Kubota, n. 1994: genetic algorithm with age structure and its application to self-organising manufacturing system

1994 IEEE Symposium on
Emerging Technologies & Factory Automation

Genetic Algorithm with Age Structure and Its Application to
Self-Organizing Manufacturing System
Naoyuki KUBOTA, Toshio FUKUDA, Fumihito ARAI, and Koji SHIMOJIMA
Dept. of Micro System Engineering, Nagoya University,
I Furo-cho, Chikusa-ku, Nagoya 464-01, JAPAN

- This paper deals with the new genetic algorithm
with the age structure. The genetic algorithm has been recently
demonstrated its effectiveness in optimization issues, but the
genetic algorithm has two major problems: a premature local
convergence ard a bias by the genetic drift In order to solve
these problems, we propose the genetic algorithm introducing
the age structure which is a continuous generation model. The
genetic algorithm with age structure is applied to the selforganizing manufacturing system, that is, a process selforganizes to the other process in the flexible manufacturing
system environment. The effectiveness of the genetic algorithm
with the age structure is demonstrated through numerical
simulations of the reorganization of the press machining line
as an example of the self-organizing manufacturing system.

Abstract

INTRODUCTION
In recent years, the intelligent manufacturing system,
which has been discussed by many researchers, is required
alvanced flexible processes in a flexible manufacturing system
(FMS) environment[l,2]. We have been proposed selforganizing cellular robotic system (CEBOT) which is
composed of a number of autonomous robotic units with
simple functions[3]- [6J. The form of the CEBOT is
reconfigured dynamically in order to suit to the environment
and tasks. Further, as a manufacturing system held the idea of
the CEBOT, we propose the self-organizing manufacturing
system (SOMS), that is, each process self-organizes effectively
to the other process in the FMS. The optimization of each
process in the FMS is ne:eCed in <rder to crerue an ideal
manufacturing system environment, ard the FMS environment
includes many optimization problems which are ill-defined.
There are stochastic search methods for these problems such as
the simulated annealing, the genetic algorithm(GA}, ard so on .
The GA[7]-[9], which simulates the process of natural
evolution, is defired as an optimization method with the set,
called a population of individuals. Each individual has a fitness

Q-7603 -2114-61941$4 .00

©

1994

IEEE.

value corresponding with its genotype, ard the next generation
of a population is reproduced by selection according to a fitness
value of each individual. The simple GA(SGA)[2] as one of the
GAs, in general, composes of genetic operators: roulette
strategy selection, one-point crossover ard mutation. The GA
has been demonsrrated its effectiveness in combinatorial
optimization issues, scheduling problems ard so on[JOH13].
However, the GA has two major problems of premature local
convergence ard the bias by the genetic drift. These problems
occurred when genetic diversity in the population is reduced.
Then ways to solve these problems have been proposed
following : a fitness scaling, a dynamically conrrol of a
mutation rate, a parallelization by subpopulations, and so on .
Then, in tl'der to solve these problems, we propose the GA
introducing the age structure (ASGA) which is a continuous
generation model. In the ASGA, a coexistence of parents and
offspring in a population is pennitted. As optimization
problems to compare in the performances among the GAs.
most of the GAs are applied fer a scheduling problem or a
traveling salesman problem. The job shop scheduling problem
(JSSP) is in general refined as an optimization problem to
search for optimal scheduling of required works in orckr to
shorten makespan performed in the environment composed of
several machines[!]. However, in th is JSSP there are many
restrictions about transportation methods ard others. lt is
required to consider these restrictions in ceder to apply for the
FMS. In such a F1S environment , however, there are lots of
flow shop scheduling problem which are defined as a
sequencing. The sequence of machining line is effective ' n
respect to paths of automated guided vehicles(AGVs) or
placemems of belt conveyers, for the di.rection of AGYs are the
same. There are many cases that the sequencing of works is
optimized according to the several available machines in the
FMS environment. In contrast to those cases, there are few
cases that the form of machines is optimized according to the
sequeoce of given works. Consequently, "e deal with an
application for the latter cases. In this popcr, the ASGA is
applied to a press machining line (PML) which is capable of

472

Material

Tool providing port

providing port

llo
I
0
AGV

SELF-ORGANIZING MA'<VFACfURING SYSTEM
The FMS is composed of numerically controlled
machines , machining centers, assembling stations arrl robots,
<l1d so on . Further, as automatic transportation methods, belt
conveyors, transportation vehicles, monorail cars are handled in
this system. The purpose of the FMS is to automatically carry
out the process which is composed of design, machining ,
control, ard management by integrating flexible machines ard
computerized control. The effectiveness of the FMS is an
ability to correspond to high variety. Then in order to create an
ideal manufacturing system environment, we propose the
S0 M S, that is, a process self-organizes in accordance with the
other process in the such FMS environment(Fig.l ). The selforganization of SOMS is to reorganize hardware as well as
software of manufacturing system. As an example of the
SOMS, assuming that there is a manufacturing system
composed of machining centers which is capable of
reorganizing for itself and a number of AGVs(Fig.2).
Machining centers are equipped exchangeable tools according to
required machining. AGVs carry not only materials/products
but also tools which are equipped machining center. In this
system, machining control and manufacturing management is
performed not by the centralization but by the decentralization.

~I
Machining center

••

Tool providing port

Fig. 1 Self-organizing manufacturing system

reorganizing the machine in itself as an example of the SOMS.
However, it is very difficu lt to optimize all manufacturing
process for the demanded works. The optimization of the PML
is here to reorganize the form of the PML by using the ASGA .
The effectiveness of the proposed method is demonstrated
through numerical simulations.

o€';;:.;<ii .i;V

0

0
AGV

0

oil~~~

Product
providing port

Fig.2 An example of manufacturing system
The machining information about each material is held by the
bucket kept materials. Therefore, each AGV carries bucket to
the machining center according to machining information. The
flow of processes is generally summarized as follows:
designing of the machining center, planning of the
manufacturing schedule, ard producing products actually
according to its schedule. In these processes, it is important to
reduce manufacturing cost and makespan to optimize all the
manufacturing system as is demanded However, it is very
difficult, ard the optimized system is vulnerable to breakdown
of system or delays of schedules. Therefore, the selforganization according to other process such as the SOMS is
effective with regard to the flexibility of all the manufacturing
system.

AGE STRUCfURED GENETIC ALGORITIIM
In this chapter, we propose the ASGA as one of
improvements to maintain genetic diversity in a population. A
typical population with age structure in nature[ 14, 15] is
presented in Fig.3. The ASGA simulates simply this
population in nature. In this paper, one generation is defined as
a unit of the dis~Tete time. Each individual in the ASGA is
introduced the parameter called an age ard is removed from a
population when its age amounts to the fixed lethal age. All
the offspring, which are generated from parents by the crossover
an:l mutation operator, are at age 0. Further, the next generation
of a population is reproduced by the selection among the
population included parents m those offspring. The procedure

473

Population

4

4

3

3

2

2

l
Age

Age
Age 0

t + l
Time( Generation)

t

Fig.3 Population with age structure in narure

Fig .4 Press machining line in cluding an AGV

of the ASGA is simply as follows.

The material of each job is transported from the place for
material to the press machine am after perfomned machining the
product is cransported to the place for the product by an AGV.
That is, in th is line the flow shop scheduling is carried out.
The assumptions of the PML in thi s case are written as
follows.

am

Step 1 Generation of initial population
initialization of age.
Step2 Calculation of fitnes s value
selection.
Step3 Crossover ard mutation .
Step4 Increase of age.
Step5 Removal of indivtdual amounted to lethal age.
Step6 Go to Step2

oro

•A worlc is composed of n jobs.
•The sequence of given jobs is fixed.
•Each job requires operations by m molds a-d its
machining sequence is thed.
•It is able to attach up to three mold in each pallet
on the press machine.
•The mold, which is required on the job. is
automatically selected am the machining is carried
o ut by its required mold.
•When a press machine in front of the AGV is in
process, the AOV stands by in from of the press
machine till finishing the machining.
•When the pallet of the press machine in front of
the AGV does not include the mold required in the
next operation of the job, the AGV passes it by.

am

There are two major differences between the SOA
the ASGA. First , the parents of the last generation is capable
of e<isting in the next generation by the selection of the
ASO A. That is, the parents are pemnitted coexistence with their
offspring. Second, in the ASGA e<JCh individual is removed
from a population when its age amounts to the lethal age
without considering fitness value. Therefore, the ASOA is
capable of better regulation of the number of the same
individual.

APPLICATION TO PRESS MACHINING LINE

Press manufacturing line
The ASGA is applied for the PML(Fig.4), which is
capable of reorganizing the system in itself as an example of
the SOMS . In this PML, the number of press machine is
bigger than the number of the machining process per job, for
to give the PML further redundancy is flexible to manufacture
several types of products at one line . As the PML in th is case
is a series of line, the direction of the flow of jobs is one-way.

In this PML, there are optimization of flow shop
scheduling of jobs on the work, reorganizing press machine, a
path planning of AGVs an:! so on. The scheduling problem is
several types of search
well known as a NP-hard problem
algorithms for the scheduling problem have been proposed.
However, as described before. reorganization of the PML is
dealt in this paper. Consequently, the optimization of the
attachment, i.e. mold type of the PML to suit with the given
work is dealt.

474

am

'-.

c••<Omm;~,...~-':-;---4- :oo;vi~u.aJ.
t2
:-·,-'_ _ _ _ _ _ _ _ _ _ _ _J
• .J

Molds on the pallet
Fig.5 A genotype of individual

.

Individual

Individual 2

Each individual of population has three chromosomes
whose length is the number of pallet on the PML. As for
coding of the GA, the strings of each gene are defined as the
number of mold type and the number of locus is defined as the
numerical Olrler of the pallet. That is. the set of the i-th locus
genes of the chromosomes in the iooividual refer 10 the set of
the molds included in the i-th pallet(Fig.5). Further, the overlap
of same mold type on the pallet is not permitted . The multipoint crossover is handled as the crossover operator ~ the
crossover is performed between the same number of
chromosome of each individual(Fig.6). The mutation operator
replaces a string with other strings except strings on the pallet.
The transposition operator is an operator to replace position of
chromosome in the individual. The reproduction of the next
population
is performed
by
selection: the roulette
strategy(SGA), elitism strategy(GA_E, ASGA_E).

Numerical simulations
In this section, numerical simulations among the GAs
concerning selection operator are shown. The purpose of the
proposed PML is to shorten makespan. The numericill
Individual I
simulation is performed by 6 type of works. The parameters of
these works are shnwn in Table I.
The purpose of Workl is a comparison of the
makespam between the previous PML with the PML after the
(
reorganization of the PML. Its job sequence and machining
time of ea::h mold is shown in Table 2 and Table 3. The
Fig.6 Crossover of multi-chromosome
sequence of machining of each job on the Work2-Work6 and a
machining time of each mold arc randomly generated on each
work( machining time limit to 20 discrete time). In the Work I,
Application to press machining line
I 0 types of jobs are entered in sequence from job 1 to job I 0. A
As the proposed PML is a flow shop model, the comparison between Work2 and Work3 is to examine variation
purpose of the PML is to reorganize the pallet of the PML in to the job type. A comparison among Work4- Work6 is to
CKder to shorten makespan, that is defined as the total amount examine variation to the mold type and the number of job.
of machining time of the work. Let Fi be the time of job 1 is And the parameters of GA on the numerical simulations are
shown in Table 4. We eanied out numerical simulations among
finished of all the machining from starting time of first job.
Makespan F is as defined eq.(l) and the purpose is to minimize the proposed ASGA with the elitism strategy (ASGA_E) and
the SGA ~ GA_E, whose selection is elitism strategy in
ofF:
stead of roulette strategy in the SGA. A numerical simulation
(1)
min F =max F;
result of Work I is demonstrated in Fig.7 ifii simulation results
of 10 runs of Worki-Work6 are demonstrated in Table 5. As
Assume that the transportation time of the AGV is ignored in
the result of numerical simulations of Work!, The reorganized
comparison with the machining time by a press machine and
PML, whose makespan is shorter than the makespan of the
the loading/unloading time of material is equal without relation
previous PML was genemted. Further, The ASGA is performed
10 materials. Fitness function: fitncssx: of individual x is as
better than the SGA ifii the GA_E. The performance of the
follows:
PML applied the ASGA is improved its makespan up to 10%
reduction in average. There is no distinctive difference among
(2)
fitness,= max Fi- sF,
three GAs on the Workl-WorkJ. The GA_E ~ the ASGA_E
where sis scaling score and it is while constant.
are performed better than the SGA on the Work4 and WorkS

Crossing site

Crmsover

rzz

??ZZ/).

475

which are complicated relatively. The ASGA is perfonned best
of three GAs on the Work6 which is the most complicated of
all the works.

[3]T.Fukuda, T.Ueyama, "Cellular Robotics n1 Micro
Robotic Systems", World Scientific Series in Robotic
m Automated Systems Vol.IO, World Scientific (1994)
[4] T . Fukuda, T. Ueyama, "Self-Evolutionary Robotic
System -Sociobiology ;nt Social Robotics-" , Journal of
Robotics m Mechatronics, Vol.4, No .2, 96/103 (1992)
[5] Y. Kawauchi, T. Fukuda, "Genetic System and
Evolution ", Journal of Robotics and Mechatronics.
Vo1.4, No.2, 108/114 (1992)
161 T . Ueyama, T. Fukuda, "Self-Organization of
Hierarchical Structure on Cellular Robotic System".
Proc . of IEEE International Conference on Robotics and
Automation, 3224/3229, (1994)
17] J. H. Holland, "Adaptation in Natural and Ani tidal
Systems", University of Michigan Press (1975)
[8] D. E. Goldberg, "Genetic Algorithm -in Search,

CONCLUSIONS
In this paper, fi rst, we proposed the self-organizing
manufacturing system. The proposed system organizes the
manufacturing system in itself. Second, we proposed the
genetic algorithm introduced the age structure. As one of the
self-organi:dng manufacturing system, the genetic algorithm
with age structure is applied for a reorganization of a press
machining line . Through the simulation the effectiveness of
the proposed system is demonstrated. Further subjects are as
follows:

Optimization, and Machine Learning-", Addison
Wesley Publishing Company, Inc. (1989)
[9] G. Syswerda, "A Study of Reprodu ction in
Generational and Steady-State Genetic Algorithms ",
Foundation of Genetic Algorithms, Morgan Kaufmarnn,
94/101 (1991)
[10] K. Juliff, "A multi-chromosome Genetic
Algorithm for Pallet Loading", Proc . of the Fifth
International Conference on Genetic Algorithms,
467/473 (1993)
[II] A. Homaifar, S. Guan, G. E. Liepins, "A New
Approach on the Traveling Salesman Problem by
Genetic Algorithms", Proc. of the Fifth International
Conference on Genetic Algorithm s, 460/466 (1993)
[12] K. Shimojima, T. Fukuda, F . Arai, Y. Hasegawa,
"Unsupervised/Supervised Learning for RBF-Fuzzy
Inference -Adaptive Rules ;n! Membership Function and
Hierarchical Structure by Genetic Algorithm-", Proc . of
the IEEE World Wisemen/women Workshop, 97/104
(1994)
[13] N. Baba, N. Kubota, "Collision Avoidance
Planning of a Robot Manipulator by Using Genetic
Algorithm -A Consideration for the Problem in Which
Moving Obstacles and/or Several Robots Are Included
in the Workspace-", Proc. of The First IEEE Conference
on Evolutionary Computation , 714nJ9 (1994)
[14] J. F. Crow, "Basic Concepts in Population,
Quantitative, ;n! Evolutionary Genetics", W. H.
Freeman m Company, New York (1986)
[15] A. A. Berryman, "Population systems , A General
Introduction", Plenum Press, New York (IY81)

• As we only dealt with a specialized case that
sequences for work is given and the purpose of
the optimization is to determine the
reorganization to shonen makespan of the press
machining line, it is required for the proposed
system to extend the job shop scheduling
problem in order to apply for actual systems .
• In Older to show the effectiveness of the
proposed system, we reed to deal with several
types of self-organization of other processes
according to the interaction between process.
• In order to adjust the proposed system to
breakdown of the system <n1 delays of schedule,
we reed to extend the proposed system to the
autonomous distributed system.

ACKNOWLEDGEMENTS
The authors would like to thank Dr. Y. Kawauchi for
many useful comments and suggestions .

REFERENCE
[I I P . Pu, J.Hughes, "Integrating AGV Schedules in a
Scheduling System for a Flexible Manufacturing
Environment", Proc . of IEEE International Conference
on Robotics ;nt Automation, 3149/3154 (1994)
[2] R.Macchiaroli, S.Riemma, "Clustering Methods for
Production Planning ;nt Scheduling in a Flexible
Manufacturing System", Proc. of IEEE International
Conference on Robotics and Automation, 315513I60
(1994)

476

Table I Parameters of each work
Work!

i=='-Job type
Machining per job

I

Work2

10
5

Number_E~llet

8

8

5

5

--- -

Job 4
Job 5
Job 6 _

r ·

Job 7
Job 8

~j

Job 10 ]

5
4
1
1
1

5

--15
7

130

1 4 5 4
·· 5 4 5 2
4 1 4 5
4

15

135

2 5 I 3 2

Job 1

10
10

Makes pan

~~~ce o_ ~ch~in_g
f

Job 2
Job 3

Work6

10
10

7

Is

Table 2 Job sequence of work I

WorkS

c-- -

8

Mold type

Work4
..
10
7
12

Work3

~.-.2?
_
i
5
5

2
-3
2
3 5 2 3
2 I 4 3
2 4 I 4
5 I 2 5
5 I 5 4
4 5 2 I

125
120
115
110~------------------------~

100

50

Generation
Fig .7 A simulation result of Work!

Table 3 Machining time of each mold

Table 5 Simulation resu lts of Work l - Work 6

ASGA E

SGA

~-

GA E

128

126

I

123
116

Work I

Mean

120

116.7

I

=o

Min

115

114

I

322

1

322

.I

Population size
Chromosome le ngth
Selection strateg~
Crossover rate
Mutation ra1e
Lethal age

Work 3

ASGA E

Roulette

-- -r---

I

3
Pallet
Elite

Work 4
I

Elite
Work 5

0.7
0.001

....
I

322.9

318.6

i

317.9

3 19

315

I

315

487

480

I

480

472.8

470.5

466

466

466

Max
Mean
Min

295
281.2
271

274
266.2
261

273
264.2
257

276
270

264

262

258.6

258 .2

256

254

254

352
338.6

332

331

Mean

il

Min

-·

100

Number of chromosome

~~~

114

Max

Table 4 Parameters of GA on numerical simu lation

GA_E

-· -· ·-r

328

Max

=
I

-I

Min

Work 2

SGA

Max

5
Work 6

Mean
Min
Max
Mean Min
I

- - ---

477

326

325.4
--~

319

i

470

i-~~~~4

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