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Chapter 1: GENETIC ALGORITHMS – AN INTRODUCTION

In recent years, Genetic Algorithms are gaining wide attention by the research community.

Genetic algorithm (GA) is rapidly growing area of Artificial Intelligence. It is categorised as

subclass of evolutionary algorithms. It is applicable to large number of optimisation

techniques in science and industry.

1.1 Optimisation- Need of an hour Optimisation is the process of making things better. Optimisation can be defined as the

science of determining the ‘best’ solutions to mathematically defined problems which are

often models of physical reality. It can also be defined as the process of finding solutions that

satisfy given constraints and achieve the objective at its optimal value [Fletcher 1980]. The

fundamental principle of optimisation algorithm is “search for an optimal state”. Optimisation

aims for efficient allocation of scarce resources. The bottleneck of optimisation is finding an

algorithm which solves a given class of problems. There are no methods which can solve all

optimisation problems. Optimisation is hard but finding the global optimum is much harder.

Optimisation algorithm either minimises or maximises the value of the objective function

depending upon certain criteria. It optimises certain properties of a system by pertinently

choosing the system parameters.

In other words, Optimisation is the process of adjusting the inputs or characteristics of a

device, mathematical process or experiment to find the minimum or maximum output or

result. The input consists of variables. The process or function is known as cost function or

objective function or fitness function and the output is known as cost or fitness [Fletcher

1980]. Optimisation varies the input to achieve desired output. The process of optimisation is

shown in Figure 1.1.

Input or variables function or process output or cost

Figure 1.1: Process of Optimisation

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Optimisation algorithms are categorised into two major groups – deterministic and

probabilistic [Weise 2007]. Deterministic algorithms do not contain instructions that use

random numbers in order to decide what to do or how to modify data. They employ heuristics

in order to define the processing order of solution candidates. Probabilistic algorithms find

their applications in problems where there is correlation between possible solutions and their

utility for a given problem. They are non-deterministic and employ random numbers for

finding solution. They are also referred to as stochastic algorithms.

Various types of optimisation algorithms and their classification is illustrated in hierarchical

diagram in Figure 1.2.

Figure 1.2 : Structural Hierarchy Of Optimisation Algorithms

1.2 Evolution- Nature’s Inspiration

Evolution is the basic principle of life. Evolution is a collective phenomenon of adapting to

the environment and survival in forthcoming generations [Ridley 1996]. Evolution is the

result of interplay between the creation of new genetic information and its evaluation and

selection. Since the population of organisms is continuously evolving, ratio of different

genetic types in organisms is also changing and new types are created.

Artificial Intelligence

Computational Intelligence-

Soft Computing

Evolutionary

Computation

OptimisationAlgorithms

Stochastic

or Probabilistic Monte Carlo Algorithms

Evolutionary Computation

MemeticAlgorithms

Swarm Intelligence

Ant Colony Optimisation

Particle Swarm

Optimisation

Artificial Bee Colony

Optimisation

Evolutionary Algorithms

Genetic Algorithms

Evolutionary Strategies

Differential Evolution

Genetic Programming

Learning Classifier System

Evolutionary Programming

Hill Climbing

TabuSearch

Simulated Annealing

Random Optimisation

Deterministic

State Space Search

Branch and Bound

Algebraic Geometry

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Genetic algorithms are based on Charles Darwin’s theory of evolution that describes the

principle of natural selection “Survival of Fittest”. Genetic algorithm imitates the process of

evolution and follows the process of natural selection. In this process of imitation, genetic

algorithm allows populations of potential solutions to optimisation problems to die or

reproduce with variations gradually becoming adapted to their environment.

Darwin’s ideas about the principles of life can be summarized by the following three basic

principles:

There is a population of individuals with different properties and abilities. An upper limit

for the number of individuals in a population exists.

Nature creates new individuals with similar properties to the existing individuals.

Promising individuals are selected more often for reproduction by natural selection.

Darwin described the idea of natural selection as foundation behind biological evolution in

his research ‘Origin of Species’ in 1859 and few lines describing the fact from his work are

reproduced.

“Owing to this struggle for life, variations, however slight and from whatever cause

proceeding, if they be in any degree profitable to the individuals of a species, in their

infinitely complex relations to other organic beings and to their physical conditions of life,

will tend to the preservation of such individuals, and will generally be inherited by the

offspring. The offspring, also, will thus have a better chance of surviving, for, of the many

individuals of any species which are periodically born, but a small number can survive. I

have called this principle, by which each slight variation, if useful, is preserved, by the term

Natural Selection.” [Darwin 1859]

Natural selection is probabilistic but favours the fittest individual in the generation. A single

individual of a population is affected by other individuals of the population as well as by the

environment. Individuals with an advantage have a greater chance for survive. Natural

selection results from the differing abilities of individuals to survive and reproduce in their

environment. Adaptation is a progressive increase in the degree to which a species becomes

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genetically well suited to its environment. A principal mechanism of adaptation is natural

selection, in which individuals superior in survival or reproductive ability in prevailing

environment contribute a disproportionate share of genes to future generations, thereby,

gradually increasing the frequency of favourable alleles in the whole population.

For example, the ancestors of giraffes had a short neck, but they had the habit of eating leaves

high up on the trees. As they reached for high leaves their necks became longer. The

character of longer neck was passed on to their descendants, making a long-necked giraffe

[Weblink1]. As a result of struggle for existence, "natural selection" is at work in nature,

allowing to survive only those individuals that are suitably adapted to the environment This is

called “survival of the fittest”. In the third edition of the Origin [Darwin 1861], Darwin

mentioned the neck of Giraffe as an adaptation for feeding as shown in Figure 1.3. Darwin

called it as beautiful adaptations in nature;—such as the long neck of the giraffe for browsing

on the branches of trees. In sixth edition of the Origin [Darwin 1872] that Darwin gave

consideration to the long neck as an adaptation for feeding. It inferences natural selection

plays a major role in this survival process.

Figure 1.3: Adaptation and Natural Selection in Giraffes

Image Source : [Weblink1]

Another example is Peppered Moth – Biston betularia. Before industrial revolution, the

common form of this moth – typica was light in colour with small dark spots which acted as

good camouflage on light coloured lichen. With increase in pollution, tree trunks became

dark and mutated form carbonaria became prevalent as shown in Figure 1.4. When moths

landed on these trees and other blackened surfaces, the dark coloured ones were harder to

spot by birds who ate them and, subsequently, they more often lived long enough to

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reproduce. Over generations, the environment continued to favour darker moths. As a result,

they progressively became more common. By 1895, 98% of the moths in the vicinity of

English cities like Manchester were mostly black [Weblink4]. Since the 1950's, due to

control measures for air pollution, amount of air pollutants has reduced. As a result, lichen

has grown back, making trees lighter in colour and natural selection favours lighter moth

variety - typica in non-polluted forests [Weblink3]. Adaptation over generations of peppered

moth is shown in Figure 1.5.

Figure 1.4: Natural Selection in Peppered Moth Figure 1.5: Adaptation over Generations

Image Source: [Weblink2] in Peppered Moth

Image Source: [Weblink3]

1.3 Biological Linkage – Cell and Genetics Cell is a basic unit of structure and function of living beings capable of all biological

activities and characteristics of life. Structurally, cell is a unit mass of protoplasm.

Protoplasm has four components – plasmalemma (cell membrane), cytoplasm, nucleus and

vacuoles. Nucleus is a specialised protoplasmic body which contains all the genetic

information for controlling cellular metabolism and transmission to the posterity. Nucleus has

its role in transmission of hereditary information [Boveri 1889,1892]. Nucleus contains

hereditary material called chromatin which is DNA protein complex and is required for

growth and development of organism, its reproduction, metabolism and behaviour

[Hammerling 1953]. Chromatin is made of a number of fine fibres that condense to form

chromosomes. Number of chromosomes is fixed for a species. Chromosomes occur singly or

in pairs. Hapolid refers to single set of chromosomes and diploid refers to two set of

chromosomes. Amoeba proteus contains 250 haploid chromosomes, Human beings have 23

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pairs of diploid chromosomes totalling to 46 chromosomes. Cell and its organisation is

depicted in Figure 1.6.

Chromosomes are thread like or rod like DNA protein hereditary structures which store,

replicate and transmit coded genetic information. Sutton and Boveri [Sutton 1902, Boveri

1902] proposed the chromosome theory of inheritance. It was established that chromosome is

the physical basis of inheritance and DNA is the chemical basis of inheritance. Shape and

size of chromosome differs from phase to phase in cell cycle. Chemical composition of

chromosomes is 40% DNA, 15% RNA, 50% Histone proteins, 8.5% Non-histone proteins,

traces of lipids and traces of minerals like Ca, Mg and Fe [Bonner et al. 1968].

DNA represents the hereditary or genetic material. It is double helix polynucleotide which is

long but lies packed in only a few micrometer long chromosome as shown in Figure 1.7.

DNA controls the inheritance of traits from one generation to the next through two processes

– Replication and Information Transfer [Gardener 1984].

Figure 1.6: Organisation of Life : Figure 1.7: Double Helix Structure

Cell-Nucleus-Chromosome-DNA-Gene of DNA ( 3 models)

Image Source: [Weblink5] Image Source: [Weblink6]

Chromosomes bear genes. All the hereditary information is located in the genes.

Chromosomes form a link between the offspring and the parents. Genes code the

characteristics of an individual. The possibilities of the genes for one property are called

allele and a gene can take different alleles [Sivanandam et al. 2007]. For example, there is a

gene for eye colour. Its possible alleles are black, brown, blue and green. Set of all possible

alleles present in particular population forms a gene pool. This gene pool determines all

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different possible variations for the future generations. The size of the gene pool helps in

determining the diversity of the individuals in the population. The set of all the genes of a

specific species is called genome. Each and every gene has an unique position on the genome

called the locus. Figure 1.8 shows the positions of various genes on the chromosomes in

different colours and Figure 1.9 depicts the gene constitution on a DNA molecule represented

by different colours.

Figure 1.8: Coloured Representation Figure 1.9: Gene Representation on

of Genes on Chromosome DNA Molecule

Image Source: [Weblink7] Image Source: [Weblink8]

Genetics is the study of biologically inherited traits including traits that are influenced in part

by the environment. Each species of a living organism has a unique set of inherited

characteristics. Inherited traits are determined by elements of heredity called genes that are

transmitted from parent to offspring in reproduction. Genes have an organisation within

chromosomes that can be changed and thus provide variation in the traits of organisms.

Genes not only have a basic role in the origin and life of individual organisms but they also

cause changes in populations through gene variations. Genetics deals with the inherent

mechanisms that control constancy and change in living organisms in contrast to evolution

that leads to progressive changes in the gene pool [Hartl 2001].

1.4 Cell Reproduction

Reproduction of species via genetic information is carried out by Mitosis or Meiosis. Mitosis

is cell division process in which chromosomes replicate and become equally distributed both

quantitatively and qualitatively into two daughter nuclei. It is also called somatic cell

division. Mitosis keeps all the somatic cells of an organism genetically similar. It is involved

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in asexual reproduction and regeneration. Mitosis ensures that each daughter cell has the

same genetic information as the mother cell. Mitosis is a process of nuclear division that

maintains the chromosome number when a somatic cell divides.

Meiosis is a double division which occurs in a diploid cell and gives rise to four haploid cells.

Meiosis represents sexual reproduction. Meiosis is a process in sexual reproduction through

which the chromosome number of diploid (2n) germ cells is reduced to half (n) in formation

of mature reproductive cells or gametes. It involves two successive cell divisions. Meiosis is

the mode of cell division that results in haploid daughter cells containing only one member of

each pair of chromosomes [Gardener 1984, Hartl 2001]. The process generates genetic

diversity because each daughter cell contains different set of alleles. Meiosis reduces diploid

number of chromosomes to the haploid number. Figure 1.10 shows the pictorial

representation of both Meiosis and Mitosis – cell division process.

Figure 1.10: Pictorial Differentiation of Meiosis and Mitosis

Image Source : [Weblink9]

1.5 Genotype and Phenotype Organisms may have multiple chromosomes in each cell. Genome refers to the complete set

of an organism’s genetic material. The term genotype refers to the particular set of genes

contained in a genome. Two individuals that have identical genomes are said to have the

same genotype. Phenotype refers to the physical and mental characteristics of trait

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corresponding to the genotype. An organism’s genotype is the set of genes that it carries. An

organism’s phenotype is all of its observable characteristics—which are influenced both by

its genotype and by the environment. For example, differences in the genotypes can produce

different phenotypes. In house cats, the genes for ear form are different, causing one of these

cats to have normal ears and the other to have curled ears (shown in Figure 1.11). Phenotype

is the outward, physical manifestation of the organism. Genotype is the internally coded,

inheritable information carried by all living organisms. This stored information is used as a

blueprint or set of instructions for building and maintaining a living creature. Figure 1.12

shows different phenotypes for eye colour in human beings.

Figure 1.11: Different Phenotypes for Cat’s Ears Figure 1.12: Different Phenotypes

for Human Eye Colour

Image Source : [Weblink10] Image Source : [Weblink11]

The relationship between the genotype and phenotype is that the Genotype codes for the

Phenotype. The internally coded, inheritable information, or Genotype, carried by all living

organisms, holds the critical instructions that are used and interpreted by the cellular

machinery of the cells to produce the outward, physical manifestation, or Phenotype of the

organism. A change in the environment also can affect the phenotype. For example pink

colour of flamingoes is not encoded into their genotype (See Figure 1.13). The food intake of

flamingoes makes their phenotype white or pink [Weblink10].

Figure 1.13: Phenotypic Difference due to Environment

Image Source : [Weblink10]

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1.6 Linkage between Nature and Computation

In the previous sections, evolution and biological concepts of genetics have been detailed. In

short, it can be said that evolution is cumulative genetic change in a population through time.

In the past few decades, various computational methods have been developed which have

their working inspired from the nature. One such computational method is Evolutionary

algorithm.

Evolutionary algorithms are generic, optimisation algorithms that are biology-inspired

mechanisms. Genetic algorithms are probabilistic algorithms categorised under evolutionary

algorithms. Nature is source of inspiration for them. Nature is itself the best example to solve

problems in an efficient and effective manner. Functioning of genetic algorithms is analogous

to natural evolution. Genetic algorithms have been developed for solving numerical and

combinatorial optimisation problems. In spite being artificial, Genetic Algorithms have the

tendency to solve the optimisation problems similar to natural phenomenon i.e. evolution.

The detailed functioning of genetic algorithm, its operators, its parameters and applications

are discussed in the following sections of the chapter.

1.7 Genetic Algorithm – Definition

Genetic algorithms were invented by John Holland in 1975 at University of Michigan as a

means of studying adaptive behaviour. Various definitions of genetic algorithms have been

coined by researchers of great repute.

John Holland presented genetic algorithm in his book Adaptation in Natural and Artificial

Systems in 1975 as an abstraction of biological evolution. He defined GA as: [Holland 1975]

“A method for moving from one population of "chromosomes" to a new

population by using a kind of "natural selection" together with the

genetics−inspired operators of crossover, mutation, and inversion”.

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David E. Goldberg in 1989 defined genetic algorithms as: [Goldberg 1989]

“Genetic Algorithms are adaptive heuristic search algorithms based on the

evolutionary ideas of natural selection and natural genetics”.

John Koza defined genetic algorithms as: [Koza 1992]

“Genetic algorithm is a mathematical algorithm that transforms a set of population of

mathematical objects ( typically fixed length binary character strings), each with an

associated fitness value, into a new set or new generation of the population of the

offshoring objects, using operations patterned after naturally occurring genetic operations

and the Darwinian principle of reproduction and survival for the fittest”.

Genetic algorithms were introduced by John Holland and subsequently studied by many

researchers. Genetic algorithm was found to be a general model of adaptive process but by far

the largest application of the technique is in the domain of optimisation.

Genetic algorithm is equated to Darwinian evolution. It works on Darwinian principle of

natural selection. Whether the specifications are non-linear, constrained, discrete, multimodal

or even NP-hard, genetic algorithm is entirely equal to the challenge.

1.8 GA – Contrast to Traditional Methods

Genetic algorithm differs from traditional or conventional algorithms. -

They work with a string coding of variables instead of simple variables. Coding of

variables discretizes the search space even if the function is continuous. Coding of

variables eliminates illegal and infeasible search space.

Genetic algorithm works with population of points instead of single point. This feature of

genetic algorithm avoids the algorithm getting trapped in local optima and helps the

algorithm to capture multiple optimal solutions easily. Genetic algorithm can use

previously found good information [Goldberg 1989].

Genetic algorithm works with fitness function information and can handle non differential

functions, discontinuous functions and multimodal functions with great ease.

Genetic algorithm’s transition scheme is probabilistic instead of fixed one. This is

because none of the GA operator works deterministically.

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1.9 Fitness Function Genetic algorithms are robust, stochastic optimisation algorithms which find the optimal

value for a particular objective function depending on the problem to be solved. The standard

approach to an optimisation problem begins by designing an objective function that can

model the problem’s objectives while incorporating any constraints. Objective function of an

optimisation technique corresponds to fitness function in genetic algorithm. Fitness function

helps to evaluate the chromosomes depending upon its fitness value. Fitness is proportional to

the utility or ability of individual which the chromosome represents. Measure of fitness helps

in evolving good solutions and implementing natural selection. Fitness function forms the

basis for selection and facilitates improvements in forthcoming generations. Mathematically,

fitness function is associated with maximising or minimising the value of fitness depending

on the problem to be solved. The fitness function can be any of the three types – firstly,

objective function representing mathematical model, computational model or computer

simulation, or subjective function where humans choose better solutions over worse ones or

lastly it can be co-evolved arising out of cooperative and competitive environments [Sastry

2002]. Fitness function should be problem specific. Fitness can be quantified by single

numerical fitness in single objective optimisation or as multiple measures in multi-objective

optimisation problem.

1.10 Descriptive Sketch of Genetic Algorithm

The genetic algorithm is a search algorithm that iteratively transforms a set of strings, each

with an associated fitness value, called a population into a new population of offspring

objects using the Darwinian principle of natural selection and using operations such as

crossover and mutation. Algorithm begins with a set of solutions represented by population of

chromosomes. Solutions from one population are taken and used to form a new population.

This is motivated by a hope that the new population will be better than the old one. Solutions

which are then selected to form new solutions (offspring) are selected according to their

fitness - the more suitable they are the more chances they have to reproduce. This is repeated

until some condition is satisfied.

The space of all feasible solutions is called search space or state space. Each point in the

search space represents one possible solution. Each possible solution can be marked by its

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value or fitness for the problem. The problem is that the search can be very complicated. One

may not know where to look for a solution or where to start. There are many methods one can

use for finding a suitable solution, but these methods do not necessarily provide the best

solution. Genetic Algorithms aids to look for the best solution among a number of possible

solutions.

A simple genetic algorithm that yields good results in many practical problems is composed

of four operators [De Jong 1975, Beasley et al. 1993a]:

i) Selection: This operator is an artificial version of natural selection based on Darwinian

survival of the fittest among string creatures. Reproduction operator can be implemented in

algorithmic form in a number of ways.

ii) Crossover: It occurs after reproduction or selection. It creates two new population or

strings from two existing ones by genetically recombining randomly chosen parts formed by

randomly chosen crossover point.

iii) Mutation: It is the occasional random alteration of the value of a string position. Mutation

creates a new string by altering value of existing string.

iv) Replacement: It is the last step in breeding step of any genetic algorithm cycle. It is used

to decide which individuals stay or get replaced in a population.

The following section describes in detail the sequence of steps in a genetic algorithm and

Figure 1.14 shows the pictorial representation of genetic algorithm in the form of a flowchart.

Steps in Basic Genetic Algorithm

1. [Start] Define the fitness function f(x) according to the problem definition.

2. [Initialise] Generate random population of n chromosomes – each chromosome being

the potential solution.

3. [Fitness] Evaluate the fitness f(x) of each chromosome x in the population.

4. [New population]Repeat the following steps to create the new population of

chromosomes:

a. [Selection] Select some parent chromosomes from a population according to

their fitness to form mating pool

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b. [Crossover] Mate the selected chromosomes as per given crossover probability

to form new offsprings.

c. [Mutation]Mutate new chromosomes as per given mutation probability.

d. [Replace] Replace the old population of chromosomes with the new

population.

5. [Convergence check] If the maximum number of generations is reached, then stop,

and return the best solution.

6. [Loop] Go to step 3

Figure 1.14: Basic flowchart of Genetic Algorithm

Encoding of a Chromosome:

Encoding of chromosomes is the first question to ask when starting to solve a problem with

genetic algorithm. A chromosome should in some way contain information about solution

that it represents. The most used way of encoding is a binary string. Each chromosome is

represented by a binary string (shown in Figure 1.15). Each bit in the string can represent

some characteristics of the solution. Another possibility is that the whole string can represent

a number. Of course, there are many other ways of encoding. The encoding depends mainly

Define fitness function

Generate initial population

Evaluate fitness of each chromosome

Selection

Crossover

Mutation

Replace old population by new generation

End

Convergence Check

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on the solved problem. For example, one can encode directly integer or real numbers,

sometimes it is useful to encode some permutations and so on.

gene

0 1 0 1 1 1 0 0 1 1

allele

Figure 1.15: Illustration of Binary Encoded Chromosome

Selection:

Chromosomes are selected from the population to be parents for crossover. The problem is

how to select these chromosomes. According to Darwin's theory of evolution the best ones

survive to create new offspring. There are many methods in selecting the best chromosomes.

Examples are roulette wheel selection, rank selection, steady state selection and some others.

Crossover:

Crossover depends upon the encoding scheme used for the problem. Crossover operates on

selected genes from parent chromosomes and creates new offspring. The simplest way of

performing crossover is to choose randomly some crossover point and copy everything before

this point from the first parent and then copy everything after the crossover point from the

other parent. There exist many other ways to perform crossover like n-point crossover,

uniform crossover, order crossover etc. Crossover can be quite complicated and depends

mainly on the encoding of chromosomes [Beasley et al. 1993b, Ryan 2000]. Specific

crossover made for a specific problem can improve performance of the genetic algorithm.

One point crossover operation on binary strings is illustrated in Figure 1.16.

Parent 1 1001101 1001110 Offspring 1

Parent 2 0101110 0101101 Offspring 2

Figure 1.16: Illustration of Crossover

Crossover Point

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Mutation: After a crossover is performed, mutation takes place. Mutation is intended to

prevent falling of all solutions in the population into a local optimum of the solved problem.

Mutation operation randomly changes the offspring resulted from crossover. In case of binary

encoding we can switch a few randomly chosen bits from 1 to 0 or from 0 to 1. Mutation can

be then illustrated as follows:

Chromosome A 101100101100101011100101

After Mutation 101000101100101011100101

Figure 1.17: Illustration of Mutation

The technique of mutation (as well as crossover) depends mainly on the encoding of

chromosomes. For example, in case of permutation encoding, mutation could be performed

as an exchange of two genes.

Replacement:

When a new generation of offsprings is produced, the next question is which of these newly

generated offsprings would move forward to the next generation and would replace which

chromosomes of the current generation. The answer to this question is based on Darwin’s

principle of “Survival of Fittest” [Fogel 1995]. So better fit individuals have more chances to

survive and carried forward to next generation leaving behind the less fit ones. The process of

forming next generation of individuals by replacing or removing some offsprings or parent

individuals is done by replacement operator. This process in evolution is known as

replacement scheme [Sivanandam et al. 2007]. Basically, there are two kinds of replacement

strategies for maintaining the population – generational replacement and steady state

replacement. In generational replacement, entire population of genomes is replaced at each

generation. In elitism, complete population of genome is replaced except for the best member

of each generation which is carried over to next generation without modification [Affenzeller

et al. 2009]. In this case, generations are non-overlapping. Steady state replacement involves

overlapping population which means only a small fraction of the population is replaced

during each iteration. In a steady state replacement, new individuals are inserted in the

population as soon as they are created [Sarma et al. 1997].

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1.11 Parameters of Genetic Algorithms A number of parameters control the precise operation of the genetic algorithm. They are:

a) Crossover probability: It is the measure of how often crossover will be performed. If there

is no crossover, offspring are exact copies of parents. If there is crossover, offspring are

made from parts of both parent's chromosome. If crossover probability is 100%, then all

offspring are made by crossover. If it is 0%, whole new generation is made from exact

copies of chromosomes from old population. Crossover is made in hope that new

chromosomes will contain good parts of old chromosomes and therefore the new

chromosomes will be better.

b) Mutation probability: It is the measure of how often parts of chromosome will be

mutated. If there is no mutation, offspring are generated immediately after crossover

without any change. If mutation is performed, one or more parts of a chromosome are

changed. If mutation probability is 100%, whole chromosome is changed, if it is 0%,

nothing is changed. Mutation generally prevents the genetic algorithm from falling into

local extremes and helps in recovering the lost genetic material. Mutation should not

occur very often, because then genetic algorithms would act as to random search.

c) Population size: It is the number of how many chromosomes are present in the population

(representing one generation). If there are too few chromosomes, genetic algorithm has

few options available for crossover and only a small part of search space is explored. On

the counterpart, if there are too many chromosomes in one population then the speed of

genetic algorithm slows down.

d) Selection Pressure: Each of the genetic operations - crossover, mutation or replacement

involves both parent and child chromosomes. The selection of parent chromosomes is

biased towards highly fit chromosomes. More fit chromosome is more likely to be a

parent than an unfit one in genetic operations. The selection pressure is defined as the

ratio between the probability that the most fit member of the population is selected as a

parent to the probability that an average member is selected as a parent. Too high

selection pressure would result in the population converging too early, sometimes leading

to premature convergence.

e) Number of Operations: The genetic algorithm starts off with a random population of

chromosomes. Genetic operations (crossover, mutation, replacement) are then applied

iteratively to the population. The parameter - number of operations is the number of

operators that are applied over the course of a genetic algorithm run.

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f) Elitism: When creating a new population by crossover and mutation, there are chances

that the best chromosome is lost. Elitism is the name of the method that first copies the

best chromosome (or few best chromosomes) to the new population [De Jong 1975]. The

rest of the population is constructed according to GA. Elitism can rapidly increase the

performance of GA, because it prevents a loss of the best found solution.

1.12 Applications of Genetic Algorithms

Genetic algorithms are powerful and broadly applicable stochastic search and optimisation

techniques. They have been used in large number of scientific and engineering problems and

models. Optimisation problems occur in many technical, economic and scientific projects like

cost, time, risk minimisation or quality, profit and efficiency maximisation. Thus the

development of general strategies is of great value.

Genetic Algorithms have wide implementation as function optimizer in different areas of

scientific and engineering applications. In certain applications, they are used as problem

solvers or basis for competent machine learning or computational model or as guiding

philosophy. Genetic algorithms have been used for NP-hard problems, for machine learning

and also for evolving simple programs. They have been also used for some art, for evolving

pictures and music.

Some of the applications of Genetic Algorithms are:

[Negnevitsky 2002, Lawrence 1989, Geoffrey et al. 1989, Grefenstette 1986, Natowicz et al.

1990, Meng et al. 1993, Meng et al. 1997]

Automobile Design: Genetic Algorithms are used to design composite materials and

aerodynamic shapes for racing cars and aviation vehicles. They can return

combinations of best materials and best engineering to provide faster, lighter, more

fuel efficient and safer vehicles.

Automatic Programming: They are used to evolve computer programs for specific

tasks and to design other computational structures as in Cellular automata and sorting

networks.

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Optimisation: Genetic algorithms are widely used for optimisation tasks including

both numerical and combinatorial optimisation problems such as Travelling Salesman

Problem, Circuit Design [Louis 1993], job shop scheduling [Goldstein 1991], video &

sound quality optimisation, Telecommunication routing, State assignment problem,

Time tabling problem, Traffic and Shipment routing etc.

Engineering Design: They are also used to optimise the structure and operational

design of buildings, factories, machines etc. They are used to design heat exchangers,

robot gripping arms, flywheels, turbines etc.

Robotics: Robot’s design is dependent on the job it is intended to do. So there are

many different designs for robots. A range of optimal designs and components can be

searched with the help of genetic algorithms for each specific use and return entirely

new type of robots.

Machine Learning: These algorithms are used for machine learning applications like

classification and prediction, protein structure prediction etc. They are also used to

design neural networks, to evolve rules for learning classifier systems and symbolic

production systems.

Economic Model: Genetic algorithms find their usage in modelling process of

innovation, development of bidding strategies and emergence of economic markets.

They are also applicable to develop new Finance and Investment strategies.

Ecological Model: Genetic algorithms are used to model ecological phenomena such

as biological arm races, host parasite evolution, symbiosis and resource flow in

ecologies.

Evolvable Hardware: Genetic algorithms are used develop computer models that use

stochastic operators to evolve new configurations from old ones so as develop new

electronic circuits that can be termed as evolvable hardware.

Strategy planning and Decision making: Genetic algorithms find their wide usage in

solving different business problems in functional areas such as finance, marketing,

and production. They can be used in activities like tactical information management,

grouping and network design, job scheduling for better decision making and

management.

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Game Playing: Genetic algorithms are also applied in Game theory and so they are

widely used in developing computer games, simulated environments.

Computer Aided Molecular Design: Creating novel designs of new chemical

molecules is emerging field of applied chemistry. Genetic algorithms are used to

understand chemical structures, analyse the effects of substitution and predict new

designs for chemical molecules like proteins, industrial chemicals etc.

Encryption and code breaking: Genetic algorithms can be used both to create

encryption for sensitive data as well as to break those codes.

Biomimetic Invention: Biomimicry or Biomimetics is an emerging area which

involves development of technologies inspired by designs in nature. Biomimetics uses

genetic algorithms as one of its design tool.

1.13 Summary

Living organisms’ exhibit extremely sophisticated learning, decision making and processing

abilities that allow them to survive and proliferate. Nature has always served as inspiration

for several scientific and technological developments. Genetic Algorithm is one such nature

inspired technique used to solve search and optimisation problems. Genetic algorithms are

based on the principles of evolution via natural selection, employing a population of

individuals that undergo selection in the presence of variation inducing operators such as

mutation and crossover. They find their usage in vast range of applications like search,

optimisation, decision making, machine learning, robotics and many more.