Jaya with Experienced Learning

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 494
Jaya with Experienced Learning
Prasenjit Baruah1
UG-Student,Dept.ofProduction Engineering,N.I.T Tiruchirapalli,Tiruchirapalli,India
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Abstract -Jaya Algorithm has emerged as a simple but the
most effective approach in the field of engineering
optimization and beyond. Unlike the conventional heuristic
algorithms like PSO, GA, etc, it doesn't require any algorithm
specific parameters. A modified version of the Jaya
Algorithm has been proposed in this paper that can be used
for solving constrained and unconstrained problems. Jaya
tried to learn only from the 'best and the 'worst' of the
candidate solutions. Such combination is expected to have
biasness and may result local optimal. In order to avoid this,
it is proposed in the modified Jaya to seek additional
guidance from one each from the top and the bottom most
10% candidate solutions when endeavoring to look for
improvement in subsequent iterations. The performance of
the proposed algorithm is observed by implementing it on 5
test functions having different characteristics and the
results obtained show much better results as compared to
that from existing Jaya Algorithm.
Key Words: Optimisation, Jaya, Evolutionary Approaches,
Endeavouring, Iterations.
1. INTRODUCTION
Optimization is basically seeking for the best or most
effective use of a resource. In the field of Engineering,
various optimization techniques have been employed to
solve real life problems like cost reduction, scheduling, etc.
The population based heuristic algorithms have two
approaches: Evolutionary and Swarm Intelligence. As this
paper deals with the modification of recently evolved
random search algorithm 'Jaya', the concepts involved in
the predecessors like TLBO, PSO, GA, etc have contributed
greatly to understand the origin of the same.
PSO:- This Algorithm is based on the behavior of a flock of
birds searching for food in a particular search space. These
particles(i.e. candidates solutions) are moved around in
the search space as per some formula. They are guided by
their respective best solution in the search space(i.e. pbest)
as well as the entire swarm's best known position(i.e.
gbest). Thus it takes both its own solution and the leader's
solution(i.e. most experienced) into account while
searching for the optimal solution.
TLBO:- With the advent of TLBO, a parameter less
optimization approach which gained great acceptance
among the researchers, people started analyzing natural
phenomenon to improve the random search and
optimization techniques. TLBO replicates the events
taking place inside a classroom. It consists of 2 phases -
The Teacher Phase and The Learner's Phase. What
happens in a classroom is the students(i.e. learners) gain
knowledge in two ways! Either from what he has been
taught by the teacher or by the mutual interaction with his
fellow mates. Now the Teacher, being the most learned is
considered as the 'best' solution. However, the learning
capacity of every individual may be different. After gaining
knowledge from the 'best', the students get themselves
involve in group discussions where they interact with
others and try to improve their knowledge.
JAYA:- It is a new random search optimization algorithm
which is similar to TLBO in terms of consideration of
parameters. But unlike TLBO, it has only one phase in
which the solutions are moved towards the best by
avoiding the worst. The success of this algorithm is due to
the fact that it takes the worst solution into account while
trying to improve each solution. Owning to its victorious
nature, it has been named 'Jaya' which is a Sanskrit word
meaning victory.
JAYA WITH EXPERIENCED LEARNING:- The proposed
algorithm differs from the Jaya Algorithm in terms of the
fact that it takes the neighbors of the Best and the Worst
into consideration to make the search process more
flexible and ultimately reach the optimum result. The
immediate candidates to both the best and the worst act as
an effective medium to transfer experience from the
extremities(i.e. Best and Worst) to the rest. Unlike Jaya
where the flow of information is discrete, here the very
thing has been liquefied to ensure flow of more detailed
information.

1.1 Model
Let's take the situation of occurrence of a natural calamity
like Earthquake. The population near the epicenter would
be the worst affected whereas the population far away
from it would be safe and least affected(i.e. Best). However,
the population in between these extremities will try to rush
to an immediate safer place in reaction to the trembling .So,
the concept of information flow must be continuous and
versatile. It is beneficial to take guidance from both the
individuals which are close to the Best and the Worst in
addition to the two(i.e. Best & Worst).
Blue Dots--No. of Candidates(say 20).
The encircled region shown in figure corresponds to Top
10% near Best and Bottom 10% near Worst.10% of 20 is
2,there are 2 candidates each in addition to the Best and
the Worst.
Now the remaining candidates between the two
extremities will try to rush out to an immediate better
place by taking guidance from anyone who are in the
encircled region following the equations-
(#)x' = x + rand(xtop - |x|) - rand(xbottom -
|x|).......towards top 10% and away from the bottom 10%
After taking guidance from the candidates within the
marked regions , we seek guidance from the Best and the
Worst as these are regarded as the most experienced to get
finer results.
2. PROPOSED ALGORITHM
Let f(x) is the objective function to be minimized(or
maximized). At any iteration i, assume that there are n
number of candidates (population size, i.e. (i.e. k=1,2,3,...,n)
) and m number of design variables (i.e. j=1,2,3,...,m). Let
the best candidate obtains the best value of objective
function(f(x)best) and the worst candidate obtains the
worst value of objective function(f(x)worst) in the entire
candidate solution. Rank each candidate according to the
objective function value. Obtain 10% of the population size
and extract the values near the Best and the Worst
solutions respectively. Select two random solutions each
among the Top 10% and the Bottom 10% and modify each
solution as per the following the equation:
x' = x + rand(xtop - |x|) - rand(xbottom - |x|).......towards top
10% and away from the bottom 10%.
where, xtop = randomly chosen number from top 10%,
xbottom = randomly chosen number from bottom 10%. x' is
the new value of x and rand is a random number in the
range[0 1]. The term "rand(xtop - |x|)" sets the direction of
the candidates' solutions towards the neighborhood of the
Best. Whereas the term "- rand(xbottom- |x|)" sets the
direction of the candidates' solutions away from the
neighborhood of the Worst.
Ultimately, the candidates would seek guidance from the
most experienced candidates that are the Best and the
Worst. Therefore, the candidate solutions in the previous
step are modified according to the Jaya equation which
allows already oriented solutions to refine and gain the
desired the result. The Jaya equation goes as follows :
x' = x + rand(xbest - |x|) - rand(xworst - |x|)
Fig.1 shows the flowchart of the proposed algorithm. The
algorithm always tries to get closer to success (i.e. reaching
the best solution) and tries to avoid failure (i.e. moving
away from the worst solution) gaining knowledge from the
neighborhood. The algorithm strives to become successful
by reaching the best solution in less number of iterations as
compared to its parent algorithm(i.e. Jaya Algorithm) and
hence it is modified. The proposed method is illustrated by
means of an unconstrained benchmark function known as
Sphere function in the next section.

unconstrained benchmark function of Sphere is
considered. The objective function is to find out the values
of xi that minimize the value of the Sphere function.
min f(x)=∑xi2
subject to:
-100<x
i
<100
Since the objective function is to be minimized, thus the
minimum value of the given benchmark function is 0 for all
xi values of 0.Now to demonstrate the modified Jaya
algorithm, let us assume a population size of 20 (i.e.
candidate solutions), two design variables x and y and two
iterations as the termination criterion. The initial
population is randomly generated within the ranges of the
variables and the corresponding values of the objective
function are shown in Table 1. As it is a minimization
function, the lowest value of f(x) is considered as the best
solution and the highest value of f(x) is considered as the
worst solution.
Table -1: Initial Population
corresponding to Candidate 12 and the Worst solution is
corresponding to Candidate 15. As we know 10% of 20
candidates in 2 thus we obtain two solutions each near the
Best and near the Worst. Then we choose any random
number from each two solutions to get rough direction.
Rank 3- Candidate 16
Rank 18- Candidate 13
Now each value of x1 and x2 are modified so as to move
towards the Top 10%(neighborhood of Best) and away
from the Bottom 10%(neighborhood of Worst) according
to the equation
x' = x + rand*(x(top) - |x|) -rand*(x(bottom)-|x|)
Table 2:- Intermediate Values of x & y
Candidate X1 X2 f(x)
1) -1.13032 -11.0012 122.304
2) 1.6754 3.2095 13.107
3) -10.6589 -1.7176 116.562
4) -5.0974 1.098 27.189
5) 4.5655 -5.8762 55.373
6) 5.0714 -6.7306 71.020
7) -0.41 0.4715 0.390
8) -5.1839 4.5263 47.360
9) 2.6381 -9.8639 104.256
10) 5.1398 -10.5914 138.595
11) -2.7599 -14.6612 222.567
12) 1.2258 -1.5318 3.848
13) 7.5609 0.4371 57.358
14) -5.0043 -9.9355 123.757
15) -11.0092 -16.3155 387.195
16) 3.1478 -4.9816 34.724
17) 3.3089 -5.7573 44.095
18) -0.4448 -4.7152 22.430
19) -8.6951 -5.2508 103.175
20) 5.4819 -2.5033 36.317
Candidate X1 X2 f(x) Rank
1) -2 -8 68 13
2) 4 5 41 7
3) -9 0 81 17
4) -2 6 40 6
5) 8 -3 73 14
6) 6 -3 45 9
7) 0 7 49 11
8) -4 5 41 7
9) 5 -7 74 15
10) 8 -6 100 19
11) 1 -8 65 12
12) -1 -1 2 1
13) 8 5 89 18
14) -4 -8 80 16
15) -8 -9 145 20
16) 4 -1 17 3
17) 6 -3 45 9
18) 2 -1 5 2
19) -6 0 36 4
20) 6 1 37 5
From Table 1, it can be seen that the Best solution is

Table 3:- New values of the variables and the objective
function during first iteration by applying Jaya equation
Table 4:- Updated values of the variables and the objective
function based on fitness comparison at the end of first
iteration
Table 4 has been updated based on the fitness of the
Objective function by comparing the values among Table
1,2 &3. Thus, the Updated table has values from all the 3
tables depending on the goal(i.e. minimization or
maximization). It validates the fact that the candidates are
acquiring information from the neighborhood of the Best
and the worst too. In this way, it approaches the optimum
result by executing the required number of iterations.
2.2Approach
The working of the proposed algorithm has been found out
by comparing the results of the following four cases:
(1) Jaya Algorithm
(2) Jaya Algorithm + Top 10%(near the BestSol)
(3) Jaya Algorithm + Bottom 10%(near the WorstSol)
(4) Jaya Algorithm + Top 10% + Bottom 10%.
All the above mentioned algorithms have been coded in
Matlab and the outcomes are compared on the basis of
convergence rate and better results. For this purpose the
objective function is taken as the Sphere function and the
other parameters like range of design variables, max
iterations, etc are kept constant.
No. of Candidates: 20
Design Variables: 2
Max Iterations: 100
Lower Bound: -100
Upper Bound: 100
It is observed that the results of the first two cases are
almost similar(Fig(1) & Fig(2)). However, when a random
candidate solution from the neighborhood of the Worst is
Candidate X1 X2 f(x)
1) -3.1368 -5.7610 43.028
2) 8.6872 12.1429 222.917
3) -13.7594 3.3264 200.386
4) -1.9240 19.9074 400.006
5) 4.4683 -0.6958 20.449
6) 6.2774 -1.3923 41.344
7) 1.8268 14.2776 207.187
8) 0.3468 12.3851 153.510
9) 11.4634 -10.1755 234.950
10) 13.9739 -4.2168 213.051
11) -0.7326 -6.6909 45.304
12) 3.8758 2.8432 23.105
13) 8.1448 13.4868 248.231
14) -6.5320 0.3247 42.772
15) -9.0659 -2.7507 89.756
16) 13.8833 6.4337 234.138
17) 8.9978 5.5559 111.828
18) 0.4113 1.7064 3.080
19) 2.4192 4.8777 29.644
20) 9.4932 4.0549 106.563
Candidate X1 X2 f(x) Rank
1) -3.1368 -5.7610 43.028 13
2) 1.6754 3.2095 13.107 4
3) -9 0 81 18
4) -5.0974 1.098 27.189 7
5) 4.4683 -0.6958 20.449 6
6) 6.2774 -1.3923 41.344 11
7) -0.41 0.4715 0.390 1
8) -4 5 41 10
9) 5 -7 74 17
10) 8 -6 100 20
11) -0.7326 -6.6909 45.304 15
12) -1 -1 2 2
13) 7.5609 0.4371 57.358 16
14) -6.5320 0.3247 42.772 12
15) -9.0659 -2.7507 89.756 19
16) 4 -1 17 5
17) 3.3089 -5.7573 44.095 14
18) 0.4113 1.7064 3.080 3
19) 2.4192 4.8777 29.644 8
20) 5.4819 -2.5033 36.317 9

considered along with the normal Jaya, the results
converge towards the optimum in lesser iterations(Fig(3)
illustrates the Best Objective function value at 100th
iteration).Now in the 4th case, we combine both Top 10%
and the Bottom 10% along with normal Jaya
Algorithm(Refer Fig(4)). Even though the results of the 3rd
and 4th cases are almost comparable, it is always better to
seek information from both the side(i.e. the top & the
bottom).
Thus, the 4th case is retained for further study. The very
Algorithm is implemented on various unconstrained test
functions like Sphere, Matyas, Booth, etc and constrained
Himmelblau function.
Fig(1)- Jaya Algorithm :- Iteration 100: Best Obj = 1.7865e-
09
Fig(2)-Jaya Algorithm + Top 10%:- Iteration 100: Best Obj
= 8.1968e-11
Fig(3)-Jaya Algorithm + Bottom 10%:- Iteration 100: Best
Obj = 7.6219e-248
Fig(4)-Jaya Algorithm + Top 10% + Bottom 10%:-
Iteration 100: Best Obj = 6.0578e-249
3. CONCLUSIONS
This paper highlights the flexibility in information flow by
disregarding the biased culture(i.e. considering only the
best & the worst) which is being followed in the Jaya
Algorithm. However, by including random solutions from
the surrounding of the Best and the Worst, the number of
solutions generated in each iteration gets increased. But
there is a significant difference in the results obtained by
the modified Jaya(Refer Fig(5)). While the Jaya Algorithm
converges to around 10-10, the modified one converges to
around 10-249 for 100 iterations.
The proposed algorithm is implemented on 5 constrained
and 1 unconstrained functions . The results obtained by

the proposed algorithm are compared with the Jaya
Algorithm and it has shown satisfactory results for the
proposed algorithm.
Fig(5)- Jaya V/S Proposed algorithm.
The following table shows the results obtained by
implementing Jaya Algorithm on the below mentioned 5
test functions taking 100 iterations for every case.
ACKNOWLEDGEMENT
I would like to extend my heartfelt gratitude to Professor
Anil Kumar Agrawal, Mechanical Engineering Department,
Indian Institute of Technology (IIT-BHU) who expertly
guided me through my research work as a part of Summer
Internship, 2017.His generous behavior and constant
guidance helped me to enjoy learning during the work.
My humble appreciation also goes to my friends who stand
by me and support me in every small step I take towards
trying something new.
At last but not the least, I would love to mention my family
who unconditionally support me and let me build my
dreams come true.
REFERENCES
[1] Rao, R., 2015. Jaya: A simple and new optimization
algorithm for solving constrained and unconstrained
optimization problems. International Journal of Industrial
Engineering Computations, 7(1), pp.19-34.
[2] Rao, R.V., Savsani, V.J. and Vakharia, D.P., 2012.
Teaching–learning-based optimization: an optimization
method for continuous non-linear large scale problems.
Information Sciences, 183(1), pp.1-15.
[3] Rao, R.V., Savsani, V.J. and Vakharia, D.P., 2011.
Teaching–learning-based optimization: a novel method for
constrained mechanical design optimization problems.
Computer-Aided Design, 43(3), pp.303-315.
[4] Atul B. Patil M.Tech Student Department of Computer
Science and Engineering,2016,Bus driver scheduling
problem using Jaya Algorithm and Teaching Learning
Based Optimisation(TLBO) Techniques.
JAYA PROPOSED
Func X1 X2 Optim
um
X1 X2 Opti
mum
Sphere 9.53
06e-
06
-
1.58
73e-
05
3.427
8e-10
5.90
09e-
124
-
9.71
16e-
125
3.576
4e-
247
Booth 1.02
41
2.98
52
0.001
1
1.00
06
2.99
96
5.996
3e-07
Matyas -
0.00
36
-
0.00
32
4.972
6e-07
-
2.82
78e-
62
-
3.27
82e-
62
4.235
5e-
125
Three
hump
camel
functio
n
3.86
74e-
05
1.38
54e-
04
2.754
3e-08
4.25
28e-
125
-
4.27
85e-
124
1.684
7e-
247
Himmel
blau
3.59
35
-
1.86
81
0.008
9645
3.00
00
2.00
00
8.646
3e-08

Jaya with Experienced Learning

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