Genetic Algorithm with Success History based Parameter Adaptation

Vladimir Stanovov

, Shakhnaz Akhmedova

and Eugene Semenkin

Reshetnev Siberian State University, Krasnoyarskii rabochii ave. 31, 660037, Krasnoyarsk, Russian Federation

Keywords:

Genetic Algorithm, Optimization, Parameter Control, Metaheuristic, Simulated Binary Crossover.

Abstract:

Genetic algorithm is a popular optimization method for solving binary optimization problems. However,

its efﬁciency highly depends on the parameters of the algorithm. In this study the success history adaptation

(SHA) mechanism is applied to genetic algorithm to improve its performance. The SHA method was originally

proposed for another class of evolutionary algorithms, namely differential evolution (DE). The application

of DE’s adaptation mechanisms for genetic algorithm allowed signiﬁcant improvement of GA performance

when solving different types of problems including binary optimization problems and continuous optimization

problems. For comparison, in this study, a self-conﬁgured genetic algorithm is implemented, in which the

adaptive mechanisms for probabilities of choosing one of three selection, three crossover and three mutation

types are implemented. The comparison was performed on the set of functions, presented at the Congress on

Evolutionary Computation for numerical optimization in 2017. The results demonstrate that the developed

SHAGA algorithm outperforms the self-conﬁguring GA on binary problems and the continuous version of

SHAGA is competetive against other methods, which proves the importance of the presented modiﬁcation.

1 INTRODUCTION

The development of modern and efﬁcient optimiza-

tion methods is an important direction of research, be-

cause these methods could ﬁnd their application in the

area of various technical, engineering and scientiﬁc

problems. Today, heuristic methods, which do not

use any information about speciﬁc properties of the

problem at hand, have gained a lot of attention from

the research community as they are capable of solv-

ing any type of optimization problems, including bi-

nary, integer, real-valued, combinatorial, constrained,

multi-objective optimization problems and many oth-

ers.

One of the earliest heuristic methods is the Ge-

netic Algorithm (GA), which uses the idea of natu-

ral evolution to generate new solutions via operators

of selection, crossover, mutation and population up-

date. Modern genetic algorithms usually rely on a

set of different types of genetic operators, mentioned

above, and many of them implement self-adaptation

or self-conﬁguration schemes. The self-conﬁguration

is required because the efﬁciency of GA depends on

the type of operators used: each operator has its own

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properties, which could be helpful at different stages

of the search process. Moreover, some genetic algo-

rithm variants use parameter adaptation mechanisms

to change the probabilities of selection, crossover and

mutation operators’ application, for example, (Eiben

et al., 1999), (Semenkin and Semenkina, 2012a), (Se-

menkin and Semenkina, 2012b).

Modern GA versions rely on self-conﬁguration

schemes, developed speciﬁcally for GA, however,

there are many other evolutionary techniques which

have their own adaptation schemes. For example,

many Differential Evolution (DE) variants use the

Success History Adaptation (SHA) scheme to tune

numerical parameters, ﬁrst presented in (Tanabe and

Fukunaga, 2013). Although this adaptation method

is meant to be used only for DE, its efﬁciency was

proved many times (Al-Dabbagh et al., 2018), and

with small modiﬁcations it could be used for GA.

In this study the genetic algorithm is designed fol-

lowing the scheme of DE, and with SHA method.

The computationalexperimentsshowthe efﬁciencyof

such modiﬁcation, both on binary and real-valued op-

timization problems, compared to the self-conﬁgured

GA.

The rest of the paper is organized as follows: sec-

tion 2 describes the basics of GA and known self-

conﬁguration schemes, section 3 presents the SHA

180

Stanovov, V., Akhmedova, S. and Semenkin, E.

Genetic Algorithm with Success History based Parameter Adaptation.

DOI: 10.5220/0008071201800187

In Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019), pages 180-187

ISBN: 978-989-758-384-1

method and GA implementation, section 4 includes

experimental setup and results, and section 5 con-

cludes the paper.

2 GENETIC ALGORITHM AND

SELF-CONFIGURATION

The genetic algorithm relies on a population of so-

lutions, each encoded as a string or chromosome of

binary values, i.e. 0 or 1. Each individual represents a

potential solution to the problem at hand, and may en-

code any characteristics of the solution, including nu-

merical values, structural chraracteristics, choice be-

tween alternatives and so on. The population devel-

ops towards better solutions,according to the deﬁned

ﬁtness function, deﬁned by the goal function, via par-

ents selection, their crossover to produce offspring,

random mutation and replacement of parents with off-

spring.

The selection mechanism is used to deﬁne which

individuals will transfer their genetic information to

the next generation. All selection mechanisms de-

termine the probability values (in explicit or implicit

way) for every individual in the population to be cho-

sen. The three most popular selection schemes are:

proportional selection, rank-based selection and tour-

nament selection (Goldberg and Deb, 1991).

In proportinal selection the probability of an indi-

vidual is directly proportionalto its normalized ﬁtness

value, so that individuals with better ﬁtness get higher

probabilities. The disadvantages of proportinal selec-

tion are premature convergence and super-individual

problem. The rank-based selection assigns probabil-

ities based on the rank of the individual in the array

sorted by ﬁtness - this method allows eliminating the

disadvantages of proportional selection. The tourna-

ment selection does not explicitly calculate probabili-

ties, instead each individual is chosen as a winner in a

tournament of t randomly selected individuals in the

population. In (Stanovov et al., 2018) it was shown

that in case if t = 2, the probability of selection is the

same as for rank-based selection with linear rank as-

signment.

The crossover is used to mix the genetic informa-

tion of parents, without introducing any new infor-

mation. Popular crossover methods in GA are: one-

point, two-point and uniform crossover. In one point

crossover, a single point in the cromosome is chosen

and the binary strings exchange their tails. In two-

point crossover, two points are chosen and individuals

exchange the middle part. In uniform crossover, every

bit can be chosen from either one parent or another.

There are usually several levels of mutation prob-

abilities used in GA, referred to as weak, average and

strong mutation. In average mutation the probabil-

ity of a bit j being ﬂipped is p

ut =

, where L is

the length of the binary string encoding the solution.

Weak mutation changes the probability to be 3 times

less then average, while strong mutation increases p

by 3 times.

The self-conﬁguration method used in (Semenkin

and Semenkina, 2012a) and (Semenkin and Semenk-

ina, 2012b) is based on the idea of selecting one of

the three types of selection, crossover and mutation

depending on their efﬁciency at the moment. Initially

all probabilities are set to p

, where z is the num-

ber of different operators (3 in this study) of a certain

type. The efﬁciency is measured as the average ﬁtness

at current generation:

AvgFit

∑

j=1

i, j

, i = 1, 2, ...z (1)

where n

is the number of offspring, created with i-

th operator, f

i, j

is the ﬁtness if j-th offspring, cre-

ated with i-th operator, AvgFit

is the average ﬁtness

of individuals created with i-th operator. Based on

the AvgFit

values, the winning operator w of each

type is deﬁned, and is probability is increased by

= p

(z−1)K

, and the probabilities of other op-

erators are decreased by

, where K is a constant,

set to 0.5 and N is the population size. Also, for all

operators the minimal level of p

was set to 0.05.

This probabilities tuning method was shown to

perform better than GA with randomly chosen oper-

ator types among variety of problems, but still worse

then the best combination of selection, crossover and

mutation for a particular problem, which was deﬁned

by extensive numerical experiments. Further in the

text the described self-conﬁguring binary GA will be

reffered to as SelfCGA.

In case of continous optimization problems, usu-

ally special versions of crossover and mutation op-

erators are used, most popular are simulated binary

crossover (SBX) (Deb and Agrawal, 1995) and poly-

nomial mutation (Deb and Deb, 2014). The SBX op-

erator searches for solutions in real-parameter space

in a manner similar to single-point crossover, and

polynomial mutation applies polinomial distribution

to search for solutions next to an individual. In the

next section, the success history adaptation is pre-

sented, as well as its application to GA crossover and

mutation operators.

Genetic Algorithm with Success History based Parameter Adaptation

181

3 PROPOSED APPROACH:

GENETIC ALGORITHM WITH

SUCCESS HISTORY

ADAPTATION

The success history adaptation mechanism was origi-

nally proposed to adjust the numerical values of scal-

ing factor F and crossover rate Cr in differential evo-

lution. This tuning mechanism is based on an earlier

study, which was introduced in the JADE algorithm,

(Zhang and Sanderson, 2009), where the successful

values of F and Cr were used to deﬁne new values.

In SHA there are H memory cells, each containing

a set of parameters. In this study for binary GA there

are two tuned parameters: the mutation rate Mr and

crossover rate Cr were tuned, so that each k-th mem-

ory cell is denoted as M

Mr,k

and M

Cr,k

. The initial

value for M

Mr,k

is set to

, maximum value -

, and

Cr,k

is initially set to 0.5. For every individual in the

population, a random memory cell index i is chosen,

and the new Mr is sampled with Cauchy distribution

(scale parameter 0.1), while Cr is sampled with nor-

mal distribution (standard deviation 0.1) as follows:

Mr = randc(M

Mr,i

, 0.1), Cr = randn(M

Cr,i

, 0.1) (2)

After each application of crossover and mutation,

if there was an improvement in ﬁtness value, success-

ful Mr and Cr values are saved to S

and S

respec-

tively. At the end of the generation, h-th memory cell

is updated with new values, calculated using weighted

Lehmer mean:

mean

(S) =

∑

|S|

j=1

∑

|S|

j=1

(3)

where S could be S

or S

, w

∆f

∑

|S|

k=1

∆f

, ∆f

| f(x

new

) − f(x

old

)|. The index number h is incre-

mented in a loop every generation, and if h = H, h

is set to 1.

The crossover rate Cr is limited to [0, 1], and mu-

tation rate Mr - to [0,

]. In this manner, the SHA

adaptation mechanism identiﬁes the best parameter

values at current generation not only depending on

which values were mostly successful, but also taking

into consideration the improvement level ∆ f

The rest of the GA scheme is also changed to be

similar to DE scheme. At every generation, for ev-

ery i-th individual the second parent is selected with

tournament selection, tournament size t = 2. Next, i-

th individual and selected individual are combined in

uniform crossover operator, where Cr = 1 means that

all genetic information will be taken from the new in-

dividual - all L bits of the selected individual have

100% chance to be chosen. Also, to make sure that

at least some information is taken from the selected

individual, one randomly selected bit is copied from

the selected individual. Next, at the mutation step ev-

ery bit in the newly created individual after crossover

is ﬂipped with probability Mr. There could be situ-

ations when no bits are changed, or all of them are

changed, but the last is highly improbable.

After mutation, the replacement scheme is ap-

plied. The newly generated individual, modiﬁed in

crossover and mutation, is compared to the i-th indi-

vidual in the population. If there is an improvement

in ﬁtness value, the i-th individual is replaced, and Mr

andCr are saved. Otherwise, no actions are taken, and

the algorithm proceeds to the next individual. The de-

scribed algorithm was called SHAGA, and tested to

compare with the self-conﬁguring GA in section 2.

For the case of continous optimization, there

were 4 tuned parameters, including crossover rate

Cr in range [0, 1], mutation rate Mr in range [0,

crossover distribution index η

in range [10, 200] and

mutation distribution index η

in range [10, 200]. The

tournament size was also set to t = 2, crossover was

performed between the i-th individual and selected in-

dividual, and the replacement occured only if the gen-

erated trial individual was at least as good as the ﬁrst

parent.

The next section describes the experimental setup

and the results of algorithm comparison.

4 EXPERIMENTAL SETUP AND

RESULTS

The efﬁciency of the newly designed SHAGA algo-

rithm was tested on binary and numerical optimiza-

tion problems. Two classical binary problems were

selected for experiments, namely the onemax prob-

lem and 01 problem. For onemax problem, the goal

is to set all bits to 1, and for 01 problem the goal is to

ﬁnd a string with maximum number of ”01” combi-

nations in it. The ﬁrst problem has only one optima,

while the 01 problem has one local optima and one

global optima, which differ by a shift by one bit.

The experiments for these binary problems were

performed for the length of binary string of 100, 1000

and 3000. The amount of computational resource was

the same for both SHAGA and SelfCGA: for 100 bits

the maximum number of fucntion evaluations was set

to NFE = 10

, for 1000 bits NFE = 10

, for 3000

bits NFE = 10

. The population size was set to 100,

100 and 1000 respectively.

To track the convergence process for every of the

30 indepenent runs of the algorithm, the best achieved

ECTA 2019 - 11th International Conference on Evolutionary Computation Theory and Applications

182

ﬁtness value was saved after 0.01, 0.02, 0.03, 0.05,

0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 frac-

tions of the maximum number of function evaluations

NFE

max

. The comparison of the ﬁnal results was

performed with two-tailed Mann-Whitney rank sum

statistical test with tie braking and signiﬁcance level

p = 0.01.

Firstly, the SHAGA with ﬁxed Mr andCr parame-

ters was tested, i.e. Mr =

, Cr = 0.5. In Figure 1 the

avegaged convergencegraphs of SHAGA without pa-

rameter tuning and SelfCGA are presented. The val-

ues in the graphs are the ﬁtness of individuals, which

is the number of ones for onemax problem, and num-

ber of 01 combinations for 01 problem.

Figure 1: Convergence of SelfCGA and SHAGA with ﬁxed

parameters.

From Figure 1 it could be observed that for bi-

nary string length of 100, for Onemax problem the

convergence of SHAGA and SelfCGA is similar at

the beginning, but later on, at around 0.4NFE

max

the

SHAGA reaches the goal, while SelfCGA fails to

achieve 100 correct bits until the end of the search.

For 01 problem the situation is different, SelfCGA

demonstrates superior performance during the search

process, but SHAGA eventuallty gets the same re-

sult. For the case of D = 1000 SHAGA demon-

strates superior performance for both onemax and 01

problem. However, for 01 problem at the beginning

SelfCGA converges faster, but SHAGA takes over at

0.3NFE

max

. For D = 3000 the behaviour of algo-

rithms is quite different: for 01 problem SelfCGA

converges faster then SHAGA, although it is clearly

seen that SHAGA accelerates its convergence in a

similar way as for D = 100 and D = 1000. Also,

note that SHAGA converges to the optimum for one-

max problem in all cases. According to the Mann-

Whintney statistical test, SHAGA has shown superior

performance in 4 cases out of 6 (all onemax prob-

lems and 01 for D = 1000), and for two other cases

there was no signiﬁcant difference in algorithms per-

formance. From the graphs it could be seen that with

larger resource SHAGA will probably outperform the

SelfCGA for all 01 problem instances.

In Figure 2 the results for SelfCGA and SHAGA

with success-history adaptive parameter tuning are

presented. The algorithm without parameter adapta-

tion is denoted as SHAGA

NO ADJ.

Figure 2: Convergence of SelfCGA and SHAGA with pa-

rameter tuning.

From Figure 2 it could be seen that adding param-

eter tuning signiﬁcantly improves the performance of

SHAGA: convergence on 01 problem in comparison

to the algorithm without parameter tuning is signiﬁ-

cantly faster. This is especially seen for D = 3000,

where SHAGA with success history adaptation out-

performes SelfCGA already after 0.3NFE

max

. As for

onemax problem, there is also a small improvement

for SHAGA. The Mann-Whitney statistical signiﬁ-

cance test indicates superior performance of SHAGA

over SelfCGA in all cases except 01 problem for

D = 100. SHAGA with parameter adaptation is better

then without for D = 100 and D = 3000 for 01 prob-

lem.

The next series of experiments was performed on

a set of benchmark problems from the Congress on

Evolutionary Computation (CEC) 2017 for single-

Genetic Algorithm with Success History based Parameter Adaptation

183

objective real-valued bound-constrained optimiza-

tion. The set of benchmark problems consists of 30

functions deﬁned for dimensions 10, 30, 50 and 100.

These test problems are speciﬁcally designed to test

evolutionary optimization techniques, including GA.

The functions are characterized by various properties

that make them difﬁcult to optimize, including many

local optima, non-separability, different properties for

different variables, areas of equal ﬁtness values, i.e.

plateaus, small area of global optima attraction and

others. According to the competition rules, there were

51 independent runs performed for all dimensions and

all 30 test functions, and the difference between the

goal function value and the best achieved value was

recorded. All test problems are minimization func-

tions. To avoid cheating of some algorithms which

check the center of coordinates for optimal solution,

the whole functions were shifted by random value

from the center of coordinates, and all functions were

rotated. The function deﬁnition can be found in (Wu

et al., 2016).

First, the binary versions of SHAGA and Self-

CGA were modiﬁed to solve numerical optimization

problems in the following manner: each numerical

variable was deﬁned within the range [x

min

, x

max

] with

min

= −100, x

max

= 100. For every variable the ini-

tial accuracy of the grid was set to acc = 0.01. Next,

for every i-th variable the minimal length of the bi-

nary string required to encode the grid was calcu-

lated as L

= log

(

max

−x

min

)

acc

) rounded to the next

integer. After this, the new step was calculated as

acc

new

max

−x

min

)

. The ﬁnal string length was the

sum of all L

. Both algorithms used the reﬂected bi-

nary code (Gray encoding) for numerical values. The

population size for both SHAGA and SelfCGA was

set to 350, maximum number of function evaluations

- 10

D. Table 1 contains the detailed results of sta-

tistical tests of SelfCGA and SHAGA, where 1 means

that SHAGA was better, -1 that SelfCGA was better,

and 0 means no signiﬁcant difference.

The results presented in Table 1 demonstrate that

SHAGA is better then SelfCGA for most problems,

and according to Mann-Whitney statistical test, for

D = 10 SHAGA was signiﬁcantly better for 24 func-

tions out of 30, and worse for 2 functions, namely

F3 and F12. Moreover, SelfCGA was observed to

stagnates sometimes, in particular for F14, F15, F19,

F20, F21, F24, while SHAGA continues search for

all problems. For D = 30 SHAGA demonstrates sta-

tistically signiﬁcant better results for 23 functions out

of 30. For D = 50 there are 23 improvements out of

30, and for D = 100 - 27 improvements. SHAGA not

only demonstrates better performance for most prob-

lems, but also in some cases converged to the global

Table 1: Statistical test results for SHAGA and SelfCGA,

numerical problems.

Func D=10 D=30 D=50 D=100

f1 1 1 1 1

f2 1 1 1 1

f3 -1 -1 -1 -1

f4 1 -1 -1 1

f5 1 1 1 1

f6 1 1 1 1

f7 1 1 1 1

f8 1 1 1 1

f9 0 1 1 1

f10 1 1 1 1

f11 0 0 0 1

f12 1 1 1 1

f13 1 1 1 0

f14 1 1 1 0

f15 1 0 0 1

f16 1 1 1 1

f17 -1 1 1 1

f18 0 1 1 1

f19 1 0 0 1

f20 1 1 1 1

f21 1 1 1 1

f22 1 1 1 1

f23 1 1 1 1

f24 1 1 1 1

f25 1 0 0 1

f26 1 1 1 1

f27 0 1 1 1

f28 0 1 1 1

f29 1 0 0 1

f30 1 1 1 1

optima, for example for D = 10 for F9, despite of the

discretization of the search space and binary endcod-

ing. Table 2 summs up the statistical tests results

for SHAGA and SelfCGA. In this table ”+” stands

for signiﬁcant improvement of SHAGA against Self-

CGA, ”-” for signiﬁcant deterioration in performance,

and ”=” for insigniﬁcant difference. For binary case,

there were 2 functions, and 30 functions for numerical

case.

Table 2: Statistical test results for SHAGA and SelfCGA,

numerical problems.

Problem type SHAGA vs SelfCGA

Binary, D=100 1+/0-/1=

Binary, D=1000 2+/0-/0=

Binary, D=3000 1+/0-/1=

Numerical, D=10 23+/2-/5=

Numerical, D=30 23+/0-/7=

Numerical, D=50 23+/2-/5=

Numerical, D=100 27+/1-/2=

ECTA 2019 - 11th International Conference on Evolutionary Computation Theory and Applications

184

In the next series of experiments the continuous

version SHAGA

was used, with real-valued param-

eter encoding instead of binary, SBX crossover and

poynomial mutation as described above. First, the

efﬁciency of the parameter adaptation scheme was

tested, for this the GA

(without SHA) was tested with

the following ﬁxed parameters: Cr = 0.5, Mr =

= 50, η

= 50. The population size was set to

10D, the computational resource was set to 10000D.

Table 3 contains statistical test results for SHAGA-c

with GA-c.

Table 3: Statistical test results for SHAGA

and GA

Problem type SHAGA

and GA

D=10 13+/16-/1=

D=30 25+/4-/1=

D=50 24+/6-/1=

D=100 22+/7-/1=

In Table 3 ”+” stands for signiﬁcant improvement

of SHAGA-c againstGA-c, ”-” for signiﬁcant deterio-

ration in performance, and ”=” for insigniﬁcant differ-

ence. Except for D = 10, the SHA allowed signiﬁcant

improvement of performance.

For comparison with other approach the popular

differential evolution algorithm, SHADE, was cho-

sen, as it is known to be one of the most compete-

tive versions of DE according to (Al-Dabbagh et al.,

2018). The same set of CEC 2017 functions was used,

and SHADE had the following parameters: popula-

tion size 75D

, p parameter in current-to-pbest strat-

egy equal to 0.17, and no archiveset. Table 4 contains

the results of statistical test comparison of SHADE

and SHAGA-c for all functions and all dimensions.

Although the SHAGA-c algorithm is worse than

SHADE in most cases, according to Table 4, one

may observe that SHAGA demonstrates superior per-

formance on several functions for all or most dimen-

sions, including F5, F7, F8, F10, F16, F17, F20,

F23 and F29. Functions F5, F7 and F8 are variants

of Rastrigin function, F10 is Shwefel function, F16,

F17 and F20 are hybrid functions, which also use the

mentioned basic functions, F23 and F29 are composi-

tion functions, also containing Rastrigin and Shwefel

functions. From this, we may conclude that SHAGA-

c is capable of solving problems with many local op-

tima more efﬁciently then SHADE.

The main reasons of SHAGA high efﬁciency are

the usage of the speciﬁc algorithm scheme, where ev-

ery individual has the possibility to crossover with a

selected individual. Another reason of SHAGA high

quality results is the usage of the parameter tuning

scheme, where the probability of selection and muta-

tion are numerical parameters, but not ﬁxed parame-

Table 4: Statistical test results for SHADE and SHAGA-c.

Func D=10 D=30 D=50 D=100

f1 -1 -1 -1 -1

f2 -1 -1 -1 -1

f3 -1 -1 -1 -1

f4 -1 -1 -1 1

f5 1 1 1 1

f6 -1 -1 -1 1

f7 1 1 1 -1

f8 1 1 1 -1

f9 0 0 0 0

f10 1 1 1 1

f11 1 -1 -1 -1

f12 -1 -1 -1 -1

f13 -1 -1 -1 -1

f14 -1 -1 -1 -1

f15 -1 -1 -1 -1

f16 1 1 1 -1

f17 1 1 1 -1

f18 -1 -1 -1 -1

f19 -1 -1 -1 -1

f20 0 1 1 -1

f21 -1 1 1 -1

f22 0 -1 -1 1

f23 1 1 1 -1

f24 -1 -1 -1 -1

f25 -1 -1 -1 -1

f26 -1 1 -1 -1

f27 -1 -1 -1 -1

f28 -1 -1 -1 -1

f29 1 1 1 1

f30 -1 -1 -1 -1

ter values, as in SelfCGA, where only three mutation

levels are available, and three crossover types.

5 CONCLUSIONS

In this paper the success history adaptation mecha-

nism was applied to the genetic algorithm with a mod-

iﬁed scheme. The newly developed SHAGA algo-

rithm inherited the main loop organization from pop-

ular differential evolution algorithms, such as JADE

and SHADE. In the binary version of SHAGA al-

gorithm two parameters were tuned: the crossover

rate, i.e. the rate of new genetic information, that

will be taken from another individual, and the mu-

tation rate. In the continous version SHAGA-c, the

crossover and mutation distribution indexes were also

tuned. The tuning mechanism was taken from the

mentioned SHADE implementation.

The performed experiments have shown the supe-

rior performance of SHAGA even without parame-

Genetic Algorithm with Success History based Parameter Adaptation

185

ter tuning against another self-tuning meta-heuristic,

SelfCGA on classical binary optimization problems.

With parameter tuning SHA scheme, the results ap-

peared to be even better. Also, it should be noted

that SHAGA used only one selection mechanism,

namely tournament selection with t = 2, while Self-

CGA could automatically choose one of three selec-

tion types. Moreover, for SHAGA, there was only

one crossover type used, i.e. uniform crossover. Ac-

cording to some recent research (Piotrowski and Na-

piorkowski, 2018), many heuristic methods are over-

complicated, and could be signiﬁcantly simpliﬁed,

and SHAGA, even with ﬁxed parameters, demon-

strates the same idea. For binary-encoded numeri-

cal optimization problems SHAGA has outperformed

SelfCGA for most problems in all dimensions. The

presented results have demonstrated that SHAGA not

only gets better result at the end of the search, but also

avoids stagnation.

In comparison with differential evolution based

SHADE algorithm SHAGA has shown superior per-

formance on a number of test functions, which means

that SHAGA’s properties are important for solving

numerical problems with many local optima. As a

result, it could be stated that the newly developed

SHAGA algorithm could be used as a highly com-

petetive genetic algorithm implementation for vari-

ous binary and continous optimization problems, as

well as other problems. The directions of further re-

search may include adding different selective pres-

sure mechanisms for SHAGA, improving the param-

eter tuning scheme, application of external archive or

adding population size adjustment mechanism, such

as linear population size reduction.

ACKNOWLEDGEMENTS

Research is performed with the support of the

Ministry of Education and Science of the Rus-

sian Federation within State Assignment [project #

2.1680.2017/(project part), 2017].

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APPENDIX

Figure 3: Convergence of SHAGA and SHADE, D=50.

Genetic Algorithm with Success History based Parameter Adaptation

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