency to form
associations which in waking life would only be attained by a
strained effort. Apperception, with the power it involves of
combining and bringing to a focus all the various groups of
memories bearing on the point in hand, is defective. The focus of
conscious attention is contracted, and there is the curious and
significant phenomenon that sleeping consciousness is occasionally
unconscious of psychic elements which yet are present just outside it
and thrusting imagery into its focus. The imagery becomes
conscious, but its relation to the existing focus of consciousness is
not consciously perceived. Such a psychic mechanism, as Freud and
his disciples have shown, quite commonly appears in hysteria and
obsessional neuroses when healthy normal consciousness is
degraded to a pathological level resembling that which is normal in
dreams.[195] In such a case the surface of sleeping consciousness is,
as it were, crumpled up, and the concealed portion appears only at
the end of the dream or not at all. A simple example may make this
clear. In a dream I ask a lady if she knows the work of the poet Bau;
she replies that she does not; then I see before me a paper having
on it the name Baudelaire, clearly the name which should have been
contained in my query.[196] In such a dream the crumpling and
breaking of consciousness, at its very focus, is shown in the most
unmistakable manner.[197] But many of the most remarkable dreams
of dramatic dreamers are due to the same phenomenon, which in an
intellectual form is exactly the phenomenon which always makes a
dramatic situation effective. Robert Louis Stevenson was an](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-73-320.jpg)
![abnormally vivid dreamer, and found the germ of some of the plots
of his stories in his dreams; he has described one of his dreams in
which the dreamer imagines he has committed a murder; the crime
becomes known to a woman who, however, never denounces it; the
murderer lives in terror, and cannot conceive why the woman
prolongs his torture by this delay in giving him up to justice; only at
the end of the dream comes the clue to the mystery, and the
explanation of the woman's attitude, as she falls on her knees and
cries: 'Do you not understand? I love you.'[198]
There is another and very interesting class of dreams in which we
find not merely that some memory-groups disappear from
consciousness or become merely latent, but also that other memory-
groups, latent or even lost to waking consciousness, float into the
focus of sleeping consciousness. In other words, we can remember
in sleep what we have forgotten awake. We then have what is called
the hypermnesia, the excessive or abnormal memory, of sleep.
There can be little doubt that the two processes—the sinking of
some memory-groups and the emergence on the surface of other
memory-groups which, so far as waking life is concerned, had
apparently fallen to the depths and been drowned—are
complementarily related to one another. We remember what we
have forgotten because we forget what we remembered. The order
of our waking impressions involves a certain tension, that is to say a
certain attention, which holds them in our consciousness, and
excludes any other order which might serve to bring lost memory-
groups to sight. Sometimes we are conscious of a lost memory
which is just outside consciousness, but which, with the existing
order of our memory-groups, we cannot bring into consciousness.
We have the missing name, the missing memory, at the tip of our
tongue, we say, but we cannot quite catch it.[199] In dreams
apperception is defective, the strain of conscious attention is relaxed,
and the conditions are furnished under which new clues and strains
may come into action and the missing name glide spontaneously
into consciousness. Even the mere approach of sleep, with its](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-74-320.jpg)
![accompanying relaxation of attention, may effect this end. Thus I
was trying one day to recall the name of the unpleasant Chinese
scent, patchouli. The name, though not usually unfamiliar, escaped
me. At night, however, just before falling asleep, it spontaneously
occurred to me. In the morning, when fully awake, I was again
unable to recall it.
In such a case we see how waking consciousness is tense in a
certain direction, which happens not to be that in which the desired
thing is to be found. Attention under such circumstances impedes
rather than aids recollection. In this particular case, I felt convinced
that the name I wanted began with h, and thus my mind was
intently directed towards a wrong quarter. But on the approach of
sleep attention is automatically relaxed, and it is then possible for
the forgotten word to slip in from its unexpected quarter. On these
occasions it is by indirection that direction is found.[200]
It is interesting to observe that this same process of discovery due
to the wider outlook of relaxed attention can take place, not only in
sleep and the hypnagogic state, but also, subconsciously, in the fully
waking state when the mind is occupied with some other subject.
Thus in reading a MS., I came upon an illegible word which I was
unable to identify, notwithstanding several guesses and careful
scrutiny through a magnifying glass. I passed on, dismissing the
subject from my mind. A quarter of an hour afterwards, when
walking, and thinking of quite a different subject, I became
conscious that the word 'ceremonial' had floated into the field of
mental vision, and I at once realised that this was the unidentified
word. The instance may be trivial, but no example could better show
how the mind may continue to work subconsciously in one direction
while consciously working in an entirely different direction.
In dreams, however, we can effect more than a mere recovery of
memories which have temporarily escaped us, or the discovery of
relationships which have eluded us. The dissociation of familiar
memory-groups becomes so complete, the appearance of unfamiliar
groups so eruptive, that we can remember things that have entirely](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-75-320.jpg)
![and permanently sunk below the surface of waking consciousness,
or even things which are so insignificant that they have never made
any mark on waking consciousness at all. In this way, we may be
said, in a certain sense, to remember things we never knew. The
first dream which enabled me, some twenty years ago, to realise this
hypermnesia of the mind in dreams[201] was the following
unimportant but instructive case. I woke up recalling the chief items
of a rather vivid dream: I had imagined myself in a large old house,
where the furniture, though of good quality, was ancient, and the
chairs threatened to give way as one sat on them. The place
belonged to one Sir Peter Bryan, a hale old gentleman, who was
accompanied by his son and grandson. There was a question of my
buying the place from him, and I was very complimentary to the old
gentleman's appearance of youthfulness, absurdly affecting not to
know which was the grandfather and which the grandson. On
awaking I said to myself that here was a purely imaginative dream,
quite unsuggested by any definite experiences. But when I began to
recall the trifling incidents of the previous day, and the things I had
seen and read, I realised that that was far from being the case. So
far from the dream having been a pure effort of imagination, I found
that every minute item could be traced to some separate source,
though none of them had the slightest resemblance to the dream as
a whole. The name of Sir Peter Bryan alone completely baffled me; I
could not even recall that I had at that time ever heard of any one
called Bryan. I abandoned the search and made my notes of the
dream and its sources. I had scarcely done so when I chanced to
take up a volume of biographies of eccentric personages, which I
had glanced through carelessly the day before. I found that it
contained, among others, the lives of Lord Peterborough and George
Bryan Brummel. I had certainly seen those names the day before;
yet before I took up the book once again it would have been
impossible for me to recall the exact name of Beau Brummel. It so
happened that the forgotten memory which in this case re-emerged
to sleeping consciousness, was a fact of no consequence to myself](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-76-320.jpg)
![or any one else. But it furnishes the key to many dreams which have
been of more serious import to the dreamers.
Since then I have been able to observe among my friends several
instances of dreams containing veracious though often trivial
circumstances unknown to the dreamer when awake, though on
consideration it was found to be in the highest degree probable that
they had come under his notice, and been forgotten, or not
consciously observed. Thus a musical correspondent tells me he
once dreamed of playing a piece of Rubinstein's in the presence of a
friend who told him he had made a mistake in re-striking a tied note.
In the morning he found the dream friend was correct. But up to
then he had always repeated the note. Usually when the forgotten
or unnoticed circumstance is trivial, it is of quite recent date. That it
is not always very recent may be illustrated by a dream of my own. I
dreamed that I was in Spain and about to rejoin some friends at a
place which was called, I thought, Daraus, but on reaching the
booking-office I could not remember whether the place I wanted to
go to was called Daraus, Varaus, or Zaraus, all which places, it
seemed to me, really existed. On awaking, I made a note of the
dream, exactly as reproduced here, but was unable to recall any
place, in Spain or elsewhere, corresponding to any of these names.
The dream seemed merely to illustrate the familiar way in which a
dream image perpetually shifts in a meaningless fashion at the focus
of sleeping consciousness. The note was put away, and a few
months later taken out again.[202] It was still equally impossible to
me to recall any real name corresponding to the dream names. But
on consulting the Spanish guide-books and railway time-tables, I
found that, on the line between San Sebastian and Bilbao, there
really is a little seaside resort, in a beautiful situation, called Zarauz,
and I realised, moreover, that I had actually passed that station in
the train two hundred and fifty days before the date of my dream.
[203] I had no associations with this place, though I may have
admired it at the time; in any case it vanished permanently from
conscious memory, perhaps aided by the fatigue of a long night
journey before entering Spain. Even sleeping memory, I may remark,](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-77-320.jpg)
![only recovered it with an effort, for it is notable that the name was
gradually approached by three successive attempts.[204]
A special form of lost or unconscious memories recurring in sleep is
constituted by the cases in which people when asleep, or in a
somnambulistic state, can speak languages which they have
forgotten, or never consciously known, when awake. A simple
instance, known to me, is furnished by a servant who had been
taken to Paris for a few weeks six months before, but had never
learned to speak a word of French, and whose mistress overheard
her talking in her sleep, and repeating various French phrases, like
'Je ne sais pas, Monsieur'; she had certainly heard these phrases,
though she maintained, when awake, that she was ignorant of them.
Speaking in a language not consciously known, or xenoglossia, as it
is now termed, occurs under various abnormal conditions, as well as
in sleep, and is sometimes classed with the tendency which is found,
especially under great religious excitement, to 'speak with tongues,'
or to utter gibberish.[205] But in various sleep-like states it occurs as
a true revival of forgotten memories, sometimes of memories which
belong to childhood and in normal consciousness have been long
overlaid and lost. On one occasion, by the bedside of a lady who
was kept for a considerable period in a light condition of chloroform
anaesthesia, the patient began to talk in an unfamiliar language
which one of us recognised as Welsh; as a child, she afterwards
owned, she had known Welsh, but had long since forgotten it.[206] A
similar reproduction of lost memories occurs in the hypnotic state.
This psychic process, by which unconscious memories become
conscious in dreams, is of considerable interest and importance
because it lends itself to many delusions. Not only the ignorant and
uncultured, but even well-trained and acute minds, are often so
unskilled in mental analysis that they are quite unable to pierce
beneath the phenomenon of conscious ignorance to the deeper fact
of unconscious memory; they are completely baffled, or else they
resort to the wildest hypotheses. This is illustrated by the following
narrative received twelve years ago from a medical correspondent in](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-78-320.jpg)
![frequent communication with a practical manufacturer, assisting him
in his inventions by scientific advice. One day the manufacturer
wrote to my friend asking if the latter had been thinking of him
during the night, for he had been much puzzled by a difficulty, and
during the night had seen a vision of my friend who explained the
solution of the difficulty; in the morning the proposed solution
proved successful. There was, however, no telepathic element in the
case; the dreamer's solution was his own.
An interesting group of cases in this class is furnished by the dreams
in which the dreamer, in opposition to his waking judgment, sees an
acquaintance in whom he reposes trust acting in a manner unworthy
of that trust, subsequent events proving that the estimate formed
during sleep was sounder than that of waking life. Hawthorne (in his
American Notebooks), Greenwood, Jewell, and others have recorded
cases of this kind.
Various as these phenomena are, they fall into the same scheme.
They all help to illustrate the fact that though on one side mental life
in sleep is feeble and defective, on the other side it shows a
tendency to vigorous excess. Sleep, as we know, involves a
relaxation of tension, both physical and psychic; attention is no
longer focused at a deliberately selected spot.[207] The voluntary
field becomes narrower, but the involuntary field becomes extended.
Thus it happens that the contents of our minds fall into a new order,
an order which is often fantastic but, on the other hand, is
sometimes a more natural and even a more rational order than that
we attain in waking life. Our eyes close, our muscles grow slack, the
reins fall from our hands. But it sometimes happens that the horse
knows the road home even better than we know it ourselves.
Hypermnesia, or abnormally wide range of recollection, is not the
only or the most common modification of memory during sleep. We
find much more commonly, and indeed as one of the chief
characteristics of sleep, an abnormally narrow range of recollection.
We find, also, and perhaps as a result of that narrow range,
paramnesia or perversion of memory. The best known form of](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-80-320.jpg)
![paramnesia is that in which we have the illusion that the event which
is at the moment happening to us has happened to us before.[208]
This form of paramnesia is common in dreams, though it is often so
slightly pronounced that we either fail to recall it on awakening or
attach no significance to it.[209] I dream, for instance, that I am
walking along a path, along which, it seems to me, I have often
walked before, and that the path skirts the lawn of a house by which
stands a policeman whom, also, it seems to me, I have often seen
there before; the policeman approaches me and says, 'You have
come to see Mr. So-and-so, sir?' and thereupon I suddenly recollect,
with some confusion, that I have come to see Mr. So-and-so, and I
walk up to the door. Again, an author dreams that he sees a list of
his own books with, at the head of them, one entitled 'The Book of
Glory.' He could not recall writing it (and to waking consciousness
the name was entirely unknown), but the only reflection he made in
his dream was 'How stupid to have forgotten!' In this case there was
evidently some resistance to the suggestion, which yet was quickly
accepted. In all such dreams it seems that we are in a state of
mental weakness associated with defective apperceptual control and
undue suggestibility, very similar to the state found in some forms of
confusional insanity or of precocious dementia.[210] Consciousness
feebly slides down the path of least resistance; it accepts every
suggestion; the objects presented to it seem things that it knew
before, the things that are suggested to it to do seem things that it
already wanted to do before. Paramnesia, thus regarded, seems
simply a natural outcome of a state of consciousness temporarily
depressed below its normal standard of vigour.
It must be remembered that the suggestibility of sleeping
consciousness varies in degree, and in the face of serious
improbabilities there is often a considerable amount of resistance,
just as the hypnotised person seriously resists the suggestions that
fundamentally outrage his nature. But some degree of suggestibility,
some tendency to regard the things that come before us in dreams
as familiar—in other words, as things that have happened to us](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-81-320.jpg)
![before—is not merely a natural result of defective apperception, but
one of the very conditions of dreaming. It enables us to carry on our
dreams; without it their progress would be fatally inhibited by doubt,
uncertainty, and struggle. So it is, perhaps, that in all dreaming, or
at all events in certain stages of sleeping consciousness, we are
liable to fall into a state of pseudo-reminiscence.
It is an interesting and highly significant fact that this paramnesic
delusion of our dreams—the feeling that the thing that is happening
to us is the thing that has happened to us before or that might
happen to us again—tends to persist in the hypnagogic (or
hypnopompic) stage immediately following sleep. When we have half
awakened from a dream and are just able to realise that it was a
dream, that dream constantly tends to appear in a more plausible or
probable light than is possible a few moments later when we are
fully awake.[211]
The first experience which enabled me clearly to realise this
phenomenon, and its probable explanation, occurred many years
ago. About the middle of the night I had a very vivid dream, in
which I imagined that two friends—a gentleman and his daughter—
with a certain Lord Chesterfield (I had lately been reading the
Letters of the famous Lord Chesterfield), were together at a hotel,
that they were playing with weapons, that the lady accidentally killed
or wounded Lord Chesterfield, and that she then changed clothes
with him with the object of escaping, and avoiding discovery which
would somehow be dangerous. I was informed of the matter, and
was much concerned. I awoke, and my first thought was that I had
just had a curious dream which I must not forget in the morning.
But then I seemed to remember that it was a real and familiar event.
This second thought lulled my mental activity, and I went to sleep
again. In the morning I was able to recall the main points in my
dream, and my thoughts on awaking from it.
Since then I have given attention to the point, and I have found on
recalling my half-waking consciousness after dreams that, while it is
doubtless rare to catch the assertion 'That really occurred,' it is less](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-82-320.jpg)
![rare to catch the vague assertion, 'That is the kind of thing that does
occur.' I find that this latter impression appears, like the former, after
vivid dreams which contain no physical impossibility, but which the
full waking consciousness refuses to recognise as among the things
that are probable. As an example quite unlike that just recorded, I
may mention a dream in which I imagined that I was proving the
frequency of local intermarriage by noting in directories the
frequency of the presence of people of the same name in
neighbouring towns and villages. On half-awaking I still believed that
I had actually been engaged in such a task—that is, either that the
dream was real or that it referred to a real event—and it was not
until I was sufficiently awake to recognise the fallacy of such a
method of investigation that I realised that it was purely a dream.
This phenomenon has long been known, although its significance
has not been perceived. Brierre de Boismont pointed out that certain
vivid dreams are not recognised as dreams, but are mistaken for
reality after waking, though he scarcely recognised the normal
limitation of this mistake to the hypnagogic state. Moll compared
such dreams, thus continued into waking life, to continuative post-
hypnotic suggestions. Sully mentioned awaking from dreams which
'still wear the aspect of old acquaintances, so that for the moment I
think they are waking realities.'[212] Colegrove, in his study of
memory, recorded many cases in which young people mistook their
dreams for actual events.[213]
This persistence of the memory illusion of sleep into the subsequent
hypnagogic state is obviously related to the allied persistence, more
occasionally found, of the visual, auditory, and other sensory
hallucinations of sleep into the hypnagogic state.[214] Visions thus
seen persisting from dreams for a few moments into waking life are
often very baffling and disturbing, as has already been pointed out,
to ignorant and untrained people. Such visions may occur in the
hypnagogic state, even when there has been no conscious precedent
dream, and it is indeed probable, as Parish has argued, that it is
precisely in the hypnagogic state, the narthex of the church of](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-83-320.jpg)
![for pedantic reasons. I take the condition of consciousness to be
almost the same whether the sleep is coming on or passing away. In
the Chesterfield dream it is indeed impossible to say whether the
phenomenon is 'hypnagogic' or 'hypnopompic'; in such a case the
twilight consciousness is as much conditioned by the sleep that is
passing away as by the sleep that is coming on.
If this memory illusion of the half-waking state may be regarded as a
variety of paramnesia, a new horizon is opened out to us. May not
the hypnagogic variety throw light on the general phenomenon of
paramnesia which has led to so many strange and complicated
theories? I think it may.
Paramnesia, as we have seen, is the psychologist's name for a
hallucination of memory which is sometimes called 'pseudo-
reminiscence,' and by medical writers (who especially associate it
with epilepsy) regarded as a symptom of 'dreamy state,'[215] while
by French authors it is often termed 'false recognition' or 'sensation
du déjà vu.' Dickens, who seems himself to have experienced it, thus
describes it in David Copperfield: 'We have all some experience of a
feeling that comes over us occasionally, of what we are saying and
doing having been said or done before, in a remote time, of having
been surrounded, dim ages ago, by the same faces, objects, and
circumstances, of our knowing perfectly what will be said next, as if
we suddenly remembered it.' Sometimes it seems that this previous
occurrence can only have taken place in a previous existence,[216]
whence we probably have, as St. Augustine seems first to have
suggested, the origin of the idea of metempsychosis, of the
transmigration of souls; sometimes it seems to have happened
before in a dream; sometimes the subject of the experience is totally
baffled in the attempt to account for the feeling of familiarity which
has overtaken him. In any case he is liable to an emotion of distress
which would scarcely be caused by the coincidence of resemblance
with a real previous experience.[217]](https://image.slidesharecdn.com/86436-250225044321-a81a673b/85/Optimizing-Engineering-Problems-through-Heuristic-Techniques-1st-Edition-Kaushik-Kumar-86-320.jpg)
Optimizing Engineering Problems through Heuristic Techniques 1st Edition Kaushik Kumar
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- 5. Optimizing Engineering Problems through Heuristic Techniques 1st Edition Kaushik Kumar Digital Instant Download Author(s): Kaushik Kumar, Divya Zindani, J. Paulo Davim ISBN(s): 9781351049580, 1351049585 Edition: 1 File Details: PDF, 3.07 MB Year: 2019 Language: english
- 7. Optimizing Engineering Problems through Heuristic Techniques
- 8. Science, Technology, and Management Series Series Editor: J. Paulo Davim, Professor Department of Mechanical Engineering, University of Aveiro, Portugal This book series focuses on special volumes from conferences, workshops, and symposiums, as well as volumes on topics of current interested in all aspects of science, technology, and management. The series will discuss topics such as, mathematics, chemistry, physics, materials science, nanosciences, sustainability science, computational sciences, mechanical engineering, industrial engineering, manufacturing engineering, mechatronics engineering, electrical engineering, systems engineering, biomedical engineering, management sciences, economical science, human resource management, social sciences, engineering education, etc. The books will present principles, models techniques, methodologies, and applications of science, technology and management. Advanced Mathematical Techniques in Engineering Sciences Edited by Mangey Ram and J. Paulo Davim Soft Computing Techniques for Engineering Optimization Edited by Kaushik Kumar, Supriyo Roy, and J. Paulo Davim Handbook of IOT and Big Data Edited by Vijender Kumar Solanki, Vicente García Díaz, and J. Paulo Davim Digital Manufacturing and Assembly Systems in Industry 4.0 Edited by Kaushik Kumar, Divya Zindani, and J. Paulo Davim Optimization Using Evolutionary Algorithms and Metaheuristics Edited by Kaushik Kumar and J. Paulo Davim Integration of Process Planning and Scheduling Approaches and Algorithms Edited by Rakesh Kumar Phanden, Ajai Jain, and J. Paulo Davim For more information about this series, please visit: https://www.crcpress.com/ Science-Technology-and-Management/book-series/CRCSCITECMAN
- 9. Optimizing Engineering Problems through Heuristic Techniques Kaushik Kumar, Divya Zindani, and J. Paulo Davim
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- 11. v Contents Preface.......................................................................................................................ix Authors.................................................................................................................... xiii Section I Introduction to Heuristic Optimization Chapter 1 Optimization Using Heuristic Search: An Introduction.......................3 1.1 Introduction................................................................................3 1.2 The Optimization Problem.........................................................4 1.2.1 Local Versus Global Optima.........................................4 1.3 Categorization of Optimization Techniques...............................4 1.4 Requirement of Heuristics and Their Characteristics................6 1.5 Performance Measures for Heuristics........................................7 1.6 Classification of Heuristics.........................................................8 1.7 Conclusion..................................................................................9 Section II Description of Heuristic Optimization Techniques PART I Evolutionary Techniques Chapter 2 Genetic Algorithm...............................................................................13 2.1 Introduction..............................................................................13 2.2 Genetic Algorithm....................................................................13 2.3 Competent Genetic Algorithm................................................. 16 2.4 Improvements in Genetic Algorithms......................................20 2.5 Conclusion................................................................................21 Chapter 3 Particle Swarm Optimization Algorithm............................................23 3.1 Introduction..............................................................................23 3.2 Basics of Particle Swarm Optimization Approach...................23 3.2.1 Structure of Standard PSO..........................................24 3.2.2 Some Definitions.........................................................25 3.3 PSO Algorithm.........................................................................26 3.4 Some Modified PSO Algorithms..............................................27 3.4.1 Quantum-Behaved PSO..............................................27 3.4.2 Chaotic PSO................................................................28
- 12. vi Contents 3.4.3 Time Varying Acceleration Coefficient-Based PSO.....28 3.4.4 Simplified PSO............................................................29 3.5 Benefits of PSO Algorithm.......................................................30 3.6 Applications of PSO.................................................................30 3.7 Conclusion................................................................................ 31 PART II Nature-Based Techniques Chapter 4 Ant Colony Optimization....................................................................33 4.1 Introduction..............................................................................33 4.2 Components and Goals of ACO...............................................34 4.3 Traditional Approaches of ACO...............................................36 4.3.1 Ant System..................................................................36 4.3.2 Max-Min Ant System..................................................37 4.3.3 Quantum Ant Colony Optimization............................37 4.3.4 Cooperative Genetic Ant System................................38 4.3.5 Cunning Ant System...................................................39 4.3.6 Model Induced Max-Min Ant System.........................40 4.3.7 Ant Colony System......................................................40 4.4 Engineering Applications of Ant Colony Optimization Algorithm�������������������������������������������������������������������������������� 41 4.5 Conclusion................................................................................ 41 Chapter 5 Bees Algorithm...................................................................................43 5.1 Introduction..............................................................................43 5.2 Basic Version of Bees Algorithm.............................................44 5.3 Improvements on Bees Algorithm............................................46 5.3.1 Improvements Associated with Setting and Tuning of Parameters�������������������������������������������������46 5.3.2 Improvements Considered on the Local and Global Search Phase���������������������������������������������������47 5.3.3 Improvements Made in the Initialization of the Problem����������������������������������������������������������������������50 5.4 Conclusion................................................................................50 Chapter 6 Firefly Algorithm................................................................................ 51 6.1 Introduction.............................................................................. 51 6.2 Biological Foundations.............................................................52 6.3 Structure of Firefly Algorithm.................................................53 6.4 Characteristics of Firefly Algorithm........................................54 6.5 Variants of Firefly Algorithm...................................................55 6.5.1 Modified Variants of Firefly Algorithm......................55
- 13. vii Contents 6.5.2 Hybrid Variants of Firefly Algorithm.........................57 6.6 Engineering Applications of Firefly Algorithm.......................59 6.7 Conclusion................................................................................59 Chapter 7 Cuckoo Search Algorithm................................................................... 61 7.1 Introduction.............................................................................. 61 7.2 Cuckoo Search Methodology................................................... 61 7.3 Variants of Cuckoo Search Algorithm.....................................64 7.3.1 Adaptive Cuckoo Search Algorithm...........................64 7.3.2 Self-Adaptive Cuckoo Search Algorithm....................64 7.3.3 Cuckoo Search Clustering Algorithm.........................64 7.3.4 Novel Adaptive Cuckoo Search Algorithm.................65 7.3.5 Cuckoo Search Algorithm Based on Self-Learning Criteria������������������������������������������������65 7.3.6 Discrete Cuckoo Search Algorithm............................65 7.3.7 Differential Evolution and Cuckoo Search Algorithm....66 7.3.8 Cuckoo Inspired Fast Search.......................................66 7.3.9 Cuckoo Search Algorithm Integrated with Membrane Communication Mechanism��������������������66 7.3.10 Master-Leader-Slave Cuckoo......................................67 7.3.11 Cuckoo Search Algorithm with Wavelet Neural Network Model�����������������������������������������������������������67 7.4 Engineering Applications of Cuckoo Search...........................67 7.5 Conclusion................................................................................69 Section III Application of Heuristic Techniques Toward Engineering Problems Chapter 8 Engineering Problem Optimized Using Genetic Algorithm...............73 8.1 Introduction..............................................................................73 8.2 Details of Ultrasonic Machining Process................................ 74 8.3 Details of the Experimentation Process................................... 74 8.4 Development of Empirical Models by Using Response Surface Methodology��������������������������������������������������������������75 8.5 Optimization Using Genetic Algorithm...................................75 8.6 Conclusion................................................................................79 Chapter 9 Engineering Problem Optimized Using Particle Swarm Optimization Algorithm...................................................................... 81 9.1 Introduction.............................................................................. 81 9.2 EDM Process Details............................................................... 81
- 14. viii Contents 9.3 Experimental Details................................................................82 9.4 Response Surface Method for Empirical Models....................83 9.5 Accuracy Check for the Model.................................................84 9.6 Optimization with PSO............................................................84 9.7 Conclusion................................................................................88 Chapter 10 Engineering Problem Optimized Using Ant Colony Optimization Algorithm......................................................................89 10.1 Introduction..............................................................................89 10.2 Experimentation of the Milling Process..................................90 10.3 Optimization.............................................................................93 10.3.1 Set the Initial Values...................................................93 10.3.2 Selection......................................................................93 10.3.3 Dumping Operation and Pheromone Update Mechanism�����������������������������������������������������������������94 10.3.4 Random Search...........................................................94 10.4 Conclusion................................................................................97 Chapter 11 Engineering Problem Optimized Using Bees Algorithm...................99 11.1 Introduction..............................................................................99 11.2 Artificial Bee Colony Algorithm............................................100 11.3 Optimization of the Nd:YAG Laser Beam Machining Process Using ABC���������������������������������������������������������������102 11.4 Conclusion.............................................................................. 105 Chapter 12 Engineering Problem Optimized Using Firefly Algorithm..............107 12.1 Introduction............................................................................107 12.2 Firefly Algorithm....................................................................107 12.3 Application of Firefly Algorithm to Electrochemical Machining Optimization�������������������������������������������������������109 12.4 Conclusion.............................................................................. 113 Chapter 13 Engineering Problem Optimized Using Cuckoo Search Algorithm..... 115 13.1 Introduction............................................................................ 115 13.2 Cuckoo Search Algorithm...................................................... 116 13.3 Application of Cuckoo Search Algorithm to Abrasive Water Jet Machining�������������������������������������������������������������� 117 13.4 Conclusion.............................................................................. 119 References.............................................................................................................. 121 Index....................................................................................................................... 135
- 15. ix Preface The authors are pleased to present the book Optimizing Engineering Problems through Heuristic Techniques under the book series Science, Technology, and Management. The book title was chosen by looking at the present trend and notic- ing a book in this area, covering various popular and recent heuristic optimization techniques and its application to engineering problems to attain optimal solutions, would come in handy for various academicians, students, researchers, industrialists, and engineers. Optimization is finding a solution or an alternative with the most cost effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. Optimization can be used in any field as it involves in formulating process or products in various forms. It is the “process of finding the best way of using the existing resources while taking into the account of all the factors that influences decisions in any experiment.” The final product not only meets the requirements from an availability standpoint, but also from a practi- cal mass production criteria. There are two distinct types of optimization techniques: one traditional (statistical- and calculus-based), which is deterministic in nature, and the other heuristic, which is probabilistic in nature. The former has been in use for quite some time and has been successfully applied to many engineering problems. The heuristic technique is comparatively new and is gaining wide popularity due to certain properties which the traditional technique lacks. Due to complexity in engineering problems, an appli- cation engineer cannot afford to rely on a particular method and should know the advantages and limitations of various techniques, and therefore choose wisely the most efficient technique for the problem at hand. Heuristic optimization techniques are generally and presently being primarily utilized for non-engineering problems. The book has 13 chapters categorized into three parts, namely Section I: Introduction to Heuristic Optimization Techniques, Section II: Description of Heuristic Optimization Techniques and Section III: Application of Heuristic TechniquestowardsEngineeringProblems.SectionIcontainsChapter1,whereas Section II comprises Two Parts. Part 1 has Chapter 2 and Chapter 3 describ- ing the two most popular evolutionary techniques, namely Genetic Algorithm and Particle Swarm Optimization. Part 2, dedicated to Nature-Based Techniques, of this section has Chapter 4 to Chapter 7 describing four popular techniques, namely Ant Colony Optimization, Bees Algorithm, Firefly Algorithm and Cuckoo Search Algorithm, respectively. The last section, Section III, enlists Chapter 8 to Chapter 13. Section I, Chapter 1 introduces readers to the concept of heuristics and presents an overview of the same. Many real-life problems are modeled and solved for optimality through classical optimization techniques. One such class of optimization techniques is that of Heuristic search. Although heuristics do not guarantee optimal- ity, they produce concrete results. Heuristics have been widely applied in various industries, such as business, statistics, environment, engineering, and sports.
- 16. x Preface Chapter 2, the first chapter of Section II Part 1, illuminates its readers with the fundamental concepts, mathematical models, and operators associated with genetic algorithm (GA). It is, no doubt, one of the most well-known and popular evolution- ary algorithms. GA mimics the Darwinian theory of survival of the fittest in nature. The chapter also highlights improvements made in various components of GA, i.e., selection, mutation and crossover. Particle swarm optimization (PSO) is discussed in the next chapter i.e., Chapter 3. PSO was proposed by Kennedy and Eberhart in 1995 and is a heuristic global optimization technique and now one of the most commonly employed. The present chapter delineates comprehensively an investigation into PSO and the advances made. The authors think this chapter would be beneficial for researchers involved directly or indirectly in the field of optimization. Chapter 4, the first chapter of Section II Part 2, presents a brief overview of the structure of Ant Colony Optimization (ACO), its variants and the engineering appli- cations. ACO has received considerable attention and has therefore emerged as one of the prominent Nature-Based Heuristic Optimization Techniques. ACO solves NP hard problems inspired by ant foraging behavior i.e., searching for food, the heuris- tics used by ants and the partial guidance of the other ants in indirect format. In this chapter, the components and the goals of ACO have also been depicted. Chapter 5 provides an overview of the Bees Algorithm. The foraging behavior of honeybees is modeled by the Bees Algorithm and hence solves optimization prob- lems. Exploitative neighborhood search in combination with the random explorative search is performed by this algorithm to solve optimization problems. The Bees Algorithm can be divided into four parts: tuning of parameter, initialization, the local search process, and at last the global search processes. In the present chapter, various improvements along with the application of the Bees Algorithm are discussed. Chapter 6 presents a comprehensive outlook of firefly algorithm. The Firefly Optimization Algorithm has gained its stature from a so-called swarm intelli- gence. This algorithm has been applied to a number of domains including the field of engineering. The Firefly Optimization Algorithm has been able to successfully solve a variety of problems from different areas. Modified and hybrid variants of the Firefly Algorithm have been developed and hence its application scope has grown exponentially. Biological foundations of the Firefly Algorithm are also dis- cussed in this chapter. The structure, characteristics and modified variants of firefly algorithms are discussed. Towards the end of the chapter, engineering applications to which firefly algorithms have been applied are discussed. Chapter 7, the last chapter of Part 2 as well as Section II, provides a brief overview of the Cuckoo Search Algorithm. Yang and Deb developed this in the year 2009 inspired by bird family. The present chapter also provides various applications of the optimization technique. From the chapter, it can be clearly observed that this algorithm has been used to address a wide range of engineering problems. The main objective of this chapter is to illuminate the readers with a definition of the Cuckoo Search Algorithm and also provide an outlook of the application areas it has addressed so far. Section III, the section dedicated to solving engineering problems with heuristic techniques, starts with Chapter 8. The chapter describes the application of genetic
- 17. xi Preface algorithm to a non-traditional machining process i.e., ultrasonic machining process, which is one of the most extensively used non-traditional machining processes for the machining of non-conductive brittle materials such as glasses, carbides and bio- ceramics. The empirical models required for the optimization process were gener- ated using the response surface methodology. Genetic algorithm has been applied to minimize the roughness for a hole surface. For optimizing the process param- eters, different parameters considered were, namely, power rating, concentration of abrasive slurry and feed rate of the tool. As both the output parameters i.e., surface roughness and material removal rate are equally important, this becomes a multi- objective optimization. The next chapter, Chapter 9, deals with the optimization problem for the electrical discharge machining process, another non-traditional machining technique. Setting optimal parameters, maximizing the material removal rate and minimizing the wear of the electrode tool, has been arrived at by employing the Particle Swarm Optimization technique (PSO). Once again, response surface methodology has been employed to arrive at the relationship between the inputs and outputs of the machining process, and the effectiveness of PSO algorithm has been demonstrated to address the optimization problem in an engineering domain. In Chapter 10, the Ant Colony Optimization (ACO) technique has been employed to deal with the optimization problem in the multi-pass pocket milling process. Milling has been considered to be one of the oldest material removal processes that aids in removal of unwanted material through the use of rotating cutting tool. Setting optimal parameters, considering process parameters like speed of the spindle, depth of cut and feed rate, minimize surface roughness and machining time. The efficacy and suitability of the optimization technique have been demonstrated to address the optimization problem in the domain of a traditional machining process. Following this trend, Chapter 11 demonstrates the applicability of the Artificial Bee Colony Optimization algorithm, in order to determine the optimal combination of parameters for the Nd:YAG laser beam machining process by considering both the single- and multi-objective optimization of the responses. Nd:YAG laser beam machining process is one of the prominent non-conventional machining processes which has the potential ability to manufacture intricately shaped micro-products; however, identification of a suitable combination of parameters in order to achieve the desired machining performance is the key and the optimization technique serves it well. Chapter 12 describes the application of the Firefly Algorithm to find an optimal solution for the electrochemical machining process. All the non-traditional machin- ing processes, including electrochemical process, produce complex parts with great precision and are therefore time-consuming as well as expensive. Hence, it is nec- essary to select optimal parameters so that performance parameters such as heat affected zone (HAZ), radial overcut (ROC), and material removal rate (MRR) can be optimized. The Firefly Algorithm discussed, in this chapter was revealed to be robust and better in comparison to the results obtained by previous researchers. Chapter 13, the final chapter of the book, illustrates the applicability of the Cuckoo Search Algorithm to predict surface roughness in the case of abrasive water jet machining. The Cuckoo Search Algorithm is one of the newest nature-based
- 18. xii Preface algorithms. Various models of prediction have been developed with different initial eggs, and analysis was carried out to investigate the best predicted value for surface roughness. The validity of the results has been established by employing the t-test, which ascertains applicability of the Cuckoo Algorithm for improving the perfor- mance of abrasive water jet machining. The results have revealed that the Cuckoo Algorithm is capable of optimizing process parameters that produce improved surface finish of the abrasive water jet machining process. First and foremost we would like to thank God for allowing us to pursue our dreams. Almighty, without your support and blessings this work could not have been done. We would like to thank our ancestors, parents, and relatives for allowing us to follow our ambitions. Our families showed patience and tolerance while we took on yet another challenge that decreased the amount of time we get to spend together. They are our inspiration and motivation. We will be pleased if the readers of this book benefit from our efforts. We would also need to thank all our well-wishers, colleagues, and friends. Their involvement in the development of this book cannot be overstated. We owe a huge thanks to all of our technical reviewers and editorial advisory board members, our book development editor, and the team at CRC Press, for their work on this huge project. All of their efforts helped create this book. We couldn’t have done it without their constant coordination and support. Last, but definitely not least, we would like to thank everyone who took the time to help us during the process of writing this book. Kaushik Kumar Divya Zindani J. Paulo Davim
- 19. xiii Authors Kaushik Kumar, B.Tech (Mechanical Engineering, REC (Now NIT), Warangal), MBA (Marketing, IGNOU) and Ph.D. (Engineering, Jadavpur University), is pres- ently an Associate Professor in the Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, India. He has 18years of teaching research experience and over 11years of industrial experience in a manufacturing unit of global repute. His areas of teaching and research interest are Conventional and Non-Conventional Quality Management Systems, Optimization, Non-Conventional machining, CAD/CAM, Rapid Prototyping and Composites. He has 9 Patents, 28 Books, 19 Edited Book Volumes, 43 Book Chapters, 141 International Journal, 21 International and 8 National Conference publications to his credit. He is Editor-in- Chief, Series Editor, Guest Editor, Editor, Editorial Board Member and Reviewer for International and National Journals. He has been felicitated with many awards and honors. Divya Zindani, (B.E., Mechanical Engineering, Rajasthan Technical University, Kota), M.E. (Design of Mechanical Equipment, BIT Mesra), presently pursuing Ph.D. (National Institute of Technology, Silchar). He has over 2years of industrial experi- ence. His areas of interests are Optimization, Product and Process Design, CAD/ CAM/CAE, Rapid prototyping and Material Selection. He has 1 Patent, 4 Books, 6 Edited Books, 18 Book Chapters, 2 SCI Journal, 7 Scopus Indexed International Journal and 4 International Conference publications to his credit. J. Paulo Davim received his Ph.D. degree in Mechanical Engineering in 1997, M.Sc. degree in Mechanical Engineering (materials and manufacturing processes) in 1991, Mechanical Engineering degree (5years) in 1986, from the University of Porto (FEUP), the Aggregate title (Full Habilitation) from the University of Coimbra in 2005 and the D.Sc. from London Metropolitan University in 2013. He is Senior Chartered Engineer by the Portuguese Institution of Engineers with an MBA and Specialist title in Engineering and Industrial Management. He is also Eur Ing by FEANI-Brussels and Fellow (FIET) by IET-London. Currently, he is Professor at the Department of Mechanical Engineering of the University of Aveiro, Portugal. He has more than 30years of teaching and research experience in Manufacturing, Materials, Mechanical and Industrial Engineering, with special emphasis in Machining Tribology. He has also interest in Management, Engineering Education and Higher Education for Sustainability. He has guided large numbers of postdoc, Ph.D. and master’s students as well as has coordinated and participated in several financed research projects. He has received several scientific awards. He has worked as evalu- ator of projects for ERC European Research Council and other international research agencies as well as examiner of Ph.D. thesis for many universities in different countries. He is the Editor-in-Chief of several international journals, Guest Editor of journals, Books Editor, Book Series Editor and Scientific Advisory for many
- 20. xiv Authors international journals and conferences. Presently, he is an Editorial Board member of 30 international journals and acts as reviewer for more than 100 prestigious Web of Science journals. In addition, he has also published as editor (and co-editor) more than 100 books and as author (and co-author) more than 10 books, 80 book chapters and 400 articles in journals and conferences (more than 250 articles in journals indexed in Web of Science core collection/h-index 52+/9000+ citations, SCOPUS/ h-index 57+/11000+ citations, Google Scholar/h-index 74+/18000+).
- 21. Section I Introduction to Heuristic Optimization
- 23. 3 1 Optimization Using Heuristic Search An Introduction 1.1 INTRODUCTION Classical optimization techniques such as network-based methods, dynamic programming, non-linear programming, integer programming, linear program- ming, etc. can be used to model and optimally solve many real-life applications. These optimization techniques address different domains of research: operational research, scientific and engineering, scientific and computer science Sand manage- ment science. However, there are umpteen situations wherein the combinatorial nature of the problem makes it difficult to determine the optimal solution using the aforementioned classical optimization approaches. The time required from com- putational perspective is too large which is unrealistic to be acceptable in real-life applications. Furthermore the solution obtained may not be the optimal one i.e., global best and may be one of the local optima which may be relatively poor in comparison to the global best. Heuristic methods have been devised to overcome the aforementioned drawbacks and therefore aims to provide the user with a reasonably good solution. There are certain cases wherein heuristics only seem to be a way forward to obtain concrete results. There has been wide range of application areas for heuristics such as business, economics, statistics, engineering, medicine and sports. Heuristics are now being adopted to solve wide range of complex problems that were very difficult to be solved earlier. The performance analysis of various heuristics can be adjudged through a number of measures. “Heuristic” is a Greek word that means to discover and explore. Heuristics are referred to as approximate techniques. The major objective of heuristics lies in to construct an optimization model that is easily comprehendible and provides for good solutions in a reasonable computational time. There are number of combinatorial factors involved with such techniques such as statistics, computing, mathematical logic and human factors as such experience. Human experience in one of the crucial factors in designing a heuristic that can approach a solution faster and will be more relevant to the real-life situation. The remainder of chapter is organized into following: the manner in which a real-world problem is approached is briefly discussed which is followed with brief discussion on some performance measures for the evaluation of a given method. Categorization of heuristics has been depicted next.
- 24. 4 Optimizing Engineering Problems 1.2 THE OPTIMIZATION PROBLEM For the minimization problem, a general optimization model can be defined in the following form: Minimize st , F X X S S E ( ) ∈ ⊆ (1.1) There are cases wherein it becomes difficult to solve Equation (1.1), mainly because of the following reasons: i. E being the solution space can be finite or very large set which makes the problem as combinatorial optimization problem, or E = Rn i.e., a continuous optimization problem or E = Nn i.e., an integer optimization problem. ii. X being the decision variable may be integer, binary, continuous or combina- tion of any of these types. iii. F(X) being the objective function may not be continuous, linear or even convex and may be made up of several conflicting objectives. iv. S being the feasibility set may not be convex and may be made of disconnected subsets. v. The parameter values within definition of F and S can be probabilistic, estimated or even unknown. The optimization problem falls into a discrete optimization problem if the solution set S is discrete and if it is continuous then the optimization problem is considered to be continuous optimization problem. 1.2.1 Local Versus Global Optima Let X S and the neighborhood of X may be represented by N X S ( ) ⊂ . N(X) may be defined by a small area in the vicinity of X. X is a local minima or maxima with respect to its neighborhood if F X F X X N X ( ) ( ) ( ) ≤ ≥ ∀ ( ) . X* is a global minima or maxima if F X F X X S ( ) ( ) ( ) ≤ ≥ ∀ * . As for instance if all the neighborhoods is represented by ψ and set of all local minima or maxima is represented by Ф then global minima or maxima X* can be defined as * ArgMin ; X F X X X ψ { } ( ) ( ) = or X F X X { } ( ) = Φ * ArgMin ; . In short, global minima or maxima X* is the local minima or maxima if it yields the best solution for the objective function under consideration. Another mechanism is that of local search wherein X is obtained from X in a given neighborhood N(X). i.e., in other words X F X X N X { } ( ) ( ) = ArgMin ; . 1.3 CATEGORIZATION OF OPTIMIZATION TECHNIQUES There are two main categories wherein the optimization techniques falls into: exact algorithms and approximate or heuristic algorithms. The exact optimization algorithms guarantee optimal solution in a number of finite steps, whereas the other
- 25. 5 Optimization Using Heuristic Search category involves heuristic which are set of rules developed through experience, mathematical logics and common sense. Heuristics have the potential ability to tackle the problems in a reasonable amount of computational time. However, the solution produced by such algorithms may not be optimal. Comparison of performances of such algorithms can be done using certain criteria and a discussion on this will be made in the subsequent chapters. Although approximation and heuristic algorithms yield feasible solution, there exists some differences between heuristics and approximation algorithms. The dif- ference lies that approximations guarantee quality of the solutions on the basis of worst-case scenarios. As for instance, the Christofides’ algorithm that is used for solving the traveling salesman problem has a worst quality ratio of 1.5. Another example is that of next fit algorithm that has the worst quality ratio of 2. On the other hand, most heuristics have no similar mathematical bounds that can aid in adjudging their quality. However, research in this direction is underway to evaluate the quality of such non-optimal algorithms. A possible approach to complex real-life problems are: (i) the objective should be to apply an exact methodology to the real-life complex problem, if this is not possible then step (ii) must be approached i.e., application of heuristic approach to an exact problem, if not possible then step (iii) must be approached: application of the exact method to the modified optimization problem and if this step is not approached then final step (iv) must be followed: application of heuristic approach to an approximated problem. The main idea lies in to maintain the characteristics of identified problem and then try to apply steps (i) and (ii). The level of modification to the true problem must be considered carefully. A major modification may make it easier to solve the problem but the modified prob- lem will have a very little resemblance to the originally identified problem. On the other hand, it will be tedious to approach a little modified problem. Another plausible approach may be to incept with an easier version of optimization problem and then proceed to find a solution while keeping a check on the complex con- straints. If the complex constraints are satisfied then there is no need to worry about the optimization problem under consideration. However, if any of the constraints are violated which is likely at the beginning of the search, then introduction of additional characteristic features is required. The process is iterated until it becomes impracti- cal to solve the problem. The solution found in the previous stage then becomes the final solution of the optimization problem under consideration. Hence modifications can be done at three different stages: input stage, algorithm stage and finally the output stage. Therefore it is one of the critical decisions as to when to consider the modifications. That said, it is always better to try for modifica- tions either at the algorithm stage or the output stage. However, if by making slight changes to the initial identified problem can aid in solving the problem optimally, then such approach should be considered judiciously. A less favorable result could be produced with reference to the interrela- tionship between the end user and the researcher. This could happen owing to the lack of understanding and lack of appreciation of the difficulties encoun- tered while approaching a solution for the real-life complex problem. As a result of such outcomes the practitioners will distant themselves from the
- 26. 6 Optimizing Engineering Problems world of academics. However, on a positive note and owing to the better rela- tionship between the universities and the outside world, the trend of distancing is diminishing. In such an environment the company gains an added advantage and the academician enriches their research portfolio. The enhanced research portfolio may benefit the faculty when they are adjudged for their excellence by the universities (2014). 1.4 REQUIREMENT OF HEURISTICS AND THEIR CHARACTERISTICS As discussed in the aforementioned discussion that heuristics can only be used when there is impracticality with the employability of exact solutions which guar- antee optimal solutions. This may arise either because of the excessive computa- tional effort required or there is a potential risk of solution being trapped in local optimum. Therefore in abovementioned circumstances, heuristics become virtually the only option to aid practitioners in finding reasonably acceptable solution. Some of the favorable reasons for promoting heuristics are as follows (Salhi, 2006): (i) heuristics aid the users to obtain solutions of large and combinatorial optimization problems, (ii) heuristics present a better understanding of the search progress through graphi- cal representations, (iii) such algorithms are easy to code and implement, (iv) these algorithms are suitable for producing a number of feasible solutions and not a single one and therefore provides flexibility to the users to choose from more than one fea- sible solutions, (v) heuristics are easily accessible and adaptable to additional tasks or constraints and (vi) even personnel who have only superficial knowledge can well understand the process of optimization. While designing a heuristic algorithm, there are certain characteristics that may be followed. Some of these are added for the generalization purpose and some are just the by-products of the attributes. Certain characteristics of heuristics have been discussed below (Salhi, 2006): i. Effective and robust: The designed heuristic must be able to provide near optimal solution for the different cases under study. ii. Flexible: The flexibility must be there to incorporate any modifications. Flexibility to modify any design step may aid in accommodating new ideas and concepts and the optimization problem can be approached with retention of benefits of the originally designed heuristics. iii. Efficient: The time required needs to be acceptable and therefore must be efficient. iv. Simple: Designed heuristic must be able to follow well-defined steps. However, care must be taken that the heuristic doesn’t gets trapped into local optimum. Metaheuristics are higher levels of heuristics that are devised to reduce the risk of the local searches and heuristics to being trapped into a poor local optimum.
- 27. 7 Optimization Using Heuristic Search 1.5 PERFORMANCE MEASURES FOR HEURISTICS Performance measures of heuristics can be measured through the solution quality, computational efforts, time complexity and space complexity. Below are mentioned five measures of checking solution quality of designed heuristics that can help in testing a given heuristic. i. Worst-case analysis: An example that can show the weakness of the algorithm, which is usually referred to as pathological example, needs to be constructed. However, finding such an example is difficult especially in case of complex problems. One of the major drawbacks for carrying out such theoretically strong analysis is that the problem that is under study rarely represents the case for worst-case analysis. It is beneficial to understand well the problem under consideration to identify whether it truly resembles the example for worst-case analysis. Worst-case analysis provides for useful measures as it guarantees the performance of the algorithm that isn’t far from the real-life example. ii. Lower bounds: One way is to solve relaxed problem i.e., either LP relaxation problems wherein the difficult constraints are removed or to solve the Lagrangean relaxation problems. However, lower bound solutions must be tight so that the quality of the heuristic solution can be adjudged suitably and therefore presents the main difficulty. If this is not the case then users may draw misleading conclusions. iii. Empirical testing: This is based on the best solutions obtained by the already existing heuristics on a set of published data. The designed heuristics can be compared using certain measures such as worst deviation, average solution and the number of best solutions, etc. Empirical testing is the most promi- nent simpler approaches and can be used when results from past researchers exist. Although the accuracy of the testing approach is guaranteed but it only provides for statistical evidence. iv. Probabilistic analysis: The density function of the problem under consider- ation needs to be determined which allows for statistical measures such as worst behavior and average to be calculated. v. Benchmarking: One of the obvious ways in which the performance of heuris- tics can be compared is to compare the designed heuristics with the already existing benchmarking solutions. This provides an advantage to the practi- tioners even if their designed heuristics doesn’t fair with the benchmark solu- tions as they will be able to earn for the improvements. If the results obtained are good then this may instill self-belief and confidence in the user. A good understanding of the heuristics is vital as inferior solutions result in a wrong signal to the user which the user can only comprehend if the basics on heuristics are right and suitably conceived. Better comprehension not only results in avoiding communication hick-ups but also helps in con- struction of friendly atmosphere in which modifications can be easily imple- mented during the course of design of heuristics. There are certain cases wherein the initial runs are not perceived by the users and the user will only be able to incept with their feedback only when positive results are found.
- 28. 8 Optimizing Engineering Problems Time complexity is another measure of performance for heuristics. Time complexity of an algorithm is measured through O(g(n)) where the size of the problem is denoted by n. The problem can be solved within a reasonable time if g(n) is a polynomial function. However, it may be difficult to solve if g(n) is an exponential function. Such type of solutions are known as NP hard. Space complexity is less referenced performance measure in comparison to time complexity. However, it is critically important to understand the manner in which the data is stored and retrieved. Smallest data storage capacity will not only aid in efficient data handling but it can also save a large amount of computing time as it can avoid cal- culation of unnecessary information. The problem may be encountered not only when computational time is large but also arise in case when the computer runs out of memory. A large amount of storage capacity may be demanded by the heuristic even during its initialization phase. Hence certain ways around the problems need to be identified. Computational effort is measured through both the space as well as the time complexity. Large or small computing time is relative term and is defined by the nature of the problem and the availability of the resources for computing. The time for interfacing are usually ignored although it can constitute an important part of the total computing times. If carried out by professionals then this additional time could be taken as constant. It is the importance of the problem that dictates the impact of computing effort. As for instance the algorithm needs to be quick if the problem that is addressed by it is required to be solved once or twice a day. However, if the problem needs to be solved once every month or year then lesser priority can be given to the CPU time. In such cases, attention can be given to the quality of solution. As for instance the problems associated with identification of locations for new facility, purchasing of expensive equipment and planning the schedule of work for the employees and so on doesn’t cares for the computational time taken by the optimizer. However, the quality of solution is very critical to such investigations. Computational time can be saved through an efficient computer code. This can be achieved through minimization of already computed partial or full informa- tion. Tracking of already computed information through the aid of efficient data structures is another way of saving computational time. Introduction of reduction tests that helps to minimize the testing of certain tests also plays a critical role in reduction of computational time. This also doesn’t affect the quality of final solution. 1.6 CLASSIFICATION OF HEURISTICS Heuristics can be classified into the following ways: i. Classical and modern ii. One solution and multiple solution at a time iii. Fast and dirty and slow and powerful iv. Stochastic and deterministic
- 29. 9 Optimization Using Heuristic Search In the present book, following categorization of heuristics have been considered: i. Evolutionary techniques ii. Nature-based techniques iii. Logical search algorithms 1.7 CONCLUSION Present chapter provides an overview of the heuristics and their usage in practice. Certain measures of performance and suitable characteristics of heuristics have also been depicted in the chapter that can aid the readers especially in designing of such techniques. A classification scheme as well as the categorization of the heuristics that will be used in the book have been presented towards the end of the chapter.
- 31. Section II Description of Heuristic Optimization Techniques
- 33. 13 2 Genetic Algorithm 2.1 INTRODUCTION Computational intelligence is one of the fastest growing fields together with evo- lutionary computation in optimization sciences. There are number of optimization algorithms to solve real-world complex problems. Such algorithms mimic mostly the biology surrounding the nature. Most of the evolutionary algorithms have a similar framework. They incept with a population of random solution. The suitability of the solution obtained is adjudged through a fitness function. Through a number of iterations the solution obtained at each step is improved and the best one is chosen. Next set of solutions are then generated through combination of achieved best solution and stochastic selections. There are several random components associated with an evolutionary algorithm that select and combine solutions in each population. Therefore in comparison to the deterministic algorithms the evolutionary algorithms are unreliable in finding suitable solutions. Same solutions are obtained at each and every step by deterministic algorithms. However, slower speed and possibility of get- ting stagnated at local solution are the major problems of deterministic algorithms when applied to large-scale problems. Evolutionary algorithms are heuristics and stochastic. This means heuristic information is employed to search part of search space. These algorithms promise to search only selected regions of the solution space through finding best solution in each population and then use the generated solutions to improve other solutions. Evolutionary algorithms are now being used on large-scale applications and therefore has gained wider popularity and flexibility. Consideration of optimization problems as black boxes is another advantage associated with the evolutionary algorithms. Genetic algorithm (GA) is one of the first and well-known evolutionary algorithms. The present chapter therefore discusses and analyzes GA. 2.2 GENETIC ALGORITHM GA is inspired by theory of biological evolution that was proposed by Darwin (Holland, 1992; Goldberg and Holland, 1988). Survival of the fittest is the main mechanism which is simulated in the GA. Fitter has the highest probability of survival in nature. They transfer their genes to the next generation. In due course of time, the genes that allow species to be adaptable to the environment become dominant and play a vital role in the survival of the species of next generations. GA is inspired by the chromosomes and genes and therefore reflects a true representation of an optimization problem wherein chromosome is representative of a solution and each variable of the optimization problem is represented by a gene. As for instance, an optimization problem will have ten number of genes and
- 34. 14 Optimizing Engineering Problems chromosomes if it has ten variables. Selection, crossover and mutation are the three main operators that are employed by the GA to improve the solution or the chromo- some. Following sub-sections depict on these steps and also the representation of the optimization problem and the initial population. A chromosome is made from genes that represents the variable set of a given optimization problem. The first step to use GA is to formulate the problem and define the parameters in the form of a vector. Binary and continuous are the two variants of GA. Each gene is assigned two values in case of a binary GA, whereas continuous values are assigned in case of a continuous GA. Any continuous value having upper and lower bounds can be used in case of the continuous GA variant. A special case of binary GA is wherein there are more than two values to make a suitable choice. In such special cases, more memory i.e., bits must be allocated to the variables of the problem. As for instance if an optimization problem has two variables each of which can be assigned eight different values, then for each variable, there is a requirement of three genes each. Hence number of genes for variable with n discrete values will be log2n. Genes can be used until they are fed into fitness function and result in a fit- ness value. GA is referred to as genetic programming if different parts of a computer program is employed for each gene. Set of random genes incepts the GA process. Equation (2.1) is used in case of binary GA: = X r i i 1 0.5 0 otherwise (2.1) where i-th gene is represented by Xi and ri is any random number between 0 and 1. Equation (2.2) is used in case of continuous GA to randomly initialize the genes: ( ) = + X ub lb r lb i i i i i – * (2.2) The upper bound for the i-th gene is represented by ubi and the lower bound by lbi. The main objective of the initial population phase is to have uniformly distributed random solutions for all the variables. This is because these will be used subsequently in the following operators. Natural selection is simulated by the selection operator of GA. The chance of survival is proportionally increased to fitness in case of natural selection. The genes are propagated to be adapted by the subsequent generations after being selected. The fitness values are normalized and mapped to the probability values by the roulette wheel. The upper and lower bound of roulette wheel are 1 and 0, respectively. One of the individuals will be selected by generating a random number within this interval. The chances for an individual to get selected is represented by the larger sectorial area occupied by the individual in the roulette wheel. However, one pertinent question that may arise in the mind of readers is that why the poor individuals are not discarded. It is worth noting that even the indi- viduals that have lower fitness value may also be able to mate and contribute toward subsequent generation production. However, this is dependent on other important
- 35. 15 Genetic Algorithm factors such as competition, territory and environmental situations. An individual with poor fitness value may have chance to produce excellent features in conjunction with genes of other individuals. Hence by not discarding poor solutions, a chance is given to the poor individuals so that good features remain. Since the range of values changes and is problem dependent, normalization of values is very important. One of the issues that surround the roulette wheel is that it fails in handling the negative values. Therefore the negative values must be mapped to positive ones through fitness scaling as negative values may impact during the cumulative sum process. Some of the other selection operators (Genlin, 2004) besides roulette wheel are: steady-state reproduction (Syswerda, 1989), proportional selection (Grefenstette, 1989), fuzzy selection (Ishibuchi and Yamamoto, 2004), truncation selection (Blickle and Thiele, 1996), rank selection (Kumar, 2012), Boltzmann selec- tion (Goldberg, 1990), linear rank selection (Grefenstette, 1989), fitness uniform selection (Hutter, 2002), local selection (Collins and Jefferson, 1991), steady-state selection (Syswerda, 1991) and tournament selection (Miller and Goldberg, 1995). The natural selection process aids in selection of individuals for the crossover step and are treated as parents. This allows for gene exchange between individu- als to produce new solutions. Literature suggests a number of different methods of crossover. The chromosome is divided into two or three pieces in case of the easiest of the methods (Shenoy et al., 2005). The genes between the chromosomes are then exchanged. This can be visualized in Figure 2.2 clearly. The chromosomes of two parent solutions are swapped with each other in the single -point crossover and therefore there is one crossover point. However, in case of double-point crossover, there are two crossover points i.e., the chromosomes of the parent solutions swap between these points. The other techniques of cross- over as mentioned in different literatures are: uniform crossover (Semenkin and Semenkina, 2012), three parents crossover (Tsutsui et al., 1999), cycle crossover (Smith and Holland, 1987), position-based crossover (Fonseca and Fleming, 1995), masked crossover (Louis and Rawlins, 1991), half-uniform crossover (Hu and Di Paolo, 2009), partially matched crossover (Bäck et al., 2018), order crossover (Davis, 1985), heuristic crossover (Fogel and Atma, 1990) and multi-point crossover (Eshelman et al., 1989). The overall objective of the crossover step is to ensure that genes are exchanged and the children inherit the genes from the parent solutions. The main mechanism of exploration in GA is the crossover step. There can be crossover using random points and hence the GA is trying to check and search for different combinations of genes coming from parents. This step therefore aids in exploration of possible solutions without the introduction of new genes. Probability of the crossover i.e., Pc is an important parameter in GA that identifies the probability of accepting a new child. This parameter is a solution in the interval 0 and 1. For each child a random number is generated in the interval [0,1]. The child is propagated to the subsequent generation if the random number generated is less than the probability of crossover. If this is not the case then parent is propagated. This is also true with the nature wherein all the offspring don’t survive. The main issue associated with the crossover is the lack of introduction of new genes. If all the solutions become poor, the crossover mechanism will not result in
- 36. 16 Optimizing Engineering Problems generation of different solutions. Hence to consider this issue, GA also considers the mutation operator. Changes in the genes are randomly created through the aid of mutation phase. Probability of mutation i.e., Pm is a parameter that is used for every gene in the chromosome of child generated using the crossover phase. The parameter Pm is a number in the interval 0 and 1. A random number is generated for each gene for the new child. The gene is assigned a random number in the said interval with the upper and lower bounds if the random number is less than Pm. There are numerous mutation techniques: uniform (Srinivas and Patnaik, 1994), Gaussian (Hinterding, 1995), supervised mutation (Oosthuizen, 1987), varying probability mutation (Ankenbrandt, 1991), power mutation (Deep and Thakur, 2007), non-uniform (Neubauer, 1997), shrink (Tsutsui and Fujimoto, 1993) and uniqueness mutation (Mauldin, 1984). Mutation is also the main mechanism of exploration for the GA method. The reason may be attributed to the fact that the mutation operator allows for random changes in the solution and hence allows it to move beyond the search space. The genes in the original chromosomes are produced as a result of crossover and mutation step. There may be chances that all the parents are replaced by children depending on the probability of mutation. Hence there may be possibility of doing away with the good solutions. In order to take care of this issue, another operator known as Elitism (Ahn and Ramakrishna, 2003) is employed. A large number of research studies on GA have revealed the importance of this operator in GA. A very simple mechanism underlies the basic operation of this operator. The chromosome consists of the best genes in the current population and propa- gates it to the subsequent generation without any changes. Hence the solutions are not damaged by the mutation and crossover process leading to the creation of new population. The ranking of individuals on the basis of their fitness value updates the list of the elites. 2.3 COMPETENT GENETIC ALGORITHM It is very useful to employ innovations for explanation of working mechanisms of GA. However, innovations themselves are not understood well and therefore pose difficulty. There is a dire need of principled and mechanistic way of designing GA in order to address and successfully solve the difficult problems across a wide range of real-life complex problems. Competent GAs have been developed in last decades, and as a result of great strides, GAs are now able to solve hard problems quickly with higher accuracy and reliability. Competent GAs are able to solve difficult problems in a scalable fashion and hence are convenient from a computational standpoint. Furthermore, the burden on a user to differentiate between a good coding is eased. In case wherein GA can adapt itself to the problem, the burden on user eases as otherwise the GA would be required to adapt to the problem through appropriate coding and GA operators. Some of the important lessons associated with design of competent GAs are discussed. The discussion is, however, restricted to selector combinative GAs and
- 37. 17 Genetic Algorithm on the facets of competent GAs. Designing of competent selector combinative GAs can be decomposed into number of design steps using Holland’s notion of a building block (BB) (Holland, 1975). Although the design decomposition has been delin- eated by Goldberg (2002), a brief review of the decomposition process is discussed subsequently. It should be known that GAs process BBs. Working of GA through the process of decomposition and reassembly forms the originating root for the conceptualiza- tion of selector combinative GA. The well-adapted set of features known as building blocks were regarded as the components of the effective solution (Holland, 1975). The key conceptual framework involves implicit identification of BBs for achieving good solutions and recombination of the identified BBs to achieve solutions with very high performance. It is very critical to understand problems with hard BBs. It is a usual standpoint of cross-fertilizing innovation that the BBs are hard to acquire for problems that are hard. This may be because of the associated complexity with the BBs. Furthermore it may be due to the fact that BBs are very hard to be identified and separated. The deceptive and misleading behavior of lower-order BBs is another reason for the same (Goldberg, 1987, 1989a; Goldberg et al., 1992b; Deb and Goldberg, 1994). Another important consideration is to understanding of growth and time associ- ated with the BBs. It is believed that the BBs exist in a kind of competitive market economy. As such steps must be taken in order to ensure that the best BBs grow and takeover as a dominant player in the market share of population. Also it is critical to understand that growth rate can neither be too fast or too slow. Setting of the cross- over probability (Pc) and the selection pressure (s) such that Equation (2.3) is satisfied will aid in satisfying the growth in the market share: ≤ − − P s c 1 1 (2.3) where, ϵ is the probability of disruption of BB. There are two other approaches to understand time. The basic tutorial associated with understanding time is beyond the scope of the book. However, for interested readers following examples have been delineated: Selection-intensity models: Here the approaches in resemblance to the quan- titative genetics (Bulmer, 1985) are used and modeling of the dynamics of the average fitness of the population is achieved. Take over time models: Here the modeling of the dynamical aspects of the best individuals is achieved. The convergence time tc for a problem of size l and with all the BBs bearing equal importance or salience can be obtained using Equation (2.4) (Miller and Goldberg, 1995): = π t I l c 2 (2.4)
- 38. 18 Optimizing Engineering Problems where, I is the intensity of selection (Bulmer, 1985) and is dependent on the method of selection and the selection pressure. As for instance, for tournament selection, I can be obtained using Equation (2.5) (Blickle and Thiele, 1996): ( ) ( ) ( ) ( ) = − 2 log log 4.14log I s s (2.5) However, the convergence time will scale-up differently if the BBs have different salience. As for instance, the convergence time will be linear in case the BBs are scaled exponentially and can be calculated using Equation (2.6): ( ) = − − t I l c log2 log 1 3 (2.6) It is also quintessential to have a proper understanding on the supply and decision- making associated with the BBs. Ensuring adequate supply of raw BBs is one of the key role of the population. Larger number of complex BBs will be contained in a randomly generated population of increasing size. The population size, n, required to ensure that at least one copy of all the BBs remain can be obtained using Equation (2.7) (Goldberg et al., 2001): χ χ χ = + n m k k k log log (2.7) where, m is the number of BBs, x is the number of alphabets in each of the BB and χ is the associated cardinality. Decision-making among different BBs is another critical aspect besides ensur- ing the adequate supply of BBs. The decision-making is statistical in nature and the likelihood of making the best possible decision increases as the population size is increased. Therefore the population size required to not only ensure the ade- quacy of supply but also to ensure correct decision-making can be obtained using Equation (2.8) (Harik et al., 1999): σ α = π 2 2 log BB n d m k (2.8) where, α is the probability of incorrectly deciding among the competing BBs, d/σBB is the signal-to-noise ratio. In brief the following components make up the population sizing model: i. Probabilistic safety factor: log α. ii. Subcomponent complexity which is quantified by m i.e., the number of BBs. iii. Competition complexity which is quantified by the total number of compet- ing BBs i.e., 2k. iv. The ease of decision-making which is quantified by d/σBB.
- 39. 19 Genetic Algorithm The population size scaling can be obtained using Equation (2.9) if there is exponential scaling of BBs (Rothlauf, 2006): σ α = − n c d m o k 2 log BB (2.9) where, co is a constant and is drift effect dependent (Crow and Kimura, 1970; Asho and Muhlenbein, 1994). One of the most important lessons in GA is the identification of BBs and their exchange. These two facets form the critical path to innovative success. It is a trend and observation that the first generation GA usually fail in their ability to promote reliably this exchange. The primary aspect of challenge associated with designing a competitive GA is the need to identify BBs as well as promote exchange among them. It has been revealed that although the recombination operators exhibit polynomial scalability for the case of simplified problem, they suffer from exponential scalabil- ity in case of boundedly difficult problems. The studies using facet wise modeling approach also reveal the inadequacies associated with the recombination operators in effective identification and exchange of BBs. A control map is yielded by mixing models suggesting regions of good performance related to GAs. Control maps can aid in identification of sweet spots for GA and hence help in parameter settings. Research direction focused in designing effective GAs has led to the develop- ment of competent GAs and therefore in identification and exchange mechanisms for BBs. The developed competent GAs have the advantage of solving quickly the hard problems with greater reliability and accuracy. Hard problems are the problems that have very large sub-solutions which can’t be decomposed into simpler sub-solutions or have umpteen minima or have high associated stochastic noise. The object is to develop an algorithm that can aid in solving the problems with bounded difficulties and exhibit polynomial scaling. It is worth noting at this stage that there is a vast difference in the mechanics of competent GA. However, it is also true that there are invariant principles asso- ciated with innovative success. Messy GA markets the beginning of competent GA (Goldberg et al., 1989) which finally translated to give rise to fast messy GA. Thereafter a number of GA variants have been developed with the aid of different mechanism styles. Following discussion categorizes some of these approaches, however, a detailed discussion is beyond the scope of this book. Probabilistic model building techniques: The prominent models include population-based incremental learning (Baluja, 1994), the compact GA (Harik et al., 1999), the Bayesian optimization algorithm (Pelikan et al., 2000), the hierarchical Bayesian optimization algorithm (Pelikan and Goldberg, 2001), etc. Linkage adaptation techniques: The prominent examples include linkage learning GA. Perturbation technique: Messy GA (Goldberg et al., 1989), fast messy GA (Goldberg et al., 1989), linkage identification by nonlinearity check (Munetomo and Goldberg, 1999), the dependency structure matrix driven GA (Yu et al., 2003).
- 40. 20 Optimizing Engineering Problems 2.4 IMPROVEMENTS IN GENETIC ALGORITHMS In the previous section, discussion was made on competent GAs. The competent GAs have shown to solve successfully the hard problems and have yielded promis- ing results. However, competent GAs only solve l-variable search problems, wherein O(l2) number of function evaluations are only required. Such problems are referred to have subquadratic number of function evaluations. The competent GAs have addressed the challenges associated with the first generation GAs and have rendered the intractable to tractable. But it can be daunting and tedious task to compute and evaluate subquadratic number of functions. Single evaluation may take long hours if the fitness function evaluation involves complex simulation or computing. Even the subquadratic number of function evaluations for such cases is very high. As for instance, half a months’ time would be required to solve a 20-bit search problem given the fact that the evaluation of fitness function takes at least 1h. The role of efficiency enhancement technique becomes critical in such cases. Furthermore, in order to make an approach really effective for a particular problem, GA needs to be integrated with problem-specific methods. There are numerous literature that have been discussed and investigated on the enhancement of GAs. The four major catego- ries of GA enhancement have been discussed next with suitable references so that interested readers may connect as and when required. Evaluation relaxation: Here the less accurate but inexpensive computationally fitness estimate replaces the computationally expensive and accurate fitness evalu- ation. The less accurate and low-cost fitness estimate can either be exogenous or endogenous. Surrogate fitness function is a case of exogenous fitness evaluation where the development of fitness estimate takes place through external means. Fitness inheritance is the case associated with endogenous function estimate wherein the fitness evaluations are done internally and is based on parental fitness (Smith et al., 1995). Evaluation relaxation technique dates back to early and has built up on the empirical work in image registration by Grefenstette and Ftzpatrick (1985). Using the technique, significant speeds were achieved as the random sampling of the image pixels were reduced greatly. Since then, the technique occupied center stage and was employed to address complex optimization problems across different disciplines such as warehouse scheduling at Coors Brewery (Watson et al., 1999) and structural engineering (Barthelemy and Haftka, 1993). Design theories have been developed to evaluate the effect on population sizing and convergence time that have progressed the early empirical studies on relaxation techniques. These developments have resulted in optimizing speed-ups in approxi- mate functions. Hybridization: It is one of the effective ways of enhancing the effectiveness and performance of GAs. Coupling of GAs with the local search techniques and incor- poration of domain-specific knowledge is the most common hybridization tech- nique. Incorporation of local search operator into GA is another common form of hybridization technique. The hybridization process aids in production of stronger results in comparison to the results that can be achieved using individual approaches. However, increased computational effort is one of the limitations associated with
- 41. 21 Genetic Algorithm the hybridization techniques. Some of the examples in which case one can refer the process as hybridization of GAs are as follows: i. Repairing of infeasible solutions into legal ones. ii. Incorporation of experience of past attempts into the GA process. iii. Initialization of GA population iv. Development of specialized heuristic operators with combinative effects v. Decomposition of large problems into smaller sub-problems heuristically. Significant successes with hybridization approaches have been revealed with the difficult real-world application areas. A small number of real-world examples addressed using hybridized GA have been mentioned below: i. Machine scheduling (Sastry et al., 2005) ii. Sports scheduling (Costa, 1995) iii. Warehouse scheduling (Watson et al., 1999) iv. Nurse rostering (Burke et al., 2001) v. Electric power systems such as maintenance schedule for thermal generator (Burke and Smith, 2000) and maintenance scheduling for electricity transmission network unit commitment problem vi. University timetabling such as timetabling for courses (Paechter et al., 1995) and timetabling for examinations (Burke et al., 2001). Theoretical efforts have been scarce that underpins the hybridization of GA. Some efforts in the past have been made to address the modeling issues of GAs, to study the effect of sampling and search space and so on. Parallelization: The GAs are run on multiple processors and there is distribution of computational resources among these processors. There are number of parallel- ization approaches such as simple master slave GA, a fine-grained architecture, a coarse-grained architecture or a hierarchical architecture. The key objective is to speed up the GA process by employing several processors that take up the compu- tational loads. Time continuation: A solution possessing high quality is achieved through the capabilities associated with recombination and mutation. The solution of high quality is obtained within the constraint of computational resource. A tradeoff between the small solution with multiple convergence epochs and the large population with single convergence epochs is obtained using the concept of time relaxation or continuation. 2.5 CONCLUSION The present chapter delineated the main mechanism of GA i.e., mutation, recombi- nation and initialization. The most widely used approaches for the main mechanisms were discussed in detail. The first generation of GA can solve problems with discrete variables and therefore competent GAs were developed. These developments have been depicted in detail in the present chapter. Different enhancements technique in improving the competent GAs have also been delineated.
- 43. 23 3 Particle Swarm Optimization Algorithm 3.1 INTRODUCTION Swarm intelligence falls under the realm of evolutionary computation. It researches the collective behavior of self-organized and decentralized systems irrespective of whether the systems are natural or artificial. Simple agents or boids interact locally with one another as well as the environment in swarm intelligence framework. Nature is the main source of inspiration for such intelligence techniques (Kothari et al., 2011). Simple and multiple rules are followed by the agents in swarm intel- ligence framework. There is no centralized structure for controlling the behavior of the agents in such frameworks. The behavior of agent in the framework are real and random to a certain degree, however, intelligent behavior at global scales emerge owing to the local interactions. This global behavior is unknown to the individual agents in the swarm intelligence framework. Some of the prominent examples of swarm intelligence include fish schooling, bacterial growth, animal herding and ant colonies. An optimization algorithm based on bird flocking was proposed by Kennedy and Eberhart (Kennedy, 1995) and is referred to as particle swarm optimization (PSO). Some of the other intelligent optimization algorithms are differential evolu- tion (Storn and Price, 1997), bacterial foraging optimization (Müller et al., 2000), artificial bee colony (Karaboga and Basturk, 2007a), glowworm swarm optimization (Krishnanand and Ghose, 2005) and bat algorithm (Yang, 2010a). The present chapter focusses on PSO. Some of the studies on advancement of PSO have been presented. Various applications of PSO have also been depicted. Finally the chapter concludes with the conclusion that summarizes the improvements and the potential research directions. 3.2 BASICS OF PARTICLE SWARM OPTIMIZATION APPROACH One of the key features of swarm intelligence is self-organization. It is a feature wherein due to the local interactions between the disordered components of the system, the global coordination or the order arises. The process is spontaneous and is not controlled by any inside or outside agent. The three basic ingredients of self-organization as identified by Bonabeau et al. (1999) are as follows: i. Multiple interactions: Information from the neighbor agents is utilized by the agents in the swarm and therefore spread across the network.
- 44. 24 Optimizing Engineering Problems ii. Balance of exploration and exploitation: A valuable mean approach of creativity is provided through a suitable means by the swarm intelligence algorithms. iii. Strong dynamical nonlinearity: Convenient structures can be created from the positive feedback, while on the other hand the positive feedback also balances the negative feedback. This ultimately aids in stabilizing the collective pattern. Besides the above features, five major principles identified by Milonas (Karaboga et al., 2014) to be satisfied by the swarm intelligence framework are: adaptability, sta- bility, diverse response, quality principle and proximity principle. In accordance with the proximity principle the swarm intelligence must be able to do simple space and time computations. As a part of quality principle, the swarm must be able to respond to the quality factors in the environment. The swarm is also required not to commit its activities along excessively narrow channels as a part to fulfill the diverse response principle. In accordance with the adaptability principle, the swarm should be able to change their behavior as and when deemed suitable in accordance with the computa- tional price. Furthermore, to fulfill the stability principle, the swarm must ensure so as not to change its mode of behavior every time there occurs change in the environment. 3.2.1 Structure of Standard PSO Swarm of particles are employed by PSO to perform the search operation. These swarm of particles update for every iteration. Each particle moves in the direction to the previous best position as well as the global best position in order to seek the optimal solution. The previous best i.e., pbest and the global best i.e., gbest are given by the following equation: pbest , arg min , gbest arg min 1,2, , 1 1 1 i t f P k t f P k i N k t i i N i p p k t { } ( ) ( ) ( ) ( ) ( ) ( ) = = ∈ … = … = … = … (3.1) Theparticleindexisrepresentedbyi,totalofnumberofparticlesbyNp,fitness function is denoted by f, current iteration number by t and the position by P. Velocity V and Position P are updated in accordance with the Equations (3.2) and (3.3), respectively: 1 pbest , gbest 1 1 2 2 V t V t c r i t P t c r t P t i i i i ω ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + = + − + − (3.2) 1 1 P t P t V t i i i ( ) ( ) ( ) + = + + (3.3) where, ω is referred to as inertia weights that is employed to balance the local exploitation and global exploration, r1 and r2 are the uniformly distributed random variables and are in the interval ranging 0 and 1, c1 and c2 are known as acceleration coefficients and are positive constants.
- 45. 25 PSO Algorithm It is common practice to set up upper limit for the velocity parameter. To restrict the particles flying out of the search space, velocity clamping has been used (Shahzad, 2014). Constriction coefficient is another method that was proposed by Clerc and Kennedy (2002). Inertia is represented in the first part of Equation (3.2) and provides the necessary momentum for the particles to roam across the search space. The second part of the Equation (3.2) represents the cognitive component and is significant of individual thinking of particle. This component is a motivational factor for the particles to prog- ress toward their own best position. Cooperation component is the third part of the Equation (3.2) and reflects the collaborative efforts of the particles. This component aids the particle to search for the global optimal solution (Zhang et al., 2014). Position and velocities are adjusted at each time step, and the optimization function is then evaluated for the new coordinates. The particle stores the coordi- nates in the vector pbest id as and when the particle discovers a pattern that is better than the previously identified one. The difference between the current individual point and the best point identified by a particular agent is added to the current veloc- ity stochastically and therefore the trajectory of the particle as such is caused to oscillate around the point. Furthermore, each particle is defined within the realm of topological neighborhood that comprises the particle itself and other particles in the population. Also the particle velocity gets updated through the addition of weighted difference between the global best and neighborhood best to its current velocity. This addition is also stochastic and hence the velocity is adjusted for the next time step. 3.2.2 Some Definitions Particle (X): This is candidate solution and is represented by d dimensional vector. The dimension of vector is defined by the number of optimized parameters. Particle at any time t can be depicted as Xi(t)=[Xi1(t), Xi2(t),…,Xid(t)], where the optimized parameters are represented by X’s and Xid(t) reflects the position of ith particle w.r.t. to the value of the dth optimized parameter in the ith candidate solution. Population X(t): The set of particles is reflected in population and is represented by X(t)=[X1(t), X2(t)…Xn(t)]. Swarm: The disorganized population of moving particles is represented by swarm. In a swarm the particles tend to cluster with one another wherein each particle moves in a random direction. Particle velocity V(t): The velocity of moving particles is represented by d dimen- sional vector. The velocity of a particle at any time t can be obtained using Equation (3.2). It is represented by Vi(t)=[Vi1(t), Vi2(t)…Vid(t)] where the velocity of the ith particle with respect to the dth dimension. The value of Vid(t) fluctuates between the range −Vmin and −Vmax and is therefore referred to as velocity clamping. Inertia weight (w): The exploitation and exploration of the search space are controlled by the inertia weight. It dynamically adjusts the velocity. The effect on current velocities of the previous velocity is controlled using the inertia weight. A compromise between the global and local exploration abilities of the swarm is exhibited. Global exploration is facilitated through a large inertia weight wherein the local exploration is facilitated by a small weight. Therefore the inertia weight
- 46. 26 Optimizing Engineering Problems must be chosen carefully so as to provide a balance between the local and global exploration space. A proper balance between the two will result in yielding better solution. It is usually a better perspective to incept with a large inertia weight to pro- vide a better global exploration and then decrease it to obtain a more refined solution. Ability to search nonlinearly is one of the requirement often required by many search algorithms. Statistical features may be derived from the results obtained which will ultimately aid in understanding the PSO. This will ease the calculation of proper inertia weights for the next iteration. The inertia weight decreases linearly in accordance with the following equation: = − − × iter iter max max min max w w w w (3.4) where, wmax and wmin are the maximum and minimum values of inertia weights, the current iteration represented by iter and maximum number of iterations by itermax. Social and cognitive parameter: c1 and c2 represent the cognitive and social parameters. Each particle in PSO keeps track of its coordinates in the problem space and is associated with the best solution achieved so far. The best solution is referred to as particle best pbest. Another coordinate tracked is the overall best value of the particle and is represented by gbest. PSO aims to modify the values of particle posi- tion such that pbest and gbest are achieved. Constants c1 and c2 represent stochastic acceleration term that tends to pull a particle toward its pbest and gbest. Lower values of these constants causes the particle to move away from the target regions whereas abrupt movements are signified by the higher values. It has been revealed that values of these constants if closer to 2 then good results are obtained usually. Furthermore, fast global convergence is achieved through this value. There is no significant changes in the rate of convergence with increasing value of these constants. Small local neighborhood aids in avoidance of local minima, however, faster convergence is obtained through larger global neighborhood. 3.3 PSO ALGORITHM The steps involved in a PSO algorithm have been discussed below: Initialization: The population of random particles is initialized wherein each of the particles have random velocity and position. The lower and upper limits for the decision variables are set to confine the search space of the solution. The initialized population of particles is such that the velocity as well as the position fall into the range of variables assigned and satisfies the constraints. A population size ranging 20–50 is more common in PSO algorithm. The fitness of each particle is obtained in terms of pareto-dominance. The non- dominated solutions are recorded and are achieved. The memory of each individual is initialized and is used for the storage of personal best position. The global best position is chosen from the archive. Velocity update: The velocity of each particle is updated in accordance with Equation (3.2). Position updating: The position of particles are updated between successive iterations in accordance with Equation (3.3).
- 47. 27 PSO Algorithm The feasibility of all the generated solutions are ensured through a check on all the imposed constraints. If in case any of the inequality constraint is violated by any element, then the position of the individual is fixed to its maximum or minimum operating point. Archive is also updated that stores the non-dominated solution. Memory update: The particle’s best position as well as the global best solutions are updated using the following equations. 1 1 if 1 1 1 if 1 best best best best p t p t f p t f p t g t p t f p t f g t [ ] [ ] [ ] [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + = + + + = + + (3.5) where, f(X) is the objective function that requires to be minimized. The fitness evaluation of particles are compared with particles pbest. If current value is better than pbest(t), then pbest(t+1) is set as the new current value for subse- quent iteration in the d dimensional space. The fitness evaluation is compared with the population’s overall previous best. If the current global position gbest(t+1) is better than gbest(t) then the global best is set to gbest(t+1). Examination of termination criteria: The algorithm repeats the aforementioned steps until and unless a sufficient good fitness value is achieved or maximum number of iterations have been achieved. The algorithm, on termination, will generate the output points gbest(t) and hence f(gbest(t)). The optimal parameters that have been considered usually to yield optimal solutions are as follows: population size considered is 50, number of iterations as 100, c1 and c2 are set to 2, inertia weight w can range between 1.4 and 0.4. 3.4 SOME MODIFIED PSO ALGORITHMS 3.4.1 Quantum-Behaved PSO The concept of quantum-behaved PSO (QPSO) stemmed from quantum mechanics. A modified QPSO was proposed by Jau et al. (2013) that aided in elimination of the associated drawbacks of basic PSO. The proposed algorithm employed a high- breakdown regression estimator as well as least-trimmed square method. QPSO with differential mutation operator was employed by Jamalipour et al. (2013) for optimiza- tion of WWER-1000 core fuel management. It was revealed that QPSO-Differential mutations(QPSO-DMs)performsbetterthanthebasicPSOalgorithm.QPSOwasused by Bagheri et al. (2014) for foreign exchange market. An improved QPSO algorithm was proposed by Tang et al. (2014) for continuous nonlinear large-scale problems which was based on memory mechanism and memetic algorithm. The memetic algo- rithm aided the particles to gain some experience through the local search phase and then utilize this experience for the subsequent evolutionary process. On the other hand the memory mechanism led to the introduction of bird kingdom and therefore improving the global search ability of the QPSO algorithm. A new hybrid approach encompassing QPSO and simplex algorithms was proposed by Davoodi et al. (2014) wherein QPSO was the main optimizer and simplex algorithm was used to fine-tune the solution obtained from QPSO. Artificial fish swarm algorithm was integrated
- 48. 28 Optimizing Engineering Problems with QPSO by Yumin and Li (2014). Jia et al. (2014) proposed an enhanced approach wherein QPSO was based on genetic algorithm. Through the enhance approach, synchronous optimization of sensor array and classifier was achieved. An improved QPSO metaheuristics algorithm was proposed by Gholizadeh and Moghadas (2014) to be employed for performance-based optimum design process. 3.4.2 Chaotic PSO Chaos theory has been integrated with PSO in order to improve the overall performance of the standard PSO. The integrated version is known as chaotic PSO (CPSO). Chaotic maps were introduced into catfish swarm optimization which ulti- mately resulted in increased search capability (Chuang et al., 2011). An adaptive PSO was proposed by Zhang and Wu (2011), which was ultimately used for the develop- ment of hybrid crop classifier. A chaotic embedded PSO was proposed by Dai et al. (2012) and employed for the estimation of wavelet parameters. The chaotic variables were embedded into standard PSO and the parameters were adjusted nonlinearly and adaptively. A novel algorithm based on CPSO and gradient method known as chaotic particle swarm fuzzy clustering was proposed by Li et al. (2012). The proposed algo- rithm combined the iterative chaotic map with the adaptive inertia weight factor and ultimately with infinite collapses based on local search. The chaotic particle swarm fuzzy clustering exploited the searching capability of fuzzy c-means and therefore avoided the major limitation of standard PSO getting stuck into local optima. The convergence of the novel algorithm was steadfast through the adoption of gradi- ent operator. A novel support vector regression machine was proposed by Wu et al. (2013) and was utilized to estimate the unknown parameters associated with CPSO. A fitness scaling adaptive CPSO was proposed by Zhang et al. (2013) and was used for planning of path for an unmanned combat aerial vehicle. The robustness of the proposed algorithm was justified and it was revealed that the proposed algorithm optimized the problem in lesser time as compared to those obtained with genetic algorithm, simulated annealing and chaotic ABC. K2 algorithm was applied with CPSO to Bayesian structure learning (Zhang et al., 2013). Optimization of munici- pal waste collection in Geographic Information Systems (GIS)-based environment was done using CPSO by Son (Le Hoang, 2014). A novel hybrid model combining artificial neural network and CPSO was proposed by Lu et al. (2014) which improved the forecast accuracy of standard PSO. Classical PSO was combined with a chaotic mechanism, a self-adaptive mutation scheme and time-variant acceleration coeffi- cients (Zeng and Sun, 2014). This eliminated the premature convergence and aided in improvising the quality of the solution. A different chaotic system was proposed by Pluhacek et al. (2014) based on pseudorandom number generators. This was then applied for velocity calculation in the classical PSO algorithm. 3.4.3 Time Varying Acceleration Coefficient-Based PSO The performance of classical PSO was also improved with time varying acceleration coefficient and was referred to as PSOTVAC. A modified PSO with time varying accelerator coefficients was proposed to take care of the linear automation strategy
- 49. 29 PSO Algorithm and thereby giving rise to PSOTVAC in which a predefined velocity index aided in adjusting the cognitive and social factors. PSOTVAC has been employed to address the economic dispatch problem (Chaturvedi et al., 2009). TVAC was employed efficiently that controlled local as well as global search and hence was successful in avoiding the premature convergence. An optimal congestion management was approached by Boonyaridachochai et al. (2010) for deregulated electricity market. The redispatch cost was determined to be minimum with effective implementation of PSOTVAC. A comparative analysis between PSO and self-organizing hierarchical PSO with time varying acceleration coefficient was demonstrated by Sun et al. (2011) for data cluster- ing application. It was revealed that the self-organizing PSO had better performance in comparison to the classical PSO approach. Furthermore, it was revealed that PSO algorithm performed better in case of large-scale and high dimensional data. An effi- cient approach for economic load dispatch problems was addressed by Abedinia et al. (2014) using the PSO with time varying acceleration coefficient. A realistic look to the problem was provided through constraints as transmission loss, ramp rate limit, prohibited operating zone, nonlinear cost functions and generation limitations. An iteration PSO with time varying acceleration coefficient was employed for solving economic dispatch problems and a good convergence property was revealed by the proposed heuristic algorithm (Mohammadi-Ivatloo et al., 2012). A time varying accel- eration coefficient PSO was employed by Mohammadi-Ivatloo et al. (2013) to solve combine heat and power economic dispatch problem. The solution quality of original PSO was improved through adaptively varying the acceleration coefficients in PSO algorithm. A binary PSO with time varying acceleration coefficients was proposed by Pookpunt and Ongsakul (2013) and solved the problem associated with the optimal placement of wind turbines within a wind farm. The objective was to maximize the power output with minimum investment. A hybrid PSO with time varying accelera- tion coefficient integrated with bacteria foraging algorithm was proposed by Abedinia et al. (2013) to solve complex economic dispatch problem. A modified PSO with time varying acceleration coefficient was presented to address the economic load dispatch problem by Abdullah et al. A new best neighbor particle was employed to improve the quality of the solution of the classical PSO algorithm. A binary PSO with time varying acceleration coefficient and a chaotic binary PSO was presented by Zhang et al. (2015). These novel PSO algorithms were then used to solve the multidimensional knapsack problem. The proposed novel algorithms were found to be better to other methods in terms of mean absolute deviation, success rate, least error and standard deviation. 3.4.4 Simplified PSO Swarm were divided into three categories: ordinary particles, better particles and the worst particles by Chen (2010). The divide was done in accordance with the fit- ness value and three types of swarms evolved in accordance with the simplified PSO algorithms. Simplification of PSO was done by Pedersen and Chipperfield (2010) and the adaptability of the classical PSO was improvised. The behavior parameters were tuned using an overlaid metaoptimizer. The modification were incorporated in classical PSO and the version was referred to as many optimizing liaisons, and it was revealed through experimentations that the new PSO algorithm panned out well
- 50. 30 Optimizing Engineering Problems in comparison to the classical PSO version. A simplified PSO was proposed by dos Santos et al. (2012) and saving in computational time was revealed with better per- formance characteristics. Design and performance analysis of proportional-integral device was presented by Panda et al. (2012) using many optimizing liaisons PSO and employed it for an automatic voltage regulator system. A simplified PSO was proposed to address proportional-integral proportional derivative by Vastrakar and Padhy (2013). A parameter-free simplified PSO was proposed by Yeh (2013) and was used to adjust the weights in artificial neural networks (ANNs). 3.5 BENEFITS OF PSO ALGORITHM PSO algorithm has the following advantages: i. It can handle stochastic nature of objective function. ii. It has the potential ability to handle very large number of operating processors and hence the capability to escape the local minima. iii. Simple mathematical functions as well as logic operations are used and therefore easy to implement. iv. It is a derivative-free algorithm. v. It doesn’t require initial good solution to guarantee its convergence. vi. It can be easily integrated with the other optimization techniques. vii. It requires lesser parameters to be adjusted. viii. It can be used for discrete as well as continuous or discontinuous variables and objective functions. 3.6 APPLICATIONS OF PSO There are few applications of PSO that is specific to mechanical engineering domain. Implicit relationship between mechanical properties and the composition of as-cast Mg-Li-Al alloys was established by Ming et al. (2012). A momentum back-propagation neural network with hidden layer was employed for revealing the relationship. A procedure combining finite element analysis (FEM) and PSO was proposed by Chen et al. (2013) and was used for reliability-based optimum design of the composite structure. A good stability of the proposed method was revealed and the method was observed to be efficient in dealing with the probabilistic nature of composite design. PSO technique was employed by Mohan et al. (2013) to aid frequency response function in detection and quantification of surface damage. A better accuracy was revealed with the proposed methodology due to the fact that the data comprised of natural frequencies as well as mode shape. A surrogate-based PSO algorithm was applied by Chen et al. (2013) and employed it for reliability- based robust design of pressure vessels. Maximization of performance factor was solved considering the following design variables: the winding orientation, drop-off region size and thickness of the metal liner. Tsia-Wu failure criterion was used to construct the strength constraints of metal liners and composite layers. A methodol- ogy for identification of parameter values of Barcelona basic model was presented by Zhang et al. (2013). The difference between the measured and computed values
- 51. Another Random Scribd Document with Unrelated Content
- 52. So far we have been concerned with the tendency in dreams to objectify portions of the body by constructing out of them new personalities. But precisely the same process goes on in sleep with regard to our thoughts and feelings. We split off portions of these also and construct other personalities out of them, and sometimes even endow the persons thus formed with thoughts and feelings more native to our own normal personality than those which we reserve for ourselves. Thus a lady who dreamed that when walking with a friend she discovered a species of animal fruit, a kind of damson containing a snail, expressed her delight at finding a combination so admirably adapted to culinary purposes; it was the friend who, retaining the attitude of her own waking moments, uttered an exclamation of disgust. Most of the dreams in which there is any dramatic element are due to this splitting up of personality; in our dreams we may experience shame or confusion from the rebukes or the arguments of other persons, but the persons who administer the rebuke or apply the argument are still ourselves.[167] Some writers on dreaming have marvelled greatly at this tendency of the sleeping mind to objectify portions of itself, and so to create imaginary personalities and evolve dramatic situations. It has seemed to them quite unaccountable except as the outcome of a special gift of imagination appertaining to sleep. Yet, remarkable as it is, this process is simply the inevitable outcome of the conditions under which psychic life exists during sleep. If we realise that a more or less pronounced degree of dissociation of the contents of the mind occurs during sleep, and if we also realise that, sleeping fully as much as waking, mind is a thing that instinctively reasons, and cannot refrain from building up hypotheses, then we may easily see how the personages and situations of dreams develop. Much the same process might, under some circumstances, occur in waking life. If, for instance, we heard an unknown voice speaking behind a curtain, we could not fail to build up an imaginary person in connection with that voice, the characteristics of the imaginary person being largely determined by the nature of the voice and of the things it uttered: it would, further, be quite easy to enter into
- 53. conversation with the person we had thus constructed. That is what seems to occur in dreams. We hear a voice behind the curtain of darkness, and to fit that voice and the things it utters we instinctively form a picture which, in virtue of the hallucinatory aptitude of sleep, is thrown against the curtain; it is then quite easy to enter into conversation with the person we have thus constructed. It no more occurs to us during sleep to suppose that the voice we hear is only a voice and nothing more, than it would occur to us awake to suppose that the voice behind the curtain is only a voice and nothing more. The process is the same; the difference is that in dreams we are, without knowing it, living among what from the waking point of view are called hallucinations. This process by which dreams are formed in sleeping consciousness through the splitting of the dreamer's personality for the construction of other personalities has been recognised ever since dreams began to be seriously studied. Maury referred to the scission of personality in dreams.[168] Delboeuf dealt with what he termed the altruising by the dreamer of part of his representations.[169] Foucault terms the same process personalisation.[170] Giessler attempts elaborately to explain the enigma of self-diremption—the formation of a secondary self—in dreams; if, he argues, a touch or other sensation exceeds the dream-body's capacity of adaptation— i.e., if the state of stimulus is above the apperceptive threshold— only one part of the perception is referred to the dream-body and the other is transferred to a secondary self.[171] This explanation, while it very fairly covers the presentative class of dreams, directly connected with sensory stimuli, cannot so easily be applied to the dramatisation of our representative dreams, which are not obviously traceable to direct bodily stimulation. The splitting up of personality is indeed a very pronounced and widely extended tendency of the mind, and has, during recent years, been elaborately studied. We thus have the basis of that psychic phenomenon which is variously termed secondary personality, double personality, duplex personality, multiple personality,
- 54. alternation of personality, etc.,[172] and in earlier ages was regarded as due to possession by demons. Such conditions seem to be usually associated with hysteria. The essential fact about hysteria is, according to Janet, its lack of synthetising power, which is at the same time a lack of attention and of apperception, and has as its result a disintegration of the field of consciousness into mutually exclusive parts; that is to say, there is a process of dissociation. Now that is a condition resembling, as we have seen, the condition found in dreaming. It is not, therefore, difficult to accept the view of Sollier and others, that hysteria is a condition allied to sleep, a condition of vigilambulism in which the patients are often unable to obtain normal sleep, simply because they are all the time in a state of abnormal sleep; as one said to Sollier: 'I cannot sleep because I am asleep all the time.' It may thus be the case that hysterical multiple personalities[173] furnish a pathological analogue of that tendency to the dramatic objectivation of portions of our personality which is normal and healthy in dreams. Similarly in insanity we have an even more constant and pronounced tendency for the subject to attribute his own sensations to imaginary individuals, and to create personalities out of portions of the real personality. All the illusions, delusions, and hallucinations of the insane are merely the manifold manifestations of this tendency. Without it the insanity would not exist. It is not because he is subjected to unusual sensations—visionary, auditory, tactile, olfactory, visceral, etc.—that a man is insane. It is because he creates imaginary personalities to account for these sensations; if his food tastes strange some one has given him poison if he hears a strange voice it is some one communicating with him by telephones or microphones or hypnotism; if he feels a strange internal sensation it is perhaps because he has another person inside him. The case has even been recorded of a man who attributed any feeling he experienced, even the most normal sensations of hunger and thirst, to the people around him. It is exactly the same process as goes on in our dreams. The sane man, the normal waking man, may
- 55. experience all these strange sensations, but he recognises that they are the spontaneous outcome of his own organisation. We may, however, advance a step beyond this position. This self- objectivation, this dramatisation of our experiences, is not confined to sleep and to pathological conditions which resemble sleep. It is natural and primitive in a far wider sense. The infant will gaze inquisitively at its own feet, watch their movements, play with them, 'punish' them; consciousness has not absorbed them as part of the self.[174] The infant really acts and feels towards the remote parts of his own body as the adult acts and feels in dreaming. We are reminded of the generalisation of Giessler that dream consciousness corresponds to the normal psychic state in childhood, while sleeping subconsciousness corresponds to the embryonic psychic state; so that the dream state represents the renascence of the ego disentangling itself from the impersonal sensations and indistinct images of the embryonic stage of life. That sleeping consciousness is the primitive embryonic consciousness is, indeed, indicated, it has often seemed to me, by the fact that in many animals the embryonic position is the position of rest and sleep. Ducklings and chicks in the shell have their heads beneath their wing. The dog lies with his feet together, head flexed, and hind-quarters drawn up. Man, alike in the womb and asleep, tends to be curled up, with the flexors predominating over the extensors. The savage has gone beyond the infant in ability to assimilate the impressions of his own limbs, but on the psychic side he still constantly tends to objectify his own feelings and ideas, re-creating them as external beings. Primitive man has done so from the first, and this impulse has struck its roots into all our most fundamental human traditions even as they survive in civilisation to-day. The man of the early world moves, like the dreamer, among a sea of emotions and ideas which he cannot recognise the origin of, and, like the dreamer, he instinctively dramatises them. But, unlike the dreamer, he gives stability to the images he has thus created and in good faith mistaken for independent beings. Thus we have the animistic stages
- 56. of culture, and early man peoples his world with gods and spirits and demons and fairies and ghosts which enter into the traditions of his race, and are more or less accepted even by a later race which no longer creates them for itself. In our more advanced civilisations we are still struggling with later forms of that Protean tendency to objectify the self and to animate the things and even the people around us with our own spirit. The impatient and imperfectly bred child, or even man, kicks viciously the object he stumbles against, animate or inanimate, in order to revenge a wrong which exists only in himself. On a slightly higher plane, the men of mediæval times brought actions in the law courts against offending animals and solemnly pronounced sentence against them as 'criminals,'[175] while even to-day society still 'punishes' the human criminal because it has imaginatively re- created him in the image of an ordinary normal person, and lacks the intelligence to perceive that he has been moulded by the laws of his nature and environment into a creature which we do well to protect ourselves against, but have no right to 'punish.'[176] Everywhere we still see around us the surviving relics of this primitive tendency of men to project their own personalities into external objects. A fine civilisation lies largely in the due subordination of this tendency, in the realisation and control of our own emotional possibilities, and in the resultant growth of personal responsibility. It is thus impossible to over-estimate the immense importance of the primitive symbolic tendency to objectify the subjective. Men have taken out of their own hearts their best feelings and their worst feelings, and have personalised and dramatised them, bowed down to them or stamped on them, unable to hear the voice with which each of their images spoke: 'I am thyself.' Our conceptions of religion, of morals, of many of the mightiest phenomena of life, especially the more exceptional phenomena, have grown up under this influence, which still serves to support many movements of to- day by some people imagined to be modern.
- 57. Dreaming, as we have seen, is not the sole source of such conceptions. But they could scarcely have been found convincing, and possibly could not even have arisen, among races which were wholly devoid of dream experiences. A large part of all progress in psychological knowledge, and, indeed, a large part of civilisation itself, lies in realising that the apparently objective is really subjective, that the angels and demons and geniuses of all sorts that once seemed to be external forces taking possession of feeble and vacant individualities are themselves but modes of action of marvellously rich and varied personalities. In our dreams we are brought back into the magic circle of early culture, and we shrink and shudder in the presence of imaginative phantoms that are built up of our own thoughts and emotions, and are really our own flesh.
- 58. CHAPTER VIII DREAMS OF THE DEAD Mental Dissociation during Sleep—Illustrated by the Dream of Returning to School Life—The Typical Dream of a Dead Friend— Examples—Early Records of this Type of Dream—Analysis of such Dreams—Atypical Forms—The Consolation sometimes afforded by Dreams of the Dead—Ancient Legends of this Dream Type—The Influence of Dreams on the Belief of Primitive Man in the Survival of the Dead. Our memories tend to fall into groups or systems. We all possess a great number of such systematised groups of impressions. Every period of life, every subject we have occupied ourselves with, every intimate friend we have had, each represents a more or less separate mass of ideas and feelings. Within each system one idea or feeling easily calls up another belonging to the same system. Moreover, in full and alert waking life, each system is in touch with the systems related to it. If there crowd into the field of consciousness the memories belonging to one period of life, or one country we have lived in, we can control and criticise those memories by reference to others belonging to another period or another country. If we are overwhelmed by the thoughts and emotions associated with the memory of one friend we can restore our mental balance by evoking the thoughts and emotions associated with another friend. The various systems are in this way co-ordinated in apperception.[177] In sleep, however, these groups are not usually so firmly held together by the cords along which we can move in our waking moments from one to the other. They are, as it were, loosened from
- 59. their moorings, and on the sea of sleeping consciousness they drift apart or jostle together in new and what seem to be random associations. This is that process of dissociation which we find so marked in dreaming, and in all those psychic phenomena— hallucinations, hysteria, multiple personality, insanity—which are allied to dreaming. A simple illustration of the clash and confusion of two opposing systems of memories in dreams, when due apperceptive control is lacking, is supplied by a common and well-recognised type of dream, the dream of returning to the school of youth.[178] Many people are occasionally liable to this dream, which is often vivid and disturbing. We may have left the schoolroom thirty years or more ago, and never seen it since; it may have vanished from our waking thoughts. Yet from time to time we find ourselves there in our dreams, and called upon to take our old place, always with a sense of conflict, a vague discomfort, a feeling of something incongruous and humiliating, for we realise that we are now too old. Here is a dream in illustration: I find myself back at my old school, but my old schoolmaster is not there; he is away ill, as I am told by his substitute, whose face somehow seems familiar, though I cannot recall where I have seen it. I do not know any of the boys; I am returning after an absence of some months. I realise that I am to take my old place again, and yet I feel a profound repulsion to do so, a sense that it is somehow incongruous. This latter feeling seems to prevail, for I finally assume the part of a visitor, and remark, insincerely, to the master that it is pleasant to see the old place again. In such a case as this it seems that a picture from an ancient system of memories floats across the field of sleeping consciousness, and the dreamer is naturally drawn into that system and begins to adapt himself to its demands. But, as he does so, the influence of other later and incompatible systems of memories begins unconsciously to affect the dreamer.[179] The cords of connection, however, which when awake would enable him to adjust critically the opposing
- 60. systems, are not acting; apperception is defective. Yet the opposing systems are there, outside the immediate field of consciousness, and jostling the ancient system which has come into the central focus. Finally this jostling of the ancient system by more recent systems causes a harmonising modification in consciousness. The dreamer ceases to be a boy in his old school, and assumes the part of a visitor. Dreams of our recently dead friends furnish a type of dream which is formed in exactly the same way as these dreams of a return to school life. The only difference is that they often present it in a more vivid, pronounced, and poignantly emotional shape. This is so, partly from the very subject of such dreams, and partly because the fact of death definitely divides our impressions of our dead friends into two groups, which are intimately allied to each other by their subject, and yet absolutely opposed by the fact that in the one group the friend is alive, and in the other dead. I proceed to present two series of dreams—one in a man, the other in a woman—illustrating this type of dream.[180] Observation I.—Mr. C., age about twenty-eight, a man of scientific training and aptitudes. Shortly after his mother's death he repeatedly dreamed that she had come to life again. She had been buried, but it was somehow found out that she was not really dead. Mr. C. describes the painful intellectual struggles that went on in these dreams, the arguments in favour of death from the impossibility of prolonged life in the grave, and how these doubts were finally swallowed up in a sense of wonder and joy because his mother was actually there, alive, in his dream. These dreams became less frequent as time went on, but some years later occurred an isolated dream which clearly shows a further stage in the same process. Mr. C. dreamed that his father had just returned home, and that he (the dreamer) was puzzled to make out where his mother was. After puzzling a long time he asked his sister, but at the very moment he asked it flashed upon him—more, he
- 61. thinks, with a feeling of relief at the solution of a painful difficulty than with grief—that his mother was dead. Observation II.—Mrs. F., age about thirty, highly intelligent but of somewhat emotional temperament. A week after the death of a lifelong friend to whom she was greatly attached, Mrs. F. dreamed for the first time of her friend, finding that she was alive, and then in the course of the dream discovering that she had been buried alive. A second dream occurred on the following night. Mrs. F. imagined that she went to see her friend, whom she found in bed, and to whom she told the strange things that she had heard (i.e., that the friend was dead). Her friend then gave Mrs. F. a few things as souvenirs. But on leaving the room Mrs. F. was told that her friend was really dead, and had spoken to her after death. In a fourth dream, at a subsequent date, Mrs. F. imagined that her friend came to her, saying that she had returned to earth for a few minutes to give her messages and to assure her that she was happy in another world and in the enjoyment of the fullest life. Another dream occurred more than a year later. Some one brought to Mrs. F., in her dream, the news that her friend was still alive; she was taken to her and found her as in life. The friend said she had been away, but did not explain where or why she had been supposed dead. Mrs. F. asked no questions and felt no curiosity, being absorbed in the joy of finding her friend still alive, and they proceeded to talk over the things that had happened since they last met. It was a very vivid, natural, and detailed dream, and on awaking Mrs. F. felt somewhat exhausted. Although not superstitious, the dream gave her a feeling of consolation. The next series has been observed more recently. I include all the dreams and the intervals at which they occurred. The somewhat unexpected news reached me of the death of a near and lifelong friend when I was myself recovering from an attack of influenza. No dream which could be connected with this event occurred until about a fortnight later[181] (16th January). I then dreamed that I was with
- 62. my friend and asking him (he had been a clergyman and Biblical scholar) whether, in his opinion, Jesus had been able to speak Greek. I awoke before I received his answer, but no sort of doubt, hesitation, or surprise was aroused by his appearance alive. Nineteen days later (4th February) occurred the next dream. This time I dreamed that my friend was just dead, and that I was gazing at a postcard of good wishes, written partly in Latin, which he had sent me a few days before (on the actual date of my birthday), and regretting that I had not answered it. There was no doubt in my mind as to the fact of his death. (I may remark that the last letter I had written to my friend was on his birthday, and he had been unable to reply, so that there was here one of those reversals which Freud and others have noted as not uncommon in dreams.) The next dream occurred thirty-four days later (10th March). I thought that I met my friend, and at once realised that it was not he but his wife who had died, and I clasped his hand sympathetically. Some months later (27th July) I again dreamed that I was walking with my friend and talking, as we might have talked, on topics of common interest. But at the same time I knew, and he knew that I knew, that he was to die on the morrow. Once more, a fortnight later (10th August), I dreamed that I had an appointment to meet my friend in a certain road, but he failed to appear. I began to wonder whether he had forgotten the appointment, or I had made a mistake, and I was seeking for the letter making the appointment when I awoke. It would appear that the dreams of this type are less pronounced in the ratio of the less pronounced affectional intensity of the relationship which unites the friends. The next dream concerned a man for whom I had the highest esteem and regard, but had not been intimately associated with. I dreamed that I saw this friend, who was the editor of a psychological journal, alive and well in his room, together with two foreign psychologists also known to me, who had apparently succeeded him in the editorship of the journal,
- 63. for I saw their names on the title-page of a number of it which was put in my hands. It surprised me that, though alive and well, he should have ceased to edit the journal; the theory by which I satisfactorily accounted to myself for his appearance was that, though he had been so near death that his life was despaired of, he had not actually died; his death had been prematurely reported. It flashed across my dream consciousness, indeed, that I had read obituaries of my friend in the papers, but this reminiscence merely suggested the reflection that some one had been guilty of a grave indiscretion.[182] Although no attempt had been made to analyse this type of dream before 1895, the dream itself had often been noted down, as from its poignant and affecting character it could not fail to be. An early example is furnished by the philosopher Gassendi, who states that he dreamed he met a friend, that he greeted him as one returned from the dead, and that then, saying to himself in his dream that this was impossible, he concluded that he must be dreaming.[183] Pepys, again, in his Diary, on the 29th June 1667, a few months after his mother's death, dreamed that 'my mother told me she lacked a pair of gloves, and I remembered a pair of my wife's in my chamber, and resolved she should have them, but then recollected [reflected] how my mother came to be here when I was in mourning for her, and so thinking it to be a mistake in our thinking her all this while dead, I did contrive that it should be said to any that inquired that it was my mother-in-law, my wife's mother, that was dead, and we in mourning for.' This dream, Pepys adds, 'did trouble me mightily.' Edmond de Goncourt, in his Journal (27th July 1870), well describes how in the first dream of the dead brother to whom he was so tenderly attached, the two streams of memories appeared. He dreamed he was walking with his brother, but at the same time he knew he was in mourning for him, and friends were coming up to offer condolences; the emotions caused by the conflict of these two certainties—his brother's life affirmed by his presence and his death affirmed by all the other circumstances of the dream—was profoundly distressing. A few years earlier Renan, when his dearly
- 64. loved sister Henrietta died by his side in the Lebanon, also had dreams of this type, which deeply affected even his cautious and sceptical nature. She had died of Syrian fever, from which he also was suffering, and shortly afterwards he wrote in a letter that 'in feverish dreams a terrible doubt has risen up before me; I have fancied I heard her voice calling to me from the vault where she was laid.' He comforted himself, however, with the thought that this horrible supposition was unjustified, since French doctors had been present at her death. Maury[184] also mentions that he had often had dreams of this type in which the dead appeared as living, though the sight of them always produced astonishment and doubt which the sleeping brain endeavoured to allay by some kind of explanation. Beaunis also describes how he has dreamed with surprise of meeting a friend whom even in his dream he knew to be dead.[185] It is not difficult, in the light of all that we have been able to learn regarding the psychology of the world of dreams, to account for the process here described, for its frequency, and for its poignant emotional effects. This dream type is only a special variety of the commonest species of dream, in which two or more groups of reminiscences flow together and form a single bizarre congruity, a confusion in the strict sense of the word. The death of a friend sets up a barrier which cuts into two the stream of impressions concerning that friend. Thus, two streams of images flow into sleeping consciousness, one representing the friend as alive, the other as dead. The first stream comes from older and richer sources; the second is more poignant, but also more recent and more easily exhausted. The two streams break against each other in restless conflict, both, from the inevitable conditions of dream life, being accepted as true, and they eventually mix to form an absurd harmony, in which the older and stronger images (in accordance with that recognised tendency for old psychic impressions generally to be most stable) predominate over those that are more recent. Thus, in the first observation the dreamer seems to have begun his dream by imagining that his mother was alive as of old; then his
- 65. more recent experiences interfered with the assertion of her death. This resulted in a struggle between the old-established images representing her as alive and the later ones representing her as dead. The idea that she had come to life again was evidently a theory that had arisen in his brain to harmonise these two opposing currents. The theory was not accepted easily; all sorts of scientific objections arose to oppose it, but there could be no doubt, for his mother was there. The dreamer is in the same position as a paranoiac who constantly seems to hear threatening voices; henceforth he is absorbed in inventing a theory (electricity, hypnotism, or whatever it may be) to account for his hallucinations, and his whole view of life is modified accordingly. The dreamer, in the cases I am here concerned with, sees an image of the dead person as alive, and is therefore compelled to invent a theory to account for this image; the theories that most easily suggest themselves are either that the dead person has never really died, or else that he has come back from the dead for a brief space. The mental and emotional conflict which such dreams involve renders them very vivid. They make a profound impression even after awakening, and for some sensitive persons are almost too sacred to speak of. When a series of these dreams occurs concerning the same dead friend the tendency seems to be, on the whole—though there are certainly many exceptions—for the living reality of the vision of the dead friend to be more and more positively affirmed. Whether awake or asleep, it is very difficult for us to resist the evidence of our senses. It is even more difficult asleep than awake, for, as we have seen reason to believe, apperception, with the critical control it involves, is weakened. Just as the savage or the child accepts as a reality the illusion of the sun traversing the sky, just as the paranoiac accepts the reality of the hallucinations he is subjected to, and gradually weaves them into a more or less plausible theory, so the dreamer seems to employ all the acutest powers of sleeping reason available to construct a theory in support of the reality of the visions of his dead friend.
- 66. Sometimes atypical dreams of the dead occur in which even from the first there appears little clash or doubt. When the vision can thus easily be accepted, it is sometimes a source of consolation, joy, and even religious faith which may still persist in the waking state. Chabaneix has, for instance, recorded the dream experiences of a poet and philosopher who had been deeply attached to a woman with whom his relations were both passionate and intellectual. From the night after her death onwards, at intervals, he had dreams of the beloved woman, at first appearing as a floating vision, later as a vividly seen and tangible person; these dreams caused refreshment and mental invigoration, and seemed to bring the dreamer into renewed communication with his dead friend.[186] I am indebted to a clergyman for the record of a somewhat similar experience. 'A close friendship,' he writes, 'once existed between myself and a lady, somewhat older, and of a religious temperament. We often discussed the life beyond the grave, and agreed that if she died first, and this appeared more than probable, as she was the victim of a mortal disease, she would appear to me. I may add that she was of a highly-strung and nervous nature, and though purely English had many of the psychic characteristics of the Celt. After her death, I looked for some appearance or manifestation, and about three days after dreamed that she had come back to me, and was discussing with me a matter which I much wished to speak about before her death, but was unable to, owing to her weakness and the presence of strangers. In the dream it was perfectly clear to me that she was a dead woman back from another sphere of existence. For some weeks after this I had similar experiences. They were never dreams of the old life and friendship before death, but always reappearances from the other world. Of course it may be said of this experience of mine, that it was merely the result of expectation. But I have found that the things most on my mind are rarely the subject of my dreams. Moreover, these dreams formed a series, lasting for weeks, and all of the same character, though the conversations differed.'
- 67. When a dreamer awakes in an emotional state which corresponds to a dream he has just experienced, it is usually a safe assumption that the dream was the result, and not the cause, of the emotional state. That is by no means always the case, however, and in the type of dream we are here concerned with it is rarely the case. Even though it may be quite true that an emotional state evoked the dream, it is equally true that in its turn the dream itself may arouse an emotional state. The dream of encountering a celestial visitant, especially if the visitant is a beloved friend, cannot fail to produce an especial effect of this kind. It is noteworthy that the emotional influence may be present even when the fact of dreaming has not been recalled. Thus a lady who, on waking in the morning could not remember having dreamed, realised during the day that she was feeling as she was accustomed to feel after dreaming of a beloved friend, and was ultimately able to recall fragments of the dream.[187] A man of so great an intellect as Goethe has borne witness to the consoling influence of dreams. 'I have had times in my life,' he said, in old age, to Eckermann, 'when I have fallen asleep in tears, but in my dreams the loveliest figures come to give me comfort and happiness, and I awake next morning once more fresh and cheerful.'[188] If we take a wide sweep we shall find in many parts of the world stories and legends concerning the relationship of the living with the dead which have a singular resemblance with the typical dream of the dead here investigated. Thus, in Japan, it appears that stories of the returning of the dead are very common. Lafcadio Hearn reproduces one, as told by a Japanese, which closely resembles some of the dreams we have met with. 'A lover resolved to commit suicide on the grave of his sweetheart. He found her tomb and knelt before it, and prayed and wept, and whispered to her that which he was about to do. And suddenly he heard her voice cry to him Anata! and felt her hand upon his hand: and he turned and saw her kneeling beside him, smiling and beautiful as he remembered her, only a little pale. Then his heart leaped so that he could not speak for the wonder and the doubt and the joy of that moment. But she said, Do not doubt; it is really I. I am not dead. It was all a
- 68. mistake. I was buried because my parents thought me dead—buried too soon. Yet you see I am not dead, not a ghost. It is I; do not doubt it!' It is perhaps worth mentioning that the incident told in the Fourth Gospel (xx. 11-18) as occurring to Mary Magdalene when at the tomb of Jesus, recalls the dream process of fusion of images. She turns and sees, as she thinks, the gardener, but in the course of conversation it flashes on her that he is Jesus, risen from the tomb. In quite another part of the world the Salish Indians of British Columbia have a story of a man who goes back to the spirit-world to reclaim his lost wife; this can only be done under special conditions, and for some time refraining to touch her; if he breaks these conditions she vanishes in his arms, and he is left alone.[189] That story, again, cannot fail to remind us of the almost identical Greek legend of the return of Orpheus to the under-world to reclaim his dead wife Eurydice. If these myths and legends were not directly based on the dream-process, it can only be on the ground, alleged with some force by Freud's school, that myths and legends themselves develop by means of the same mechanism as dreams. The probable influence of dreams in originating or confirming the primitive belief of men in a spirit world has often been set forth. Herbert Spencer attached great importance to this factor in the constitution of the belief in another world, in spirits and in gods.[190] Wundt even considers that such dreams furnish the whole origin of animism. Other writers, less closely associated with anthropological psychology, have argued in the same sense.[191] But while these thinkers have in some cases specifically referred to dreams of the dead, and not merely to the widespread belief of savages that in sleep the soul leaves the body to wander over the earth, they have never realised that there is a special mechanism in the typical dream of a dead friend, due to mental dissociation during sleep, which powerfully suggests to us that death sets up no fatal barrier to the return of the dead. In dreams the dead are thus rendered indestructible; they cannot be finally killed, but rather tend to reappear in ever more clearly affirmed vitality. Dreams of this sort
- 69. must certainly have come to men ever since men began to be. If their emotional effects are great to-day, we can well believe that they were much greater in the early days when dream life and what we call real life were less easily distinguished. The repercussion of this kind of dream through unmeasured ages cannot fail to have told at last on the traditions of the race.
- 70. CHAPTER IX MEMORY IN DREAMS The Apparent Rapidity of Thought in Dreams—This Phenomenon largely due to the Dream being a Description of a Picture—The Experience of Drowning Persons—The Sense of Time in Dreams —The Crumpling of Consciousness in Dreams—The Recovery of Lost Memories through the Relaxation of Attention—The Emergence in Dreams of Memories not known to Waking Life— The Recollection of Forgotten Languages in Sleep—The Perversions of Memory in Dreams—Paramnesic False Recollections—Hypnagogic Paramnesia—Dreams mistaken for Actual Events—The Phenomenon of Pseudo-Reminiscence—Its Relationship to Epilepsy—Its Prevalence especially among Imaginative and Nervously Exhausted Persons—The Theories put forward to Explain it—A Fatigue Product—Conditioned by Defective Attention and Apperception—Pseudo-Reminiscence a reversed Hallucination. The peculiarities of memory in dreams—its defects, its aberrations, its excesses—have attracted attention ever since dreams began to be studied at all. It is not enough to assure ourselves that on awakening from a dream our memory of that dream may fairly be regarded as trustworthy so far as it extends. The characteristics of memory revealed within the reproduced dream have sometimes seemed so extraordinary as to be only explicable by the theory of supernatural intervention. A problem which at one time greatly puzzled the scientific students of dreaming is furnished at the outset by the apparent abnormal rapidity of the dream process, the piling together in a brief space of
- 71. time of a great number of combined memories. Stories were told of people who, when awakened by sounds or contacts which must have aroused them almost immediately, had yet experienced elaborate visions which could only have been excited by the stimulus which caused the awakening. The dream of Maury—who, when awakened by a portion of the bed cornice falling on his neck, imagined that he was living in the days of the Reign of Terror, and, after many adventures, was being guillotined—has become famous. [192] It is unquestionably true that dreams are sometimes evoked by sensory stimuli which almost immediately awake the dreamer. But the supposition that this fairly common fact involves an extraordinary acceleration of the rapidity with which mental images are formed is due to a failure to comprehend the conditions under which psychic activity in sleep takes place. If the sleeper were wide awake, and were suddenly startled by a mysterious voice at the window or the door, he would arrive at a theory of the sound, and even form a plan of action, with at least as much rapidity as when the stimulus occurs during sleep. The difference is that in sleep the ordinary mental associations are more or less in abeyance, and the way is therefore easily open to new associations. These new associations, when we look back at them from the standpoint of waking life, seem to us so bizarre, so far-fetched, that we think it must have required a long time to imagine them. We fail to realise that, under the conditions of dream thought, they have come about as automatically and as instantaneously as the ordinary psychic concomitants of external stimulation in waking life. It must also be remembered that in all the cases in which the rapidity of the dream process has seemed so extraordinary, it has merely been a question of visual imagery, and it is obviously quite easy to see in an instant an elaborate picture or series of pictures which would take a long time to describe.[193] At the most the dreamer has merely seen a kind of cinematographic drama which has been condensed and run together in very much the way practised by the cinematographic artist, so that although the whole story seems to be shown in constant movement, in reality the
- 72. action of hours is condensed into moments. Further, it has always to be borne in mind that, asleep as well as awake, intense emotion involves a loss of the sense of time. We say in a terrible crisis that moments seemed years, and when sleeping consciousness magnifies a trivial stimulation into the occasion of a great crisis the same effect is necessarily produced. Exactly the same illusion is experienced by persons who are rescued from drowning, or other dangerous situations. It sometimes seems to them that their whole life has passed before them in vision during those brief moments. But careful investigation of some of these cases, notably by Piéron, has shown that what really happened was that a scene from childhood, perhaps of some rather similar accident, came before the drowning man's mind and was followed by five, six, perhaps even ten or twelve momentary scenes from later life. When the time during which these scenes flashed through the mind was taken into account it was found that there had by no means been any remarkable mental rapidity. Such considerations have now led most scientific investigators of dreaming to regard these problems of dream memory as settled. Woodworth's observations on the hypnagogic or half-waking state revealed no remarkable rapidity of mental processes. Clavière showed by experiments with an alarm clock which struck twice with an interval of twenty-two seconds that speech dreams at all events take place merely with normal rapidity, or are even slightly slower than under waking conditions. The imagery of sleep, Clavière concluded, is not more rapid than the imagery of waking life, though to the dreamer it may seem to last for hours or days. It is often slackened rather than accelerated, says Piéron, who refers to the corresponding illusion under the influence of drugs like hashish, though in some cases he finds that there is really a slight acceleration. The illusion is simply due, Foucault thinks, to the dreamer's belief that the events of his dream occupy the same time as real events. This illusion of time, concludes Dr. Justine Tobolowska, in her Paris thesis on this subject, is simply the
- 73. necessary and constant result of the form assumed by psychic life during sleep.[194] If this peculiarity of memory in dreaming is not difficult to explain as a natural illusion, there are other and rarer characteristics of dream memory which are much more puzzling. In attempting to unravel these, it is probable that, as in explaining the illusion of rapidity, we must always bear in mind the tendency of memory-groups in dreams to fall apart from their waking links of association, so well as the complementary tendency to form associations which in waking life would only be attained by a strained effort. Apperception, with the power it involves of combining and bringing to a focus all the various groups of memories bearing on the point in hand, is defective. The focus of conscious attention is contracted, and there is the curious and significant phenomenon that sleeping consciousness is occasionally unconscious of psychic elements which yet are present just outside it and thrusting imagery into its focus. The imagery becomes conscious, but its relation to the existing focus of consciousness is not consciously perceived. Such a psychic mechanism, as Freud and his disciples have shown, quite commonly appears in hysteria and obsessional neuroses when healthy normal consciousness is degraded to a pathological level resembling that which is normal in dreams.[195] In such a case the surface of sleeping consciousness is, as it were, crumpled up, and the concealed portion appears only at the end of the dream or not at all. A simple example may make this clear. In a dream I ask a lady if she knows the work of the poet Bau; she replies that she does not; then I see before me a paper having on it the name Baudelaire, clearly the name which should have been contained in my query.[196] In such a dream the crumpling and breaking of consciousness, at its very focus, is shown in the most unmistakable manner.[197] But many of the most remarkable dreams of dramatic dreamers are due to the same phenomenon, which in an intellectual form is exactly the phenomenon which always makes a dramatic situation effective. Robert Louis Stevenson was an
- 74. abnormally vivid dreamer, and found the germ of some of the plots of his stories in his dreams; he has described one of his dreams in which the dreamer imagines he has committed a murder; the crime becomes known to a woman who, however, never denounces it; the murderer lives in terror, and cannot conceive why the woman prolongs his torture by this delay in giving him up to justice; only at the end of the dream comes the clue to the mystery, and the explanation of the woman's attitude, as she falls on her knees and cries: 'Do you not understand? I love you.'[198] There is another and very interesting class of dreams in which we find not merely that some memory-groups disappear from consciousness or become merely latent, but also that other memory- groups, latent or even lost to waking consciousness, float into the focus of sleeping consciousness. In other words, we can remember in sleep what we have forgotten awake. We then have what is called the hypermnesia, the excessive or abnormal memory, of sleep. There can be little doubt that the two processes—the sinking of some memory-groups and the emergence on the surface of other memory-groups which, so far as waking life is concerned, had apparently fallen to the depths and been drowned—are complementarily related to one another. We remember what we have forgotten because we forget what we remembered. The order of our waking impressions involves a certain tension, that is to say a certain attention, which holds them in our consciousness, and excludes any other order which might serve to bring lost memory- groups to sight. Sometimes we are conscious of a lost memory which is just outside consciousness, but which, with the existing order of our memory-groups, we cannot bring into consciousness. We have the missing name, the missing memory, at the tip of our tongue, we say, but we cannot quite catch it.[199] In dreams apperception is defective, the strain of conscious attention is relaxed, and the conditions are furnished under which new clues and strains may come into action and the missing name glide spontaneously into consciousness. Even the mere approach of sleep, with its
- 75. accompanying relaxation of attention, may effect this end. Thus I was trying one day to recall the name of the unpleasant Chinese scent, patchouli. The name, though not usually unfamiliar, escaped me. At night, however, just before falling asleep, it spontaneously occurred to me. In the morning, when fully awake, I was again unable to recall it. In such a case we see how waking consciousness is tense in a certain direction, which happens not to be that in which the desired thing is to be found. Attention under such circumstances impedes rather than aids recollection. In this particular case, I felt convinced that the name I wanted began with h, and thus my mind was intently directed towards a wrong quarter. But on the approach of sleep attention is automatically relaxed, and it is then possible for the forgotten word to slip in from its unexpected quarter. On these occasions it is by indirection that direction is found.[200] It is interesting to observe that this same process of discovery due to the wider outlook of relaxed attention can take place, not only in sleep and the hypnagogic state, but also, subconsciously, in the fully waking state when the mind is occupied with some other subject. Thus in reading a MS., I came upon an illegible word which I was unable to identify, notwithstanding several guesses and careful scrutiny through a magnifying glass. I passed on, dismissing the subject from my mind. A quarter of an hour afterwards, when walking, and thinking of quite a different subject, I became conscious that the word 'ceremonial' had floated into the field of mental vision, and I at once realised that this was the unidentified word. The instance may be trivial, but no example could better show how the mind may continue to work subconsciously in one direction while consciously working in an entirely different direction. In dreams, however, we can effect more than a mere recovery of memories which have temporarily escaped us, or the discovery of relationships which have eluded us. The dissociation of familiar memory-groups becomes so complete, the appearance of unfamiliar groups so eruptive, that we can remember things that have entirely
- 76. and permanently sunk below the surface of waking consciousness, or even things which are so insignificant that they have never made any mark on waking consciousness at all. In this way, we may be said, in a certain sense, to remember things we never knew. The first dream which enabled me, some twenty years ago, to realise this hypermnesia of the mind in dreams[201] was the following unimportant but instructive case. I woke up recalling the chief items of a rather vivid dream: I had imagined myself in a large old house, where the furniture, though of good quality, was ancient, and the chairs threatened to give way as one sat on them. The place belonged to one Sir Peter Bryan, a hale old gentleman, who was accompanied by his son and grandson. There was a question of my buying the place from him, and I was very complimentary to the old gentleman's appearance of youthfulness, absurdly affecting not to know which was the grandfather and which the grandson. On awaking I said to myself that here was a purely imaginative dream, quite unsuggested by any definite experiences. But when I began to recall the trifling incidents of the previous day, and the things I had seen and read, I realised that that was far from being the case. So far from the dream having been a pure effort of imagination, I found that every minute item could be traced to some separate source, though none of them had the slightest resemblance to the dream as a whole. The name of Sir Peter Bryan alone completely baffled me; I could not even recall that I had at that time ever heard of any one called Bryan. I abandoned the search and made my notes of the dream and its sources. I had scarcely done so when I chanced to take up a volume of biographies of eccentric personages, which I had glanced through carelessly the day before. I found that it contained, among others, the lives of Lord Peterborough and George Bryan Brummel. I had certainly seen those names the day before; yet before I took up the book once again it would have been impossible for me to recall the exact name of Beau Brummel. It so happened that the forgotten memory which in this case re-emerged to sleeping consciousness, was a fact of no consequence to myself
- 77. or any one else. But it furnishes the key to many dreams which have been of more serious import to the dreamers. Since then I have been able to observe among my friends several instances of dreams containing veracious though often trivial circumstances unknown to the dreamer when awake, though on consideration it was found to be in the highest degree probable that they had come under his notice, and been forgotten, or not consciously observed. Thus a musical correspondent tells me he once dreamed of playing a piece of Rubinstein's in the presence of a friend who told him he had made a mistake in re-striking a tied note. In the morning he found the dream friend was correct. But up to then he had always repeated the note. Usually when the forgotten or unnoticed circumstance is trivial, it is of quite recent date. That it is not always very recent may be illustrated by a dream of my own. I dreamed that I was in Spain and about to rejoin some friends at a place which was called, I thought, Daraus, but on reaching the booking-office I could not remember whether the place I wanted to go to was called Daraus, Varaus, or Zaraus, all which places, it seemed to me, really existed. On awaking, I made a note of the dream, exactly as reproduced here, but was unable to recall any place, in Spain or elsewhere, corresponding to any of these names. The dream seemed merely to illustrate the familiar way in which a dream image perpetually shifts in a meaningless fashion at the focus of sleeping consciousness. The note was put away, and a few months later taken out again.[202] It was still equally impossible to me to recall any real name corresponding to the dream names. But on consulting the Spanish guide-books and railway time-tables, I found that, on the line between San Sebastian and Bilbao, there really is a little seaside resort, in a beautiful situation, called Zarauz, and I realised, moreover, that I had actually passed that station in the train two hundred and fifty days before the date of my dream. [203] I had no associations with this place, though I may have admired it at the time; in any case it vanished permanently from conscious memory, perhaps aided by the fatigue of a long night journey before entering Spain. Even sleeping memory, I may remark,
- 78. only recovered it with an effort, for it is notable that the name was gradually approached by three successive attempts.[204] A special form of lost or unconscious memories recurring in sleep is constituted by the cases in which people when asleep, or in a somnambulistic state, can speak languages which they have forgotten, or never consciously known, when awake. A simple instance, known to me, is furnished by a servant who had been taken to Paris for a few weeks six months before, but had never learned to speak a word of French, and whose mistress overheard her talking in her sleep, and repeating various French phrases, like 'Je ne sais pas, Monsieur'; she had certainly heard these phrases, though she maintained, when awake, that she was ignorant of them. Speaking in a language not consciously known, or xenoglossia, as it is now termed, occurs under various abnormal conditions, as well as in sleep, and is sometimes classed with the tendency which is found, especially under great religious excitement, to 'speak with tongues,' or to utter gibberish.[205] But in various sleep-like states it occurs as a true revival of forgotten memories, sometimes of memories which belong to childhood and in normal consciousness have been long overlaid and lost. On one occasion, by the bedside of a lady who was kept for a considerable period in a light condition of chloroform anaesthesia, the patient began to talk in an unfamiliar language which one of us recognised as Welsh; as a child, she afterwards owned, she had known Welsh, but had long since forgotten it.[206] A similar reproduction of lost memories occurs in the hypnotic state. This psychic process, by which unconscious memories become conscious in dreams, is of considerable interest and importance because it lends itself to many delusions. Not only the ignorant and uncultured, but even well-trained and acute minds, are often so unskilled in mental analysis that they are quite unable to pierce beneath the phenomenon of conscious ignorance to the deeper fact of unconscious memory; they are completely baffled, or else they resort to the wildest hypotheses. This is illustrated by the following narrative received twelve years ago from a medical correspondent in
- 79. Baltimore. 'Several years ago,' he writes, 'a friend made a social call at my house and in the course of conversation spoke very enthusiastically of Mascagni's Cavalleria Rusticana, the first performance of which in the United States he had attended a few nights previously. I had never even heard of the opera before, but that night I dreamed that I heard it performed. The dream was a very vivid one, so vivid that several times during the next day I found myself humming airs from the dream opera. Several evenings later I went to the theatre to see a comedy, and before the curtain rose the orchestra played a selection which I instantly recognised as part of my dream opera. I exclaimed to a lady who was with me: That selection is from Cavalleria Rusticana. On inquiring of the leader of the orchestra such proved to be the case.' Now, at that period, shortly after the first appearance of Cavalleria Rusticana, portions of it had become extremely popular and were heard everywhere, by no means merely on the operatic stage. It was difficult not to have heard something of it. There cannot be the slightest doubt that my correspondent had heard not only the name but the music, though, writing at an interval of some years, he probably exaggerated the extent of his unconscious recollections. This seems the simple explanation of what to my correspondent was an inexplicable mystery. Other people, like the late Frederick Greenwood, not content to remain baffled, go further and regard such dreams as 'dreams of revelation,' as they also consider that class of dreams in which the dreamer works out the solution of a difficulty which he had vainly grappled with when awake. This is a kind of dream which has occurred in all ages, and has at times been put down to divine interposition. Sixteen centuries ago Bishop Synesius of Ptolemais wrote that in his hunting days a dream revealed to him an idea for a trap which he successfully employed in snaring animals, and at the present time inventions made in dreams have been successfully patented. The Rev. Nehemiah Curnock, who lately succeeded in deciphering Wesley's Journal, has stated that an important missing clue to the cypher came to him in a dream. A friend of my own, an expert in chemistry, was not long since in
- 80. frequent communication with a practical manufacturer, assisting him in his inventions by scientific advice. One day the manufacturer wrote to my friend asking if the latter had been thinking of him during the night, for he had been much puzzled by a difficulty, and during the night had seen a vision of my friend who explained the solution of the difficulty; in the morning the proposed solution proved successful. There was, however, no telepathic element in the case; the dreamer's solution was his own. An interesting group of cases in this class is furnished by the dreams in which the dreamer, in opposition to his waking judgment, sees an acquaintance in whom he reposes trust acting in a manner unworthy of that trust, subsequent events proving that the estimate formed during sleep was sounder than that of waking life. Hawthorne (in his American Notebooks), Greenwood, Jewell, and others have recorded cases of this kind. Various as these phenomena are, they fall into the same scheme. They all help to illustrate the fact that though on one side mental life in sleep is feeble and defective, on the other side it shows a tendency to vigorous excess. Sleep, as we know, involves a relaxation of tension, both physical and psychic; attention is no longer focused at a deliberately selected spot.[207] The voluntary field becomes narrower, but the involuntary field becomes extended. Thus it happens that the contents of our minds fall into a new order, an order which is often fantastic but, on the other hand, is sometimes a more natural and even a more rational order than that we attain in waking life. Our eyes close, our muscles grow slack, the reins fall from our hands. But it sometimes happens that the horse knows the road home even better than we know it ourselves. Hypermnesia, or abnormally wide range of recollection, is not the only or the most common modification of memory during sleep. We find much more commonly, and indeed as one of the chief characteristics of sleep, an abnormally narrow range of recollection. We find, also, and perhaps as a result of that narrow range, paramnesia or perversion of memory. The best known form of
- 81. paramnesia is that in which we have the illusion that the event which is at the moment happening to us has happened to us before.[208] This form of paramnesia is common in dreams, though it is often so slightly pronounced that we either fail to recall it on awakening or attach no significance to it.[209] I dream, for instance, that I am walking along a path, along which, it seems to me, I have often walked before, and that the path skirts the lawn of a house by which stands a policeman whom, also, it seems to me, I have often seen there before; the policeman approaches me and says, 'You have come to see Mr. So-and-so, sir?' and thereupon I suddenly recollect, with some confusion, that I have come to see Mr. So-and-so, and I walk up to the door. Again, an author dreams that he sees a list of his own books with, at the head of them, one entitled 'The Book of Glory.' He could not recall writing it (and to waking consciousness the name was entirely unknown), but the only reflection he made in his dream was 'How stupid to have forgotten!' In this case there was evidently some resistance to the suggestion, which yet was quickly accepted. In all such dreams it seems that we are in a state of mental weakness associated with defective apperceptual control and undue suggestibility, very similar to the state found in some forms of confusional insanity or of precocious dementia.[210] Consciousness feebly slides down the path of least resistance; it accepts every suggestion; the objects presented to it seem things that it knew before, the things that are suggested to it to do seem things that it already wanted to do before. Paramnesia, thus regarded, seems simply a natural outcome of a state of consciousness temporarily depressed below its normal standard of vigour. It must be remembered that the suggestibility of sleeping consciousness varies in degree, and in the face of serious improbabilities there is often a considerable amount of resistance, just as the hypnotised person seriously resists the suggestions that fundamentally outrage his nature. But some degree of suggestibility, some tendency to regard the things that come before us in dreams as familiar—in other words, as things that have happened to us
- 82. before—is not merely a natural result of defective apperception, but one of the very conditions of dreaming. It enables us to carry on our dreams; without it their progress would be fatally inhibited by doubt, uncertainty, and struggle. So it is, perhaps, that in all dreaming, or at all events in certain stages of sleeping consciousness, we are liable to fall into a state of pseudo-reminiscence. It is an interesting and highly significant fact that this paramnesic delusion of our dreams—the feeling that the thing that is happening to us is the thing that has happened to us before or that might happen to us again—tends to persist in the hypnagogic (or hypnopompic) stage immediately following sleep. When we have half awakened from a dream and are just able to realise that it was a dream, that dream constantly tends to appear in a more plausible or probable light than is possible a few moments later when we are fully awake.[211] The first experience which enabled me clearly to realise this phenomenon, and its probable explanation, occurred many years ago. About the middle of the night I had a very vivid dream, in which I imagined that two friends—a gentleman and his daughter— with a certain Lord Chesterfield (I had lately been reading the Letters of the famous Lord Chesterfield), were together at a hotel, that they were playing with weapons, that the lady accidentally killed or wounded Lord Chesterfield, and that she then changed clothes with him with the object of escaping, and avoiding discovery which would somehow be dangerous. I was informed of the matter, and was much concerned. I awoke, and my first thought was that I had just had a curious dream which I must not forget in the morning. But then I seemed to remember that it was a real and familiar event. This second thought lulled my mental activity, and I went to sleep again. In the morning I was able to recall the main points in my dream, and my thoughts on awaking from it. Since then I have given attention to the point, and I have found on recalling my half-waking consciousness after dreams that, while it is doubtless rare to catch the assertion 'That really occurred,' it is less
- 83. rare to catch the vague assertion, 'That is the kind of thing that does occur.' I find that this latter impression appears, like the former, after vivid dreams which contain no physical impossibility, but which the full waking consciousness refuses to recognise as among the things that are probable. As an example quite unlike that just recorded, I may mention a dream in which I imagined that I was proving the frequency of local intermarriage by noting in directories the frequency of the presence of people of the same name in neighbouring towns and villages. On half-awaking I still believed that I had actually been engaged in such a task—that is, either that the dream was real or that it referred to a real event—and it was not until I was sufficiently awake to recognise the fallacy of such a method of investigation that I realised that it was purely a dream. This phenomenon has long been known, although its significance has not been perceived. Brierre de Boismont pointed out that certain vivid dreams are not recognised as dreams, but are mistaken for reality after waking, though he scarcely recognised the normal limitation of this mistake to the hypnagogic state. Moll compared such dreams, thus continued into waking life, to continuative post- hypnotic suggestions. Sully mentioned awaking from dreams which 'still wear the aspect of old acquaintances, so that for the moment I think they are waking realities.'[212] Colegrove, in his study of memory, recorded many cases in which young people mistook their dreams for actual events.[213] This persistence of the memory illusion of sleep into the subsequent hypnagogic state is obviously related to the allied persistence, more occasionally found, of the visual, auditory, and other sensory hallucinations of sleep into the hypnagogic state.[214] Visions thus seen persisting from dreams for a few moments into waking life are often very baffling and disturbing, as has already been pointed out, to ignorant and untrained people. Such visions may occur in the hypnagogic state, even when there has been no conscious precedent dream, and it is indeed probable, as Parish has argued, that it is precisely in the hypnagogic state, the narthex of the church of
- 84. dreams, as I may term it, that hallucinations are most liable to occur. That illusions may momentarily occur in this state is obvious; thus falling asleep for a few minutes when seated before a black hollow smouldering fire, with red ashes at the bottom, I awake with the illusion that I see a curtain on fire, and have already leaned forward to snatch it away before I realise my mistake. Under normal conditions, the liability of a dream memory to be mistaken for an actual event seems to be greater when an interval has elapsed before the dream is remembered, such an interval making it difficult to distinguish one class of memories from the other, provided the dream has been of a plausible character. Thus Professor Näcke has recorded that his wife dreamed that an acquaintance, an old lady, had called at the house; this dream was apparently forgotten until forty or fifty hours afterwards when, on passing the old lady's house, it was recalled, and the dreamer was only with much difficulty convinced that the dream was not an actual occurrence. When we are concerned with memories of childhood, it not infrequently happens that we cannot distinguish with absolute certainty between real occurrences and what may possibly have been dreams. In normal physical and mental health, however, it seems rare for the hallucinatory influence of dreams to extend beyond the hypnagogic state, but any impairment of the bodily health generally, and of the brain in particular, may extend this confusion. Thus in a case of heart disease terminating fatally, the patient, though in health he was by no means visionary or impressionable, became liable during sleep in the day-time to dreams of an entirely reasonable character which he had great difficulty in distinguishing from the real facts of life, never feeling sure what had actually happened, and what had been only a dream. In disordered cerebral and nervous conditions the same illusion becomes still more marked. This is notably the case in hysteria. In some forms of insanity, as many alienists have shown, this mistake is sometimes permanent and the dream may become an integral and persistent part of waking life. At this point,
- 85. however, we leave the normal world of dreams and enter the sphere of pathology. In the normal persistence of the dream illusion into the hypnagogic state with which we are here concerned, the dream usually presents a possible, though, it may be, highly improbable event. The half- waking or hypnagogic intelligence seems to be deceived by this element of life-like possibility. Consequently a fallacy of perception takes place strictly comparable to the fallacious perception which, in the case of an external sensation, we call an illusion. In the ordinary illusion an externally excited sensation of one kind is mistaken for an externally excited sensation of another kind. In this case a centrally excited sensation of one order (dream image) is mistaken for a centrally excited sensation of another order (memory). The phenomenon is, therefore, a mental illusion belonging to the group of false memories, and it may be termed hypnagogic paramnesia. The process seems to have a certain interest, and it may throw light on some rather obscure phenomena. When we are able to recall a vivid dream, usually a fairly probable dream, with no idea as to when it was dreamed, and thus find ourselves in possession of experiences of which we cannot certainly say that they happened in waking life or in dream life, it seems probable that this hypnagogic paramnesia has come into action; the half-waking consciousness dismisses the vivid and life-like dream as an old and familiar experience, shunting it off into temporary forgetfulness, unless some accident again brings it into consciousness with, as it were, a fragment of that wrong label still sticking to it. Such a paramnesic process may thus also help to account for the mighty part which, as so many thinkers from Lucretius onwards have seen, dreams have played in moulding human action and human belief. It is a means whereby waking life and dream life are brought to an apparently common level. By hypnagogic paramnesia I mean a false memory occurring in the ante-chamber of sleep, but not necessarily before sleep. Myers's invention of the word 'hypnopompic' seems scarcely necessary even
- 86. for pedantic reasons. I take the condition of consciousness to be almost the same whether the sleep is coming on or passing away. In the Chesterfield dream it is indeed impossible to say whether the phenomenon is 'hypnagogic' or 'hypnopompic'; in such a case the twilight consciousness is as much conditioned by the sleep that is passing away as by the sleep that is coming on. If this memory illusion of the half-waking state may be regarded as a variety of paramnesia, a new horizon is opened out to us. May not the hypnagogic variety throw light on the general phenomenon of paramnesia which has led to so many strange and complicated theories? I think it may. Paramnesia, as we have seen, is the psychologist's name for a hallucination of memory which is sometimes called 'pseudo- reminiscence,' and by medical writers (who especially associate it with epilepsy) regarded as a symptom of 'dreamy state,'[215] while by French authors it is often termed 'false recognition' or 'sensation du déjà vu.' Dickens, who seems himself to have experienced it, thus describes it in David Copperfield: 'We have all some experience of a feeling that comes over us occasionally, of what we are saying and doing having been said or done before, in a remote time, of having been surrounded, dim ages ago, by the same faces, objects, and circumstances, of our knowing perfectly what will be said next, as if we suddenly remembered it.' Sometimes it seems that this previous occurrence can only have taken place in a previous existence,[216] whence we probably have, as St. Augustine seems first to have suggested, the origin of the idea of metempsychosis, of the transmigration of souls; sometimes it seems to have happened before in a dream; sometimes the subject of the experience is totally baffled in the attempt to account for the feeling of familiarity which has overtaken him. In any case he is liable to an emotion of distress which would scarcely be caused by the coincidence of resemblance with a real previous experience.[217]
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