International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014

Memetic Search in Differential Evolution Algorithm
Sandeep Kumar

Vivek Kumar Sharma, Ph.D

Rajani Kumari

Jagannath University
Chaksu, Jaipur, Rajasthan,
India - 303901

Jagannath University
Chaksu, Jaipur, Rajasthan,
India - 303901

Jagannath University
Chaksu, Jaipur, Rajasthan,
India - 303901

ABSTRACT
Differential Evolution (DE) is a renowned optimization
stratagem that can easily solve nonlinear and comprehensive
problems. DE is a well known and uncomplicated population
based probabilistic approach for comprehensive optimization.
It has apparently outperformed a number of Evolutionary
Algorithms and further search heuristics in the vein of Particle
Swarm Optimization at what time of testing over both
yardstick and actual world problems. Nevertheless, DE, like
other probabilistic optimization algorithms, from time to time
exhibits precipitate convergence and stagnates at suboptimal
position. In order to stay away from stagnation behavior while
maintaining an excellent convergence speed, an innovative
search strategy is introduced, named memetic search in DE. In
the planned strategy, positions update equation customized as
per a memetic search stratagem. In this strategy a better
solution participates more times in the position modernize
procedure. The position update equation is inspired from the
memetic search in artificial bee colony algorithm. The
proposed strategy is named as Memetic Search in Differential
Evolution (MSDE). To prove efficiency and efficacy of
MSDE, it is tested over 8 benchmark optimization problems
and three real world optimization problems. A comparative
analysis has also been carried out among proposed MSDE and
original DE. Results show that the anticipated algorithm go
one better than the basic DE and its recent deviations in a
good number of the experiments.

General Terms
Computer Science, Nature Inspired Algorithms, Metaheuristics

Keywords
Differential Evolution, Swarm intelligence, Evolutionary
computation, Memetic algorithm

1. INTRODUCTION
Population-based optimization algorithms find near-optimal
solutions to the easier said than done optimization problems
by inspiration from nature or natural entities. A widespread
characteristic of each and every one population-based
algorithm is that the population consisting of potential
solutions to the problem is tailored by applying some
operators on the solutions depending on the information of
their fitness. Hence, the population is moved towards better
solution areas of the search space. Two essential classes of
population-based optimization algorithms are evolutionary
algorithms [1] and swarm intelligence-based algorithms [2].
Although Genetic Algorithm (GA) [3], Genetic Programming
(GP) [4], Evolution Strategy (ES) [5] and Evolutionary
Programming (EP) [6] are popular evolutionary algorithms,
DE comes underneath the class of Evolutionary algorithms.
Among an assortment of EAs, differential evolution (DE),
which characterized by the diverse mutation operator and
antagonism strategy from the other EAs, has shown immense

promise in many numerical benchmark problems as well as
real-world optimization problems. Differential evolution (DE)
is a stochastic, population-based search strategy anticipated by
Storn and Price [9] in 1995. While DE shares similarities with
other evolutionary algorithms (EA), it differs considerably in
the sense that distance and direction information from the
current population is used to steer the search progression. In
DE algorithm, all solutions have an equal opportunity of being
preferred as parents, i.e. selection does not depend on their
fitness values. In DE, each new solution fashioned competes
with its parent and the superior one wins the contest. DE
intensification and diversification capabilities depend on the
two processes, that is to say mutation process and crossover
process. In these two processes, intensification and
diversification are evenhanded using the fine tuning of two
parameters that is to say scale factor ‘F’ and crossover
probability ‘CR’. In DE the child vector is generated by
applying the mutation and crossover operation. In mutation
operation, a trial vector is generated with the help of the
objective vector and two erratically preferred individuals. The
perturbation in objective vector depends on F and the
difference between the randomly selected individuals. Further,
a crossover operation is applied between the objective vector
and parent vector for generating the child vector using
crossover probability (CR). So, it is clear that the discrepancy
in the child vector from the parent vector depends on the
values of F and CR. This discrepancy is measured as a step
size for the candidate solution/parent vector. Large step size
may results in skipping of actual solutions that is due to large
value of CR and F while if these values are low then the step
size will be small and performance degrades.
The hybridization of some local search techniques in DE may
diminish the possibility of skipping factual solution. In
hybridized search algorithms, the global search capability of
the main algorithm explore the search space, trying to identify
the most promising search space regions while the local
search part scrutinizes the surroundings of some initial
solution, exploiting it in this way. Therefore, steps sizes play
an important role in exploiting the identified region and these
step sizes can be controlled by incorporating a local search
algorithm with the global search algorithm.
Differential evolution (DE) has come into sight as one of the
high-speed, robust, and well-organized global search
heuristics of in progress significance. Over and over again real
world provides some very complex optimization problems
that cannot be easily dealt with existing classical
mathematical optimization methods. If the user is not very
susceptible about the exact solution of the problem in hand
then nature-inspired algorithms may be used to solve these
kinds of problems. It is shown in this paper that the natureinspired algorithms have been gaining to a great extent of
recognition now a day due to the fact that numerous realworld optimization problems have turn out to be progressively
more large, multifarious and self-motivated. The size and

40

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014
complication of the problems at the present time necessitate
the development of methods and solutions whose efficiency is
considered by their ability to find up to standard results within
a levelheaded amount of time, rather than an aptitude to
guarantee the optimal solution. The paper also includes a
concise appraisal of well-organized and newly developed
nature-inspired algorithm, that is to say Differential
Evolution. In addition, to get better effectiveness, correctness
and trustworthiness, the considered algorithm is analyzed,
research gaps are identified. DE has apparently outperformed
a number of Evolutionary Algorithms (EAs) and other search
heuristics in the vein of the Particle Swarm Optimization
(PSO) at what time tested over together benchmark and real
world problems. The scale factor (F) and crossover
probability (CR) are the two major parameters which controls
the performance of DE in its mutation and crossover
processes by maintain the balance between intensification and
diversification in search space. Literature suggests that due to
large step sizes, DE is somewhat less capable of exploiting the
on hand solutions than the exploration of search space.
Therefore unlike the deterministic methods, DE has intrinsic
negative aspect of skipping the accurate optima. This paper
incorporates the memetic search strategy inspired by golden
section search [42] which exploits the best solution after each
and every iteration in order to generate its neighborhood
solutions. To validate the proposed MSDE’s performance,
experiments are carried out on 11 benchmark as well as real
life problems of different complexities and results reflect the
superiority of the proposed strategy than the basic DE.
Rest of the paper is systematized as follows: Sect. 2 describes
brief overview of the basic DE. Memetic algorithms explained
in Sect. 3. Memetic search in DE (MSDE) is proposed and
tested in Sect. 4. In Sect. 5, a comprehensive set of
experimental results are provided. Finally, in Sect. 6, paper is
concluded.

2. DIFFERENTIAL EVOLUTION
ALGORITHM
Differential evolution is a strategy that optimizes a dilemma
by iteratively trying to enhance an individual solution with
regard to a specified gauge of excellence. DE algorithm is
used for multidimensional real-valued functions but it does
not put together the ascent of the problem being optimized,
which means DE does not have need of that the optimization
problem to be differentiable as is mandatory for traditional
optimization methods such as gradient descent and quasiNewton techniques. DE algorithm optimizes a problem by
considering a population of candidate solutions and
generating new contestant solutions by combining existing
ones according to its straightforward formulae, and then
memorizing whichever candidate solution has the superlative
score or fitness on the optimization problem at hand. Thus in
this manner the optimization problem is treated as a black box
that simply makes available a gauge of quality specified a
candidate solution and the gradient is for that reason not
considered necessary. DE has a number of strategies based on
method of selecting the objective vector, number of difference
vectors used and the crossover type [8]. Here in this paper
DE/rand/1/bin scheme is used where DE stands for
differential evolution, ‘rand’ indicates that the target vector is
preferred haphazardly, ‘1’ is for number of differential vectors
and ‘bin’ notation is for binomial crossover. The popularity of
Differential Evolution is due to its applicability to a wider
class of problems and ease of implementation. Differential
Evolution has properties of evolutionary algorithms as well as

swarm intelligence. The detailed description of DE is as
follows:
In the vein of other population based search algorithms, in DE
a population of probable solutions (individuals) searches the
solution. In a D-dimensional search space, an individual is
represented by a D-dimensional vector (xi1 , xi2, . . ., xiD ), i
= 1, 2, . . ., NP where NP is the population size (number of
individuals). In DE, there are three operators: mutation,
crossover and selection. Initially, a population is generated
randomly with uniform distribution then the mutation,
crossover and selection operators are applied to generate a
new population. Trial vector generation is a critical step in DE
progression. The two operators, mutation and crossover are
used to engender the tryout vectors. The selection operator is
used to decide on the best tryout vector for the subsequently
age bracket. DE operators are explained for a split second in
following subsections.

2.1 Mutation
A tryout vector is generated by the DE mutation operator for
each individual of the in progress population. For generating
the tryout vector, an objective vector is mutated with a biased
differential. A progeny is fashioned in the crossover operation
using the recently generated tryout vector. If G is the index for
generation counter, the mutation operator for generating a trial
vector vi(G) from the parent vector xi(G) is defined as follows:




Choose a objective vector xi1(G) from the population
such that i and i1 are poles apart.
All over again, haphazardly pick two individuals, xi2 and
xi3, from the population such that i, i1, i2 and i3 all are
distinct to each other.
After that the objective vector is mutated for calculating
the tryout vector in the following manner:
(1)

Here F ∈ [0, 1] is the mutation scale factor which is used in
controlling the strengthening of the differential variation [7].

2.2 Crossover
Offspring x’i(G) is generated using the crossover of parent
vector xi(G) and the tryout vector ui(G) as follows:
∈

(2)

Here J is the set of cross over points or the points that will go
under perturbation, xij(G) is the jth element of the vector xi(G).
Diverse methods possibly will be used to settle on the set J in
which binomial crossover and exponential crossover are the
most commonly used [7]. Here this paper used the binomial
crossover. In this crossover, the crossover points are
arbitrarily preferred from the set of potential crossover points,
{1, 2, . . ., D}, where D is the dimension of problem.

2.3 Selection
There are a couple of functions for the selection operator:
First it selects the individual for the mutation operation to
generate the trial vector and second, it selects the most
excellent, between the parent and the offspring based on their
fitness value for the next generation. If fitness of parent is
superior than the offspring then parent is selected otherwise
offspring is selected:
(3)

41

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014
The above equation makes sure that the population’s average
fitness does not get worse. The Pseudo-code for Differential
Evolutionary strategy is described in Algorithm 1 [7].
Algorithm 1 Differential Evolution Algorithm
Initialize the control parameters, F and CR (F (scale
factor) and CR (crossover probability)).
Generate and initialize the population, P(0), of NP
individuals (P is the population vector)
while stopping criteria not meet do
for each individual, xi(G) ∈ P(G) do
Estimate the fitness, f(xi(G));
Generate the trial vector, vi(G) by using the
mutation operator;
Generate an offspring, x′i(G), by using the crossover
operator;
if f(x′i(G) is better than f(xi(G)) then
Add x′i(G) to P(G + 1);
else
Add xi(G) to P(G + 1);
end if
end for
end while
Memorize the individual with the best fitness as the
solution

3. MEMETIC ALGORITHMS
Memetic algorithms (MA) characterize one of the most up to
date mounting fields to do research in evolutionary
computation. The name MA is now a day commonly used as
coactions of evolutionary or several population-based
algorithms with separate individual learning or local
development events for problem search. Sometimes MA is
moreover specified in the text as Baldwinian evolutionary
algorithms (EA), Lamarckian EAs, genetic local search
strategy or cultural algorithms. The theory of “Universal
Darwinism” was given by Richard Dawkins in 1983[12] to
make available a amalgamate structure governing the
evolution of any intricate system. In particular, “Universal
Darwinism” put forward that development is not restricted to
biological systems; i.e., it is not limited to the tapered
circumstance of the genes, but it is applicable to almost all
multifarious system that show evidence of the principles of
inheritance, disparity and assortment, thus satisfying the
individuality of an evolving system. For instance, the new
science of memetics symbolizes the mind-universe
corresponds to genetics in way of life progression that
stretches transversely the fields of biology, psychology and
cognition, which has fascinated significant concentration in
the last two decades. The term “meme” was also introduced
and defined by Dawkins in 1976[13] as “the basic unit of
cultural transmission, or imitation”, and in the English
Dictionary of Oxford as “an element of culture that may be
considered to be passed on by non-genetic means”.
Inspired by both Darwinian philosophy of ordinary evolution
and Dawkins’ conception of a meme, the term “Memetic
Algorithm” (MA) was first given by Moscato in his technical
report [14] in 1989 where he observed MA as being very
analogous to a outward appearance of population-based
hybrid genetic algorithm (GA) together with an individual
learning modus operandi talented to perform local
refinements. The allegorical analogous, one side occupied by
Darwinian evolution and, other side, between memes and

domain specific (local search) heuristics are incarcerate within
memetic algorithms as a consequence rendering a
methodology that balances well between generality and
problem specificity. In a more assorted context, memetic
algorithms are now used under a variety of names together
with Baldwinian Evolutionary Algorithms, Cultural
Algorithms, Genetic Local Search, Hybrid Evolutionary
Algorithms and Lamarckian Evolutionary Algorithms. In the
circumstance of intricate optimization, many different
instantiations of memetic algorithms have been reported
athwart an extensive range of application domains, in general,
converging to premium solutions more efficiently than their
unadventurous evolutionary matching part. In broadspectrum, using the thoughts of memetics surrounded by a
computational structure is called "Memetic Computing or
Memetic Computation" (MC) [15]16] With MC, the
individuality of Universal Darwinism are more appropriately
captured. In all viewpoints, MA is a more constrained
impression of MC. Exclusively; MA covers vicinity of MC, in
meticulous dealing with areas of evolutionary algorithms that
get hitched other deterministic enhancement techniques for
solving optimization problems. MC lengthens the impression
of memes to cover up conceptual entities of knowledgeenhanced measures or representations.
Memetic algorithms are the area under discussion of intense
scientific research and have been fruitfully applied to a
massive amount of real-world problems. Even though many
people make use of techniques intimately associated to
memetic algorithms, unconventional names such as hybrid
genetic algorithms are also in employment. Moreover, many
people name their memetic techniques as genetic algorithms.
The prevalent use of this misnomer hampers the measurement
of the total amount of applications. MAs are a course group of
stochastic global search heuristics in which Evolutionary
Algorithms-based approaches are pooled with problemspecific solvers. After that might be implemented as local
search heuristics techniques, approximation algorithms or,
sometimes, even precise methods. The hybridization is
preordained to either speed up the discovery of good
solutions, for which evolution alone would take too long to
discover, or to attain solutions that would otherwise be out-ofthe-way by evolution or a local method alone. As the great
preponderance of Memetic Algorithms use heuristic local
searches rather than precise methods. It is tacit that the
evolutionary search provides for an extensive exploration of
the search space while the local search by some means zoomin on the sink of magnetism of talented solutions Researchers
have used memetic algorithms to embark upon many
conventional NP problems. To mention some of them: bin
packing problem, generalized assignment problem, graph
partitioning, max independent set problem, minimal graph
coloring, multidimensional knapsack, quadratic assignment
problem, set cover problem and travelling salesman problem.
MAs have been demonstrated very triumphant transversely an
extensive range of problem domains. More topical
applications take account of (but are not limited to) artificial
neural network training,[17] pattern recognition,[18] motion
planning in robotic,[19] beam orientation,[20] circuit
design,[21] electric service restoration,[22] expert systems for
medical field,[23] scheduling on single machine,[24]
automatic timetabling,[25] manpower scheduling,[26] nurse
rostering and function optimization [27] allocation of
processor,[28] maintenance scheduling (for instance, of an
electric distribution network),[29] multidimensional knapsack
problem by E ozcan et al.[30] VLSI design,[31] clustering of
gene expression profiles,[32] feature/gene selection or

42

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014
extraction,[33][34] and multi-class, multi-objective feature
selection.[35][36]. M Marinaki et al. [37] proposed an island
memetic differential evolution algorithm, for solving the
feature subset selection problem while the nearest neighbor
categorization method is used for the classification task. CG
Uzcátegui et al. [38] developed a memetic differential
evolution algorithm to solve the inverse kinematics problem
of robot manipulators. S Goudos [39] designed a memetic
differential evolution algorithm to design multi-objective
approach to sub arrayed linear antenna arrays. Memetic
algorithm also hybridized with artificial bee colony algorithm
like JC Bansal et al. [40] anticipated a memetic search in
artificial bee colony algorithm. S Kumar et al. [41] developed
a randomized memetic artificial bee colony algorithm and
applied those algorithms to solve various problems.

4. MEMETIC SEARCH IN
DIFFERENTIAL EVOLUTION (MSDE)
ALGORITHM
Exploration of the entire search space and exploitation of the
most favorable solution region in close proximity may be
unprejudiced by maintaining the diversity in the early hours
and later on iterations of any random number based search
algorithm. It is unambiguous from the Eqs. (1) and (2) that
exploration of the search space in DE algorithm controlled by
two parameters (CR and F). In case of DE algorithm,
exploration and exploitation of the search space depend on the
value of CR and F that is to say if value of CR and F are high
then exploration will be high and exploitation will be high if
value of CR and F are low. This paper introduced a new
search strategy in order to balance the process of exploration
and exploitation of the search space. The new search strategy
is inspired from the memetic search in Artificial Bee Colony
(MeABC) algorithm [40]. The MeABC algorithm developed
by J. C. Bansal et al [40] aggravated by Golden Section
Search (GSS) [42]. In MeABC only the best individual of the
in progress population updates themselves in its concurrence.
GSS processes the interval [a = −1.2, b = 1.2] and initiates
two intermediate points (f1, f2) with help of golden ratio (Ѱ =
0.618). The GSS process summarized in algorithm 2 as
follow:
Algorithm 2: Golden Section Search
Repeat while termination criteria meet
Compute f1  b  (b  a)  , and f 2  a  (b  a)  ,

 f1  and f  f2 
f  f1  < f  f 2  then

Calculate f
If

b = f2 and the solution lies in the range [a, b]
else
a = f1 and the solution lies in the range [a, b]
End of if
End of while

detailed Memetic search in DE (MSDE) outlined in algorithm
3 as follow:
Algorithm 3 Memetic Search in Differential
Evolution (MSDE) Algorithm
Initialize the control parameters, F and CR (F (scale
factor) and CR (crossover probability)).
Generate and initialize the population, P(0), of NP
individuals (P is the population vector)
while stopping criteria not meet do
for each individual, xi(G) ∈ P(G) do
Estimate the fitness, f(xi(G));
Generate the trial vector, vi(G) by using the
mutation operator and incorporate algorithm 2
as per the following equation;

Generate an offspring, x′i(G), by using the
crossover operator;
if f(x′i(G) is better than f(xi(G)) then
Add x′i(G) to P(G + 1);
else
Add xi(G) to P(G + 1);
end if
end for
end while
Memorize the individual with the best fitness as the
solution

5. EXPERIMENTAL RESULTS
5.1 Test problems under consideration
Differential Evolution algorithm with improvement in search
phase applied to the eight benchmark functions for whether it
gives better result or not at different probability and also
applied for three real world problems. Benchmark functions
taken in this paper are of different characteristics like unimodel or multi-model and separable or non-separable and of
different dimensions. In order to analyze the performance of
MSDE, it is applied to global optimization problems (f1 to f8)
listed in Table I. Test problems f1 –f8 are taken from [8],[44].
Three real world problems (Pressure Vessel Design, Lennard
Jones and Parameter estimation for frequency modulated
sound wave) are described as follow:
Pressure Vessel Design (f9): The problem of minimizing total
cost of the material, forming and welding of a cylindrical
vessel [43]. In case of pressure vessel design generally four
design variables are considered: shell thickness (x1), spherical
head thickness (x2), radius of cylindrical shell (x3) and shell
length (x4). Simple mathematical representation of this
problem is as follow:

The proposed memetic search strategy modifies the mutation
operator of DE algorithm and modifies the Eqs. (1) as follow:
Subject to
Here fj is decided by algorithm 2.
The proposed changes in original DE algorithm control the
search process adaptively and provide more chances to
explore the large search space and exploit the better solution
in more efficient way. This change in DE tries to balance
intensification and diversification of search space. The

The search boundaries for the variables are
1.125 ≤ x1 ≤12.5, 0.625 ≤ x2 ≤ 12.5,
1.0*10-8 ≤ x3 ≤ 240 and 1.0*10-8 ≤ x4 ≤ 240.

43

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014
The best ever identified global optimum solution is f(1.125,
0.625, 55.8592, 57.7315) = 7197.729 [43]. The tolerable error

for considered problem is 1.0E-05.

Table 1. Test Problems
Test Problem

Objective Function

f1 ( x) 

Step Function



D
i 1

(  xi  0.5)

2

f 2 ( x)  100( x2  x12 )2  (1  x1) 2  90( x4  x32 ) 2  (1  x3 ) 2

Colville
function

10.1[( x2  1)2  ( x4  1)2 ]  19.8( x2  1)( x4  1)

Kowalik
function

f3 ( x) 

f 4 ( x) 

Shifted
Rosenbrock



11
i 1



(ai 

D 1
i 1

x1(bi2  bi x2 )
bi2  bi x3  x4

)2

(100( zi2  zi 1)2  ( zi  1)2  fbias ,

z  x  o  1, x  [ x1, x2 ,...xD ], o  [o1, o2 ,.......oD ]
1 4 2
x1 ) x1  x1x2  (4  4 x22 ) x22
3

Six-hump camel
back

f5 ( x)  (4  2.1x12 

Hosaki Problem

f6 ( x)  (1  8 x1  7 x12 

Meyer and Roth
Problem

f 7 ( x) 

Shubert

f8 ( x)  



5
i 1



(

7 3 1 4 2
x1  x1 ) x2 exp( x2 )
3
4

x1x3ti
 yi )2
1  x1ti  x2vi

5
t 1

i cos((i  1) x1  1)



5
i 1

i cos((i  1) x2  1)

Parameter Estimation for Frequency-Modulated (FM)
sound wave (f11): Frequency-Modulated (FM) sound wave
amalgamation has a significant role in several modern music
systems. The parameter optimization of an FM synthesizer is
an optimization problem with six dimension where the vector
to be optimized is X = {a1, w1, a2, w2, a3, w3} of the sound
wave given in equation (4). The problem is to generate a
sound (1) similar to target (2). This problem is a highly
complex multimodal one having strong epistasis, with
minimum value f(X) = 0. This problem has been tackled using
Artificial bee colony algorithms (ABC) in [43].The
expressions for the estimated sound and the target sound
waves are given as:

Search
Range

Optimum Value

D

Acceptable
Error

[-100, 100]

f(-0.5≤x≤0.5)=0

30

1.0E-05

[-10, 10]

f(1) = 0

4

1.0E-05

[-5, 5]

f(0.1928,
0.1908,
0.1231,
0.1357)
=
3.07E-04

4

[-100, 100]

f(o)=fbias=390

10

1.0E-01

[-5, 5]

f(-0.0898, 0.7126) = 1.0316

2

1.0E-05

-2.3458

2

1.0E-06

[-10, 10]

f(3.13, 15.16,0.78) =
0.4E-04

3

1.0E-03

[-10, 10]

f(7.0835, 4.8580)=
186.7309

2

1.0E-05

x1  [0,5],
x2  [0, 6]

-

1.0E-05

1600000
1400000
1200000
1000000
800000
600000
400000
200000
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

(4)
Fig 1: Effect of CR on AFE
(5)
Respectively where θ = 2π/100 and the parameters are defined
in the range [-6.4, 6.35]. The fitness function is the summation
of square errors between the estimated wave (1) and the target
wave (2) as follows:
100

f11( x) 

( y(t )  y (t ))

2

0

i 0

Acceptable error for this problem is 1.0E-05, i.e. an algorithm
is considered successful if it finds the error less than
acceptable error in a given number of generations.

5.2 Experimental Setup
To prove the efficiency of MSDE, it is compared with original
DE algorithm over well thought-out seventeen problems,
following experimental setting is adopted:

Population Size NP = 50

The Scale factor F= 0.5

Limit = D*NP/2.

Number of Run =100

Sopping criteria is either reached the corresponding
acceptable error or maximum function evaluation
(which is set as 200000).

Crossover probability CR = 0.9, in order to identify
the effect of the parameter CR on the performance

44

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014





of MSDE, its effect at different CR in range [0.1, 1]
is experimented as shown in figure 1. It can be
easily observed from the graph that best value of
CR is 0.9 for considered as problems.
The mean function values (MFV), standard
deviation (SD), mean error (ME), average function
evaluation (AFE) and success rate (SR) of
considered problem have been recorded.
Experimental setting for DE is same as MSDE.

5.3 Result Comparison

relationship of results based on mean function value (MFV),
standard deviation (SD), mean error (ME), average function
evaluations (AFE) and success rate (SR). Table 2 shows that a
good number of the times MSDE outperforms in terms of
efficiency (with less number of function evaluations) and
reliability as compare to other considered algorithms. The
proposed algorithm all the time improves AFE. It is due to
balancing between exploration and exploitation of search
space. Table 3 contains summary of table 2 outcomes. In
Table 3, ‘+’ indicates that the MSDE is better than the well
thought-out algorithms and ‘-’ indicates that the algorithm is
not better or the divergence is very small. The last row of
Table 3, establishes the superiority of MSDE over DE.

Mathematical results of MSDE with experimental setting as
per section 5.2 are discussed in Table 2. Table 2 show the
Table 2. Comparison of the results of test problems
Test Problem

Algorithm\Measure

f1

DE

1.20E-01

4.75E-01

1.20E-01

31942.5

91

MSDE

1.00E-02

9.95E-02

2.00E-02

21319

99

DE

1.47E-01

6.46E-01

1.47E-01

26918

89

MSDE

4.57E-04

5.12E-04

7.50E-04

31196

95

DE

5.72E-04

3.29E-04

2.65E-04

61900

71

MSDE

5.53E-04

3.55E-04

2.51E-04

74294

82

DE

3.92E+02

2.09E+00

2.13E+00

194913.5

3

MSDE

3.91E+02

2.49E+00

8.65E-01

197758

7

DE

-1.03E+00

1.42E-05

1.79E-05

112618

44

MSDE

-1.03E+00

4.58E-06

1.12E-05

57491.5

72

DE

-2.35E+00

5.96E-06

5.26E-06

10858

95

MSDE

-2.35E+00

2.53E-06

5.19E-06

1261

100

DE

1.91E-03

1.64E-05

1.95E-03

3744

99

MSDE

1.90E-03

2.33E-06

1.95E-03

4621

99

DE

-1.87E+02

5.37E-06

4.59E-06

8122

100

MSDE

-1.87E+02

2.53E-06

4.66E-06

7375.5

100

DE

7.20E+03

3.38E-05

2.43E-05

65912.5

71

MSDE

7.20E+03

1.51E-05

7.88E-06

19772

96

DE

-9.10E+00

1.45E-05

8.13E-05

72866

100

MSDE

-9.10E+00

1.65E-05

7.71E-05

69196.5

100

DE

5.83E+00

6.33E+00

5.83E+00

113179

48

MSDE

4.83E+00

6.49E+00

4.84E+00

83060

63

f2

f3

f4

f5

f6

f7

f8

f9

f10

f11

MFV

SD

ME

AFE

SR

45

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014

6. CONCLUSION
This paper, modify the search process in original DE by
introducing customized Golden Section Search process.
Newly introduced line of attack added in mutation process.
Proposed algorithm modifies step size with the help of GSS
process and update target vector. Further, the modified
strategy is applied to solve 8 well-known standard benchmark
functions and three real world problems. With the help of
experiments over test problems and real world problems, it is
shown that the insertion of the proposed strategy in the
original DE algorithm improves the steadfastness, efficiency
and accuracy as compare to its original version. Table 2 and 3
shows that the proposed MSDE is able to solve almost all the
considered problems with fewer efforts. Numerical results
show that the improved algorithm is superior to original DE
algorithm. Proposed algorithm has the ability to get out of a
local minimum and has higher rate of convergence. It can be
resourcefully applied for separable, multivariable, multimodal
function optimization. The proposed strategy also improves
results for three real world problems: Pressure Vessel Design,
Lennard Jones and Parameter estimation for frequency
modulated sound wave.
Table 3. Summary of table II outcome

[5] I Rechenberg, “Cybernetic solution path of an
experimental problem. royal aircraft establishment,
library translation 1122, 1965. reprinted in evolutionary
computation the fossil record, db fogel, ed.” Chap. 8, pp.
297-309, 1998.
[6] D Fogel and Z Michalewicz, Handbook of evolutionary
computation. Taylor & Francis, 1997.
[7] A Engelbrecht, Computational
introduction. Wiley, 2007.

intelligence:

an

[8] MM Ali, C Khompatraporn, and Z Zabinsky, “A
numerical evaluation of several stochastic algorithms on
selected continuous global optimization test problems,”
Journal of Global Optimization, vol. 31, no. 4, pp. 635–
672, 2005.
[9] KV Price, RM Storn, JA Lampinen (2005) Differential
evolution: a practical approach to global optimization.
Springer, Berlin
[10] F Kang, J Li, Z Ma, H Li (2011) Artificial bee colony
algorithm with local search for numerical optimization. J
Softw 6(3):490–497
[11] R Hooke, TA Jeeves (1961) “Direct search” solution of
numerical and statistical problems. J ACM (JACM)
8(2):212–229

Test Problem

MSDE vs. DE

f1

+

f2

+

f3

+

[12] R Dawkins (1983). "Universal Darwinism". In Bendall,
DS Evolution from molecules to man. Cambridge
University Press.

f4

+

[13] R Dawkins (1976). The Selfish Gene. Oxford University
Press. ISBN 0-19-929115-2.

f5

+

f6

+

f7

-

f8

+

f9

+

f10

+

f11

+

Total Number of + sign

10

7. REFERENCES
[1] D Fogel, “Introduction to evolutionary computation,”
Evolutionary Computation: Basic algorithms and
operators, vol. 1, p. 1, 2000.
[2] JF Kennedy, J Kennedy, and RC Eberhart, Swarm
intelligence. Morgan Kaufmann Pub, 2001.
[3] J Holland, Adaptation in natural and artificial systems.
The University of Michigan Press, Ann Arbor, 1975.
[4] JR Koza, Genetic programming: A paradigm for
genetically breeding populations of computer programs
to solve problems. Stanford University, Department of
Computer Science, 1990.

[14] P Moscato, (1989). "On Evolution, Search, Optimization,
Genetic Algorithms and Martial Arts: Towards Memetic
Algorithms". Caltech Concurrent Computation Program
(report 826).
[15] XS Chen, YS Ong, MH Lim, KC Tan, (2011). "A MultiFacet Survey on Memetic Computation". IEEE
Transactions on Evolutionary Computation 15 (5): 591–
607.
[16] XS Chen, YS Ong, MH Lim, (2010). "Research Frontier:
Memetic Computation - Past, Present & Future". IEEE
Computational Intelligence Magazine 5 (2): 24–36.
[17] T Ichimura, Y Kuriyama, (1998). "Learning of neural
networks with parallel hybrid GA using a royal road
function". IEEE International Joint Conference on Neural
Networks 2. New York, NY. pp. 1131–1136.
[18] J Aguilar, A Colmenares, (1998). "Resolution of pattern
recognition problems using a hybrid genetic/random
neural network learning algorithm". Pattern Analysis and
Applications 1 (1): 52–61. doi:10.1007/BF01238026.
[19] M Ridao, J Riquelme, E Camacho, M Toro, (1998). "An
evolutionary and local search algorithm for planning two
manipulators motion". Lecture Notes in Computer
Science. Lecture Notes in Computer Science (SpringerVerlag) 1416: 105–114. doi:10.1007/3-540-645748_396. ISBN 3-540-64574-8.
[20] O Haas, K Burnham, J Mills, (1998). "Optimization of
beam orientation in radiotherapy using planar geometry".
Physics in Medicine and Biology 43 (8): 2179–2193.
doi:10.1088/0031-9155/43/8/013. PMID 9725597.

46

International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 6, March 2014
[21] S Harris, E Ifeachor, (1998). "Automatic design of
frequency sampling filters by hybrid genetic algorithm
techniques". IEEE Transactions on Signal Processing 46
(12): 3304–3314. doi:10.1109/78.735305.
[22] A Augugliaro, L Dusonchet, E Riva-Sanseverino, (1998).
"Service restoration in compensated distribution
networks using a hybrid genetic algorithm". Electric
Power
Systems
Research
46
(1):
59–66.
doi:10.1016/S0378-7796(98)00025-X.
[23] R Wehrens, C Lucasius, L Buydens, G Kateman, (1993).
"HIPS, A hybrid self-adapting expert system for nuclear
magnetic resonance spectrum interpretation using genetic
algorithms". Analytica Chimica ACTA 277 (2): 313–324.
doi:10.1016/0003-2670(93)80444-P.
[24] P França, A Mendes, P Moscato, (1999). "Memetic
algorithms to minimize tardiness on a single machine
with sequence-dependent setup times". Proceedings of
the 5th International Conference of the Decision Sciences
Institute. Athens, Greece. pp. 1708–1710.
[25] D Costa, (1995). "An evolutionary tabu search algorithm
and the NHL scheduling problem". Infor 33: 161–178.
[26] U Aickelin, (1998). "Nurse rostering with genetic
algorithms". Proceedings of young operational research
conference 1998. Guildford, UK.
[27] E Ozcan, (2007). "Memes, Self-generation and Nurse
Rostering". Lecture Notes in Computer Science. Lecture
Notes in Computer Science (Springer-Verlag) 3867: 85–
104. doi:10.1007/978-3-540-77345-0_6. ISBN 978-3540-77344-3.
[28] E Ozcan, E Onbasioglu, (2006). "Memetic Algorithms
for Parallel Code Optimization". International Journal of
Parallel
Programming
35
(1):
33–61.
doi:10.1007/s10766-006-0026-x.
[29] E Burke, A Smith, (1999). "A memetic algorithm to
schedule planned maintenance for the national grid".
Journal of Experimental Algorithmics 4 (4): 1–13.
doi:10.1145/347792.347801.
[30] E Ozcan, C Basaran, (2009). "A Case Study of Memetic
Algorithms for Constraint Optimization". Soft
Computing: A Fusion of Foundations, Methodologies
and
Applications
13
(8–9):
871–882.
doi:10.1007/s00500-008-0354-4.
[31] S Areibi, Z Yang, (2004). "Effective memetic algorithms
for VLSI design automation = genetic algorithms + local
search + multi-level clustering". Evolutionary
Computation
(MIT
Press)
12
(3):
327–
353.doi:10.1162/1063656041774947. PMID 15355604.
[32] P Merz, A Zell, (2002). "Clustering Gene Expression
Profiles with Memetic Algorithms". Parallel Problem
Solving from Nature — PPSN VII. Springer. pp. 811–
820. doi:10.1007/3-540-45712-7_78.

IJCATM : www.ijcaonline.org

[33] Z Zexuan, YS Ong and M Dash (2007). "Markov
Blanket-Embedded Genetic Algorithm for Gene
Selection". Pattern Recognition 49 (11): 3236–3248.
[34] Z Zexuan, YS Ong and M Dash (2007). "Wrapper-Filter
Feature Selection Algorithm Using A Memetic
Framework". IEEE Transactions on Systems, Man and
Cybernetics
Part
B
37
(1):
70–76.
doi:10.1109/TSMCB.2006.883267.
[35] Z Zexuan, YS Ong and M. Zurada (2008). "Simultaneous
Identification of Full Class Relevant and Partial Class
Relevant Genes". IEEE/ACM Transactions on
Computational Biology and Bioinformatics.
[36] G Karkavitsas and G Tsihrintzis (2011). "Automatic
Music Genre Classification Using Hybrid Genetic
Algorithms". Intelligent Interactive Multimedia Systems
and Services (Springer) 11: 323–335. doi:10.1007/978-3642-22158-3_32.
[37] M Marinaki, and Y Marinakis. "An Island Memetic
Differential Evolution Algorithm for the Feature
Selection Problem." Nature Inspired Cooperative
Strategies for Optimization (NICSO 2013). Springer
International Publishing, 2014. 29-42.
[38] CG Uzcátegui, and DB Rojas. "A memetic differential
evolution algorithm for the inverse kinematics problem
of robot manipulators." International Journal of
Mechatronics and Automation 3.2 (2013): 118-131.
[39] S Goudos, K Gotsis, K Siakavara, E Vafiadis, and J
Sahalos. "A Multi-Objective Approach to Subarrayed
Linear Antenna Arrays Design Based on Memetic
Differential Evolution." Antennas and Propagation, IEEE
Transactions on (Volume: 61 , Issue: 6 ) (2013): 30423052.
[40] JC Bansal, H Sharma, KV Arya and A Nagar, “Memetic
search in artificial bee colony algorithm.” Soft
Computing (2013): 1-18.
[41] S Kumar, VK Sharma and R Kumari (2014) Randomized
Memetic Artificial Bee Colony Algorithm. International
Journal of Emerging Trends & Technology in Computer
Science (IJETTCS).In Print.
[42] J Kiefer, “Sequential minimax search for a maximum.”
In Proc. Amer. Math. Soc, volume 4, pages 502–506,
1953.
[43] H Sharma, JC Bansal, and KV Arya. "Opposition based
lévy flight artificial bee colony." Memetic Computing
(2012): 1-15.
[44] PN Suganthan, N Hansen, JJ Liang, K Deb, YP Chen, A
Auger, and S Tiwari. “Problem definitions and
evaluation criteria for the CEC 2005 special session on
real-parameter optimization.” In CEC 2005, 2005.

47

