Overview of Selection Schemes In Real-Coded Genetic ... · the important properties of the genetic algorithms and then discusses the applications of real-coded genetic algorithms

Overview of Selection Schemes In Real-Coded

Genetic Algorithms and Their Applications

Anil S. Mokhade and Omprakash G. Kakde Visvesvaraya National Institute of Technology /Computer Science & Engineering, Nagpur, India

Email: {asmokhade, ogkakde}@cse.vnit.ac.in

Abstract— The real-coded genetic algorithms are being used

by the research community for diverse applications. This

diversity is further extended into the selection schemes of

different types and combination of them have been tried by

the community. This paper is the overview of the selection

schemes in genetic algorithms with particular reference to

real-coded genetic algorithms. It discusses the evolution of

genetic algorithms, their principles of working and

advantages of real-coded genetic algorithms. It brings out

the important properties of the genetic algorithms and then

discusses the applications of real-coded genetic algorithms

with selection focus. It also points to the further research in

combining the real-coded genetic algorithm using 80:20

principles in selection involving intuition.

Index Terms—real-coded genetic algorithms, selection,

80:20 principle

I. INTRODUCTION

Its more than 50 years that biologically named

‘Evolutionary Algorithms’ are being used as

computational models depicting the evolutionary process

for problem-solving using computers. The three main

techniques used for these evolutionary computations are

‘Evolution Strategies’, ‘Evolutionary Programming’, and

‘Genetic Algorithms’. They are variedly used as a tool for

optimization in engineering problems. Common to all

these methods is the evolution of a population of

candidate solutions of the problem under consideration.

In turn, these solutions are obtained by ‘selection’,

‘crossover’, and ‘mutation’ operators resembling the

natural evolution with genetic variations [1], [2].

A. Evolutionary Techniques

Evolution Strategies: The ‘Evolution Strategies’ are

used for real-valued optimization with self-adaptation of

parameters standard. It is more applied to numerical

optimization with used to solve technical optimization

problems. Rechenberg was pioneer in using this method

that was further developed by Schwefel. These were more

rule based for the variables to change them all at once,

inconsiderably and randomly. If new set is found to be

good then it is to be retained otherwise old status of the

variable can be called for [3].

Evolutionary Programming: The ‘Evolutionary

Programming’ involves representation of the solution by

a finite-state machine. These involved stochastic

optimization with mutation operations on state-transition

diagrams. Thus the emphasis was more on the behavioral

linkages between parents and their offspring. Typically it

involved three steps process. First the initial population

for trial solution was chosen randomly. Then each

solution was replicated into new population and the

offspring solution was subject to mutation based on the

functional change imposed on the parent solution. Fogel

initially worked with the technique of evolutionary

programming, which later was further developed by

Owens, Walsh, and Atmar [1].

Genetic Algorithms: The ‘Genetic Algorithms’ were

propounded by Holland with his students and colleagues

in 60s and 70s. It involved shifting from one population

of solutions to a new population. It was done through

‘natural selection’ combined with crossover, mutation,

and inversion. Here again the inspiration was genetics

and operators involved in it. The living beings have their

chromosomes made of particular genes. These genes, in

turn, take up many different allele values. The

chromosome in Genetic Algorithm is represented by

string length or vector of parameters, each bit of the

string is gene, and the real value of the object is the allele

of the phenotypes [4]. It was a major innovative idea that

gave firm footing to theoretical foundations for the family

of Evolutionary Algorithms.

The basic purpose of any Genetic Algorithm is to

employ the method of searching amongst number of

possible solutions. Thus Genetic Algorithms is a method

of examining a small fraction of possible solutions called

candidate solutions and arrive at optimal or good

solutions. ‘Searching’ unlike the efficient retrieval of

information stored in computer memory, it is to

efficiently find set of actions that will move from a given

initial state to a given goal. In short one can say ‘search

for paths to goal’ [1].

There are two types of Genetic Algorithms, namely,

fixed-length binary coded, and real number

representations or real-coded Genetic Algorithms.

Though fixed length binary coded representations have

dominated research, it is the real coded Genetic

Algorithms, which have shown good properties for

different application problems [5].

A good number of research papers are dealing with the

real-coded genetic algorithms and their applications with

diverse application in engineering and business domains.

Though basic research in all the operator of genetic

algorithm is carried out all over the world the application

Journal of Industrial and Intelligent Information Vol. 2, No. 1, March 2014

©2014 Engineering and Technology Publishing 71doi: 10.12720/jiii.2.1.71-77

Manuscript received July 20, 2013; revised September 21, 2013

specific research is mainly confined with all the operators

combined together and their performance as genetic

algorithm as a whole. In this paper attempt is made to

take an overview of ‘selection’ operator of real-coded

genetic algorithms so as to build the base for performance

analysis of real-coded genetic algorithms.

B. Flow of the Paper

The main concern of this paper is to deal with

‘selection’ operator in real-coded genetic algorithms. In

this dealing the general working of the genetic algorithm

is first discussed. Then real coded-genetic algorithms are

placed vis-à-vis binary coded algorithms. It further

discusses the various research attempts as far as

‘selection’ operator is concerned. Here also the main

concern of the paper is to bring out the applications of

real-coded genetic algorithms with focus on ‘selection’

operator. Further the analytical aspects of research in

‘selection’ operator are discussed. The paper is divided

into six sections. The first section was Introduction. The

second section deals with general working of the Genetic

Algorithms. The third section discusses about ‘selection’

operator and their various types used by different

researchers. The fourth section deals with analysis of the

‘selection’ operator with respect to other operators in

performance of the Genetic Algorithms with particular

reference with real-coded genetic algorithms. The fifth

section deals with 80:20 principle and genetic algorithms.

The last section deals with conclusion and future research

dimensions.

II. GENERAL WORKING OF GENETIC ALGORITHMS

A. Principles of Working

Genetic Algorithms work on the principles of

probabilistic search with stochastic distribution of the

probability. They accumulate the information about initial

unknown search space. Then this information is further

exploited, to favor the subsequent search, resulting into

useful subspaces. This adaptability favors their usage in

large complex, and poorly understood search spaces,

which otherwise classical search methods like

enumerative, heuristic etc. fail to solve satisfactorily [5].

Properties: One of the important properties of Genetic

Algorithms is noise tolerance. Since Genetic Algorithms

work using sampling, populations may be sized to detect

a given degree of function difference with no more than a

specified amount of error [6].

Genetic Algorithms are robust, which is found to be

effective in solving global search problems [7]. This

property of robustness in Genetic Algorithms is due to the

ability to solve hard problems quickly and reliably;

ability to interface to existing simulations and models;

being extensible; and ability to hybridize ([6], [5]).

B. Representation of Genetic Algorithms

In a simple representation the Genetic Algorithms will

deliver the N – a set of number of potential solutions.

Each individual solution called Ji such that Ji € J where

possible individuals are represented in the space by J [8].

It may be mentioned here that all the solution in the set

are sampled simultaneously in the search space. In fact

that is distinguishing characteristics of Genetic

Algorithms. Thus a population P ={ J1, J2, …, JN } is

formed. This population is then subjected to natural

evolutionary process operators after initializing the

population. These operators are selection, crossover and

mutation. All these operations are run in a loop. One run

execution of loop is called generation and population at

the end of the loop denotes the population at that

generation. Figure 1 gives the generational model of

genetic algorithm [9].

procedure GA

begin

t = 0;

initialize P (t );

evaluate structures in P (t );

while termination condition not satisfied do

begin

t = t + 1;

select P (t ) from P (t !1);

apply genetic operators to structures in P (t );

evaluate structures in P (t );

end

end.

Figure 1. Generalized model for genetic algorithms

Thus genetic algorithm is a simple but robust

algorithm due to implicit parallelism it exhibits among

the subsets of coded parameter set within the population

under consideration using probabilistic transition of

operators without any domain specific information ([9],

[10]). These subsets are either binary-coded or real value

coded. Many theoretical studies have been done using

binary- coded genetic algorithms but many real life

applications have been dealt with using real-coded

genetic algorithms. The binary-coded genetic algorithms

can be studied in many other references including

Goldberg [11]. Here in this paper we are going to deal

with real-coded genetic algorithms.

III. REAL-CODED GENETIC ALGORITHMS

The binary-coded and real-coded genetic algorithms

differ in the usage of alphabets for representing genes or

parameters. Real-coded genetic algorithms have some

advantages over the binary-coded genetic algorithms,

which we will discuss later in this paper. It was most

natural to use real numbers to represent the genes directly.

This was particularly for problems of optimization

involving variable parameters in continuous domains [5].

Thus there is no difference between coding part and the

search space. A vector of floating point numbers

represents the chromosome. The vector length is for

solution to the problem. This makes each gene as a

variable to the problem. This forces gene values to

remain in the interval established by the variables they

represent. This requirement therefore must be fulfilled by

the genetic operators [12].

Going by the research and many studies on

comparative analysis of both these types of genetic

algorithms, the real-coded genetic algorithms are found to


©2014 Engineering and Technology Publishing 72

be superior in following aspects [5],[13]. The precession

is achievable in real-coded genetic algorithms even after

increasing the domain. Graduality as defined by Herrea

and others, which means slight change in variables causes

slight changes in the function, can be very well exploited

by using real-coded genetic algorithms. When using real-

coded genetic algorithms, there is no difference between

coding (genotype) and search space (phenotype). This

gives solutions representation near to natural

formulations. According to Arumugam [14], the

implementations are carried in real-coded genetic

algorithms so as to move them closer to the problem

space. This makes the some specific characteristics of

real space operators more problem specific with some

specific characteristics of real space [14]. Thus one can

conclude that inadequacy of binary-coded genetic

algorithms to deal with continuous search spaces with

large dimensions and considerably higher numerical

precision have been dealt very well by real-coded genetic

algorithms [5].

Going by these advantages of real-coded genetic

algorithm, it will be greatly advantageous to study them

in detail. Number of researchers in several real-life

applications has tested them. The next sections take a

look at the existing status of research on selection

operator and its applications using real-coded genetic

algorithms.

IV. SELECTION OPERATOR

We have seen in the previous sections that selection

operator is the first operation acted upon on the

population of the solution after initialization. It selects the

chromosomes in the population for reproduction. If one is

able to get fitter chromosomes, they are most likely to be

selected for reproduction. It also will decide how many

offspring each chromosome will produce. The selection

operator should be chosen of such a nature that it

maintains the balance in crossover and mutation operators

mimicked in the genetic algorithms. If we have greater

emphasis on selection operator then population will have

highly fit solutions/population resulting reduced diversity,

which is very essential for further change and progress. If

one gives less emphasis on the selection operator, it may

result in slowing down the process of optimum solution

evolution [1]. In the ultimate analysis we must understand

that selection operator’s main purpose is to improve the

average quality of the population by increasing the

probability of high quality individuals so as to enable

them to be copied into the next generation [8].

A. Different Selection Schemes

Since Holland gave his schema theorem and used

proportional selection, many researchers have used

different selection schemes. Each selection scheme has

advantages and some limitations. It has also been debated

in the research community over these advantages and

limitations. The different schemes include [15].

Proportionate reproduction

Ranking selection

Tournament selection

Steady-state selection

Roulette wheel selection

Stochastic Universal Sampling

Local Selection

Truncation Selection etc.

Which selection schemes is best is still an open

question for the research community. The research

community is using different selection schemes but the

key idea is that a “survival-of-the-fittest” mechanism

biases the generation of the new individuals [16]. We will

first present the theoretical basis for understanding the

these selection schemes.

B. Theoretical Underpinnings for Selection Operator

Over the period different researchers have analyzed the

selection operator in particular and genetic algorithms

using various concepts and terms in general. They can be

called performance measures for genetic algorithms.

These include parameters like take over time, selection

intensity, average fitness, fitness variance, reproduction

rate, loss of diversity, and selection variance [8]. These

researchers have analyzed the selection schemes based on

its interaction on the distribution of fitness values. They

have dealt with mathematical foundations for these

properties which out of purview of this paper.

By take over time one means that the number of

generations required for a single best individual to fill up

the whole generation without using recombination. The

selection intensity one means the normalized increase of

the average fitness of the population after selection [17].

Fitness here means the solution, which are perfect not

only in its form and function but also able to contribute to

the future generation [18]. Here we look at fitness from

average and variance aspects. The Reproduction rate

denotes the ratio of the number of individuals with certain

fitness value after and before selection. Loss of diversity

we mean loss of bad individuals and replacement of them

with better individuals. Selection variance is same, as

selection intensity with new variance after the selection

operator has been applied.

V. SELECTION OPERATOR AS USED IN REAL-CODED

GENETIC ALGORITHMS

The selection operator as employed by real-coded

genetic algorithms differs with the applications. In this

section we will look into some of the applications using

real-coded genetic algorithms for the analysis of selection

operator.

Cuang uses a real-coded genetic algorithm with

ranking selection with direction-based crossover and

dynamic random mutation. The whole idea behind the use

of ranking selection is to eliminate bad solutions and

reproduce good solutions. This enables whole population

attains a better average fitness [19].

Baskar et. All [20] have use Roulette wheel selection

for their hybrid real coded genetic algorithm for

economic dispatch problem.

In Fossati’s Real-coded Extended Compact Genetic

Algorithm (rECGA) applies tournament selection and

restricted tournament replacement applied between



original real population and new real population. It is

observed that as the tournament size increases, the

convergence of rECGA becomes more easier [16].

Alberto et al. [21] suggest the use of two types of

selection operators: ranking selection- surviving and

death, elitist selection and roulette wheel selection

operators using Pareto optimality for multi-objective

evolutionary algorithm. The surviving selection first

assigns higher probability to smaller rank individuals

followed by roulette wheel selection. In death selection

gives probability of not surviving i.e. higher probability

to those individuals with greater ranking. Again, then

applying roulette wheel selection to eliminate spare

individuals. Lastly elitist selection is applied randomly to

eliminate spare individuals. The main aim was to improve

the behavior of the crossover operator with the these

selections.

Arumugam and others [14] used the Roulette-wheel

selection (RWS), Tournament selection (TS) and hybrid

of both selection procedures in conjunction with elitist

strategy. Elitist strategy ensures that the best individual in

each generation is passed to the next generation. Thus it

shows two kinds of hybrid selections, namely single level

and two level hybrid selection methods. First half is TS

and next half is RWS in the single level. In the two level

hybrid selection one fourth for TS and another one fourth

for RWS and again repeating the same sequence. The

results are better for the optimal control problem. Same

authors have further introduced hybrid crossover methods

and new hybrid selection methods for integrated

processes and optimal control in manufacturing

environment.

Subbaraj and others [22] have done enhancements of

self-adaptive real-coded genetic algorithm using Taguchi

method for economic dispatch problem. Here they have

employed tournament selection scheme using powerful

exploration capability. In this they bring out tournament

between two solutions to get the better one. This again

helps in better convergence and reduced computational

burden as claimed by authors.

Tang and others [23] proposed adaptive directed

mutation operator in real-coded genetic algorithm to

solve complex optimization problems using linear fitness

scaling mechanism and then selectively applying

selection through stochastic universal sampling. This is a

variant of roulette wheel selection. But unlike roulette

wheel selection it gives a starting position by employing a

single random number and then proceeding in equal-sized

steps around the wheel. Here the number of individuals to

be selected determines the step size. The results showed a

significant improvement in global optimum solution.

Sushil Kumar and others. [24] while dealing with non-

convex economic load dispatch have proposed use of

real-coded genetic algorithm using tournament selection

to get the selective pressure towards feasible region.

Their aim is to bring out the competition among

chromosomes and ultimately achieve better

computational efficiency, which is crucial for economic

operation of a power system.

Oyama and others [25] employ ranking selection in

real-coded adaptive range genetic algorithm (ARGA) so

that one-point crossover operation can be done so as to

achieve a practical three-dimensional shape and

optimization for aerodynamic design. They have included

the binary-coded ARGA using floating-point

representation.

These uses of selection schemes in real-coded genetic

algorithm indicate that there is wide differentiation in

approaches to application of real-coded genetic

algorithms in selection schemes. The ranking selection,

tournament and roulette wheel selection schemes are

mostly being used with some variations. These variations

are not in isolation but integrated with other operators.

The various performance measures are either explicitly or

implicitly mentioned in these research. With this look at

the applications using real-coded GAs we can take a look

at some the conceptualizations analytically which lie at

the bottom of these applications in general.

VI. ANALYTICAL ASPECTS FOR THE USE OF REAL-

CODED GENETIC ALGORITHMS

In this section attempt is take a look at the various

aspects, which favor the us of real-coded genetic

algorithms. The very first among these aspects is usage of

real-coded GAs instead of binary coded GAs itself.

Shortcomings in Binary Coded GAs: Research has

pointed out following shortcomings in the usage of

binary-coded GAs:

1) Difficulty in gradual search in continuous search

space: Hamming cliffs in a binary coding compel

deliberate hindrance to gradual search, as it

requires alteration of many bits for transition to

neighboring solution.

2) Not able to get any arbitrary precision in optimal

solution: Binary coded GAs have compulsion of

choosing precision before hand. More the

precision, larger the string length, and

therebyrequiring larger population. This

increases the computational complexity.

When real-coded genetic algorithms are used operators

crossover and mutation can be used directly to real

parameter values. Fitness values can be computed with

the direct use of decision variables. This helps in working

with selection operator. Only difficulty in real-coded

genetic algorithms is that of creation of new pairs of

offsprings from a pair of real-parameter decision

variables. Significant contribution towards the real-

parameter crossover and mutation operators is carried out

by [5], [26], [27].

Conceptual Tools for Selection Operator as used in

Real-coded Genetic Algorithms: One must understand

that though there are many papers published on the

application of real-coded genetic algorithms, there are

very few studies on theoretical understanding at the

conceptual level. This is reflected in the applied research

in the applications of the real-coded genetic algorithms.

Following are some of the studies highlighting selection

operator usage conceptualization. These studies focus on

two conceptual tools:



1) Search with blocking function

2) Distribution of the population using probability

density function.

Search with blocking function: The search in real

coded genetic algorithms causes retention of above

average solutions in the population. This is because real-

coded GAs starts treating continuous search spaces as

discrete search space problem there by behaving like

binary-coded GAs. This restricts the search to certain

blocks in search space. Only strong mutation can bring

some diffusion to create solutions in the outer domain.

The blocking function thus defined on the basis of virtual

alphabets, ensures global optimum within the block or

region. Otherwise it is difficult to find global optimum as

real-coded GAs will be converging at the intersection of

virtual characters of different decision variables [28].

Distribution of the population using probability density

function: The other conceptual tools used in

understanding the real-coded genetic algorithms are

probability density function denoted by πt. This gives

distribution of population at any generation t. This

probability density function is affected by the way the

selection and mutation operators are carried out on the

population. The combination of selection and mutation

operator helps to shift towards optimum in a unimodal

problem. The selection operator causes reduction in

variance of PIT whereas spread in distribution is caused

by mutation operator. This will approach Dirac function

for large number of generations. For areas above-average

fitness, selection operator alone increases the density. If

selection and crossover effect is seen it is observed that

the hyperplanes of higher fitness value are sampled more

frequently resulting in more frequent sampling of better

solutions. If schemata equivalence is to be considered

then intersecting hyperplanes means smaller regions or

areas for real-coded GAs giving higher-order schemata.

[29], [4].

The other aspect, which is to be looked into the

research on selection operator in real-coded genetic

algorithms, is the performance rating which takes us into

the domain of Software Engineering. In order to have the

performance rating of the real-coded genetic algorithms

we can further study it by applying a universally

practiced random scheme proposed through 80:20

principle.

VI. 80:20 PRINCIPLES AS APPLIED TO GENETIC

ALGORITHMS

80:20 principle is an empirically providing the test for

the nonlinearity [30]. It is also called Pareto Law. The

principle assertion of this law is that the majority of the

results, outputs or rewards are usually caused by very less

number of causes, inputs or efforts. Many of the

solutions are weaker and in genetic algorithm they are to

be disregarded. If the survival of the fittest strategy is to

be applied then it must be able to give us those solutions,

which are good even though their number is less. These

solutions need to be identified and multiplied. By

selecting 20% of these multiplied solutions and repeating

the different stages of algorithms the optimum solutions

can be achieved. It seems that this approach is special

case of proportionate selection method as applied in

genetic algorithms.

Some of the researchers have applied this principle in

their works ([31], [32]). They have claimed the avoidance

of premature convergence problem and finding most

critical paths respectively. In the ultimate analysis it is

observed that real-life problems involving practical

decision making, involves improvement in the directions

of effective constraints and keeping track of effective and

ineffective constraints if large number of constraints exist

[33]. If one applies real-coded genetic algorithm solution

using 80:20 rule, it has to incorporate these two issues

particularly in the selection scheme itself. The researchers

will have to work on the possibilities of quantifying the

heuristics to arrive at the decision parameters.

VIII. CONCLUSION AND FUTURE WORKS

The emphasis of this paper was on taking an overview

of applications of real-coded genetic algorithms with

emphasis on selection operator both at the application

level and performance analysis level using selection

operator. We have thus studied the selection operator

with its variations in genetic algorithm in general and

real-coded genetic algorithm in particular. We see the

diverse applications for which the real-coded genetic

algorithms are being used. Though, we could not find

much reference on selection operator comparisons at the

application level in real-coded genetic algorithm. The

experimental results, which are discussed in the paper,

are indicative of almost similar kind of output of research

in applications of real-coded genetic algorithm.

Discussing them will not add much differentiation as far

as applied research is concerned. Then we have seen the

analytical aspects for the use of real-coded genetic

algorithms with particular emphasis on selection operator.

We have also seen the research efforts in the performance

analysis using 80:20 rule.

From this study attempt it is humbly put that though

real-coded genetic algorithms are widely used in many

diverse applications, there is still large scope for further

research at the singleton ‘operator’ level. The

performance of the real-coded genetic algorithms with

distribution of the population using probability density

function with selection operator effect is discussed. This

line of research further can be utilized for performance

analysis in specific applications of the genetic algorithms

using real-coded alphabets. The author proposes to

undertake work in this regard and apply it to software

development effort and cost estimation that is open for

research due to changing modeling techniques including

agile process modeling.

ACKNOWLEDGMENT

This research is supported by the Cumulative

Professional Development Allowance given by the

Government of India through Ministry of Human

Resource Development.



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1025-1027, May 1994.

Anil S. Mokhade received Bachelor of Engineering degree in Mechanical Engineering

from Visvesvaraya National Institute of

Technology (formerly Visvesvaraya Regional College of Engineering), Nagpur, Maharashtra in

India in 1986 and Master of \ Technology degree in Computer Science and Engineering from Indian

Institute of Technology, Mumbai, India in 1988.

He has worked in industry for 2 years as Software Engineer and Scientist-B and for 3 years in government as Dy. CEO. He is currently

working as Asst. Professor in Dept. of Computer Science in VNIT, Nagpur. He has co-authored a book ‘Operating Systems’, New Delhi,

Macmillan Publishers India, 2008. His areas of interests are Software

Engineering, Software Architecture, Genetic Algorithms and Optimization, Operating Systems, Business Information Systems and

Business Analysis. He is currently perusing his doctoral research work in Genetic Algorithms.

Mr. Mokhade is Professional Member of ACM and Life Member of

Computer Society of India.

Omprakash G. Kakde received Bachelor of Engineering degree in Electronics and Power

Engineering from Visvesvaraya National Institute of Technology (formerly Visvesvaraya Regional

College of Engineering), Nagpur, India and

Master of Technology degree in Computer Science and Engineering from Indian Institute of

Technology, Mumbai, India in 1986 and 1989 respectively.

He received Ph.D. from Visvesvaraya National Institute of Technology,

Nagpur, India in 2004. His research interest includes theory of computer science, language processor, image processing, and genetic algorithms.

He is having over 22 years of teaching and research experience. Presently he is Director, Veermata Jijabai Technological Institute, India.

He is the author or co-author of more than thirty scientific publications

in international journals, international conferences, and national



conferences. He also authored five books on data structures, theory of computer science, and compilers. He also worked as the reviewer for

international and national journals, international conferences, and national conferences and seminars.

He is the life member of Institution of Engineers, India.



Documents

Overview of Selection Schemes In Real-Coded Genetic ... · the important properties of the genetic algorithms and then discusses the applications of real-coded genetic algorithms