Genetic Algorithms Tutorial

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AbouttheTutorial
This tutorial covers the topic of Genetic Algorithms. From this tutorial, you will be able to
understand the basic concepts and terminology involved in Genetic Algorithms. We will
also discuss the various crossover and mutation operators, survivor selection, and other
components as well.
Also, there will be other advanced topics that deal with topics like Schema Theorem, GAs
in Machine Learning, etc. which are also covered in this tutorial.
After going through this tutorial, the reader is expected to gain sufficient knowledge to
come up with his/her own genetic algorithms for a given problem.
Audience
This tutorial is prepared for the students and researchers at the undergraduate/graduate
level who wish to get “good solutions” for optimization problems “fast enough” which
cannot be solved using the traditional algorithmic approaches.
Prerequisites
Genetic Algorithms is an advanced topic. Even though the content has been prepared
keeping in mind the requirements of a beginner, the reader should be familiar with the
fundamentals of Programming and Basic Algorithms before starting with this tutorial.
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in this tutorial, please notify us at contact@tutorialspoint.com.

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TableofContents
About the Tutorial...................................................................................................................................i
Audience .................................................................................................................................................i
Prerequisites ...........................................................................................................................................i
Disclaimer & Copyright............................................................................................................................i
Table of Contents ...................................................................................................................................ii
1. GA – INTRODUCTION ......................................................................................................... 1
Introduction to Optimization..................................................................................................................1
What are Genetic Algorithms? ...............................................................................................................1
GA – Motivation.....................................................................................................................................3
2. GA – FUNDAMENTALS ....................................................................................................... 5
Basic Terminology ..................................................................................................................................5
Basic Structure .......................................................................................................................................7
3. GA – GENOTYPE REPRESENTATION.................................................................................... 9
Binary Representation............................................................................................................................9
Real Valued Representation ...................................................................................................................9
Integer Representation ........................................................................................................................10
Permutation Representation................................................................................................................10
4. GA – POPULATION ........................................................................................................... 11
Population Initialization .......................................................................................................................11
Population Models ...............................................................................................................................11
5. GA – FITNESS FUNCTION.................................................................................................. 12
6. GA – PARENT SELECTION ................................................................................................. 14
Fitness Proportionate Selection............................................................................................................14
Tournament Selection ..........................................................................................................................17

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Rank Selection......................................................................................................................................17
Random Selection ................................................................................................................................18
7. GA – CROSSOVER............................................................................................................. 19
Introduction to Crossover.....................................................................................................................19
Crossover Operators.............................................................................................................................19
8. GA – MUTATION .............................................................................................................. 22
Introduction to Mutation .....................................................................................................................22
Mutation Operators .............................................................................................................................22
9. GA – SURVIVOR SELECTION.............................................................................................. 24
Age Based Selection .............................................................................................................................24
Fitness Based Selection ........................................................................................................................25
10. GA – TERMINATION CONDITION...................................................................................... 26
11. GA – MODELS OF LIFETIME ADAPTATION ........................................................................ 27
Lamarckian Model................................................................................................................................27
Baldwinian Model ................................................................................................................................27
12. GA – EFFECTIVE IMPLEMENTATION................................................................................. 28
13. GA – ADVANCED TOPICS.................................................................................................. 31
Constrained Optimization Problems.....................................................................................................31
Basic Theoretical Background...............................................................................................................32
GA Based Machine Learning.................................................................................................................33
14. GA – APPLICATION AREAS................................................................................................ 35
15. GA – FURTHER READINGS ................................................................................................ 36

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Genetic Algorithm (GA) is a search-based optimization technique based on the principles
of Genetics and Natural Selection. It is frequently used to find optimal or near-optimal
solutions to difficult problems which otherwise would take a lifetime to solve. It is
frequently used to solve optimization problems, in research, and in machine learning.
IntroductiontoOptimization
Optimization is the process of making something better. In any process, we have a set
of inputs and a set of outputs as shown in the following figure.
Optimization refers to finding the values of inputs in such a way that we get the “best”
output values. The definition of “best” varies from problem to problem, but in mathematical
terms, it refers to maximizing or minimizing one or more objective functions, by varying
the input parameters.
The set of all possible solutions or values which the inputs can take make up the search
space. In this search space, lies a point or a set of points which gives the optimal solution.
The aim of optimization is to find that point or set of points in the search space.
WhatareGeneticAlgorithms?
Nature has always been a great source of inspiration to all mankind. Genetic Algorithms
(GAs) are search based algorithms based on the concepts of natural selection and genetics.
GAs are a subset of a much larger branch of computation known as Evolutionary
Computation.
GAs were developed by John Holland and his students and colleagues at the University of
Michigan, most notably David E. Goldberg and has since been tried on various optimization
problems with a high degree of success.
1. GA – Introduction

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In GAs, we have a pool or a population of possible solutions to the given problem.
These solutions then undergo recombination and mutation (like in natural genetics),
producing new children, and the process is repeated over various generations. Each
individual (or candidate solution) is assigned a fitness value (based on its objective function
value) and the fitter individuals are given a higher chance to mate and yield more “fitter”
individuals. This is in line with the Darwinian Theory of “Survival of the Fittest”.
In this way we keep “evolving” better individuals or solutions over generations, till we
reach a stopping criterion.
Genetic Algorithms are sufficiently randomized in nature, but they perform much better
than random local search (in which we just try various random solutions, keeping track of
the best so far), as they exploit historical information as well.
Advantages of GAs
GAs have various advantages which have made them immensely popular. These include
–
 Does not require any derivative information (which may not be available for many
real-world problems).
 Is faster and more efficient as compared to the traditional methods.
 Has very good parallel capabilities.
 Optimizes both continuous and discrete functions and also multi-objective
problems.
 Provides a list of “good” solutions and not just a single solution.
 Always gets an answer to the problem, which gets better over the time.
 Useful when the search space is very large and there are a large number of
parameters involved.
Limitations of GAs
Like any technique, GAs also suffer from a few limitations. These include –
 GAs are not suited for all problems, especially problems which are simple and for
which derivative information is available.
 Fitness value is calculated repeatedly which might be computationally expensive
for some problems.
 Being stochastic, there are no guarantees on the optimality or the quality of the
solution.
 If not implemented properly, the GA may not converge to the optimal solution.

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GA–Motivation
Genetic Algorithms have the ability to deliver a “good-enough” solution “fast-enough”. This
makes genetic algorithms attractive for use in solving optimization problems. The reasons
why GAs are needed are as follows:
Solving Difficult Problems
In computer science, there is a large set of problems, which are NP-Hard. What this
essentially means is that, even the most powerful computing systems take a very long
time (even years!) to solve that problem. In such a scenario, GAs prove to be an efficient
tool to provide usable near-optimal solutions in a short amount of time.
Failure of Gradient Based Methods
Traditional calculus based methods work by starting at a random point and by moving in
the direction of the gradient, till we reach the top of the hill. This technique is efficient and
works very well for single-peaked objective functions like the cost function in linear
regression. But, in most real-world situations, we have a very complex problem called as
landscapes, which are made of many peaks and many valleys, which causes such methods
to fail, as they suffer from an inherent tendency of getting stuck at the local optima as
shown in the following figure.

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Getting a Good Solution Fast
Some difficult problems like the Travelling Salesperson Problem (TSP), have real-world
applications like path finding and VLSI Design. Now imagine that you are using your GPS
Navigation system, and it takes a few minutes (or even a few hours) to compute the
“optimal” path from the source to destination. Delay in such real world applications is not
acceptable and therefore a “good-enough” solution, which is delivered “fast” is what is
required.

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This section introduces the basic terminology required to understand GAs. Also, a generic
structure of GAs is presented in both pseudo-code and graphical forms. The reader is
advised to properly understand all the concepts introduced in this section and keep them
in mind when reading other sections of this tutorial as well.
BasicTerminology
Before beginning a discussion on Genetic Algorithms, it is essential to be familiar with
some basic terminology which will be used throughout this tutorial.
 Population – It is a subset of all the possible (encoded) solutions to the given
problem. The population for a GA is analogous to the population for human beings
except that instead of human beings, we have Candidate Solutions representing
human beings.
 Chromosomes – A chromosome is one such solution to the given problem.
 Gene – A gene is one element position of a chromosome.
 Allele – It is the value a gene takes for a particular chromosome.
2. GA – Fundamentals

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 Genotype – Genotype is the population in the computation space. In the
computation space, the solutions are represented in a way which can be easily
understood and manipulated using a computing system.
 Phenotype – Phenotype is the population in the actual real world solution space in
which solutions are represented in a way they are represented in real world
situations.
 Decoding and Encoding – For simple problems, the phenotype and genotype
spaces are the same. However, in most of the cases, the phenotype and genotype
spaces are different. Decoding is a process of transforming a solution from the
genotype to the phenotype space, while encoding is a process of transforming from
the phenotype to genotype space. Decoding should be fast as it is carried out
repeatedly in a GA during the fitness value calculation.
For example, consider the 0/1 Knapsack Problem. The Phenotype space consists of
solutions which just contain the item numbers of the items to be picked.
However, in the genotype space it can be represented as a binary string of length
n (where n is the number of items). A 0 at position x represents that xth
item is
picked while a 1 represents the reverse. This is a case where genotype and
phenotype spaces are different.

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 Fitness Function – A fitness function simply defined is a function which takes the
solution as input and produces the suitability of the solution as the output. In some
cases, the fitness function and the objective function may be the same, while in
others it might be different based on the problem.
 Genetic Operators – These alter the genetic composition of the offspring. These
include crossover, mutation, selection, etc.
BasicStructure
The basic structure of a GA is as follows –
We start with an initial population (which may be generated at random or seeded by other
heuristics), select parents from this population for mating. Apply crossover and mutation
operators on the parents to generate new off-springs. And finally these off-springs replace
the existing individuals in the population and the process repeats. In this way genetic
algorithms actually try to mimic the human evolution to some extent.
Each of the following steps are covered as a separate chapter later in this tutorial.

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A generalized pseudo-code for a GA is explained in the following program:
GA()
initialize population
find fitness of population
while (termination criteria is reached) do
parent selection
crossover with probability pc
mutation with probability pm
decode and fitness calculation
survivor selection
find best
return best

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One of the most important decisions to make while implementing a genetic algorithm is
deciding the representation that we will use to represent our solutions. It has been
observed that improper representation can lead to poor performance of the GA.
Therefore, choosing a proper representation, having a proper definition of the mappings
between the phenotype and genotype spaces is essential for the success of a GA.
In this section, we present some of the most commonly used representations for genetic
algorithms. However, representation is highly problem specific and the reader might find
that another representation or a mix of the representations mentioned here might suit
his/her problem better.
BinaryRepresentation
This is one of the simplest and most widely used representation in GAs. In this type of
representation the genotype consists of bit strings.
For some problems when the solution space consists of Boolean decision variables – yes
or no, the binary representation is natural. Take for example the 0/1 Knapsack Problem.
If there are n items, we can represent a solution by a binary string of n elements, where
the xth
element tells whether the item x is picked (1) or not (0).
For other problems, specifically those dealing with numbers, we can represent the numbers
with their binary representation. The problem with this kind of encoding is that different
bits have different significance and therefore mutation and crossover operators can have
undesired consequences. This can be resolved to some extent by using Gray Coding, as
a change in one bit does not have a massive effect on the solution.
RealValuedRepresentation
For problems where we want to define the genes using continuous rather than discrete
variables, the real valued representation is the most natural. The precision of these real
valued or floating point numbers is however limited to the computer.
3. GA – Genotype Representation

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IntegerRepresentation
For discrete valued genes, we cannot always limit the solution space to binary ‘yes’ or ‘no’.
For example, if we want to encode the four distances – North, South, East and West, we
can encode them as {0,1,2,3}. In such cases, integer representation is desirable.
PermutationRepresentation
In many problems, the solution is represented by an order of elements. In such cases
permutation representation is the most suited.
A classic example of this representation is the travelling salesman problem (TSP). In this
the salesman has to take a tour of all the cities, visiting each city exactly once and come
back to the starting city. The total distance of the tour has to be minimized. The solution
to this TSP is naturally an ordering or permutation of all the cities and therefore using a
permutation representation makes sense for this problem.

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Population is a subset of solutions in the current generation. It can also be defined as a
set of chromosomes. There are several things to be kept in mind when dealing with GA
population –
 The diversity of the population should be maintained otherwise it might lead to
premature convergence.
 The population size should not be kept very large as it can cause a GA to slow down,
while a smaller population might not be enough for a good mating pool. Therefore,
an optimal population size needs to be decided by trial and error.
The population is usually defined as a two dimensional array of – size population, size
x, chromosome size.
PopulationInitialization
There are two primary methods to initialize a population in a GA. They are –
 Random Initialization – Populate the initial population with completely random
solutions.
 Heuristic initialization – Populate the initial population using a known heuristic
for the problem.
It has been observed that the entire population should not be initialized using a heuristic,
as it can result in the population having similar solutions and very little diversity. It has
been experimentally observed that the random solutions are the ones to drive the
population to optimality. Therefore, with heuristic initialization, we just seed the population
with a couple of good solutions, filling up the rest with random solutions rather than filling
the entire population with heuristic based solutions.
It has also been observed that heuristic initialization in some cases, only effects the initial
fitness of the population, but in the end, it is the diversity of the solutions which lead to
optimality.
PopulationModels
There are two population models widely in use –
Steady State
In steady state GA, we generate one or two off-springs in each iteration and they replace
one or two individuals from the population. A steady state GA is also known as
Incremental GA.
Generational
In a generational model, we generate ‘n’ off-springs, where n is the population size, and
the entire population is replaced by the new one at the end of the iteration.
4. GA – Population

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The fitness function simply defined is a function which takes a candidate solution to the
problem as input and produces as output how “fit” our how “good” the solution is with
respect to the problem in consideration.
Calculation of fitness value is done repeatedly in a GA and therefore it should be sufficiently
fast. A slow computation of the fitness value can adversely affect a GA and make it
exceptionally slow.
In most cases the fitness function and the objective function are the same as the objective
is to either maximize or minimize the given objective function. However, for more complex
problems with multiple objectives and constraints, an Algorithm Designer might choose
to have a different fitness function.
A fitness function should possess the following characteristics:
 The fitness function should be sufficiently fast to compute.
 It must quantitatively measure how fit a given solution is or how fit individuals can
be produced from the given solution.
In some cases, calculating the fitness function directly might not be possible due to the
inherent complexities of the problem at hand. In such cases, we do fitness approximation
to suit our needs.
5. GA – Fitness Function

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The following image shows the fitness calculation for a solution of the 0/1 Knapsack. It is
a simple fitness function which just sums the profit values of the items being picked (which
have a 1), scanning the elements from left to right till the knapsack is full.

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Parent Selection is the process of selecting parents which mate and recombine to create
off-springs for the next generation. Parent selection is very crucial to the convergence rate
of the GA as good parents drive individuals to a better and fitter solutions.
However, care should be taken to prevent one extremely fit solution from taking over the
entire population in a few generations, as this leads to the solutions being close to one
another in the solution space thereby leading to a loss of diversity. Maintaining good
diversity in the population is extremely crucial for the success of a GA. This taking up of
the entire population by one extremely fit solution is known as premature convergence
and is an undesirable condition in a GA.
FitnessProportionateSelection
Fitness Proportionate Selection is one of the most popular ways of parent selection. In this
every individual can become a parent with a probability which is proportional to its fitness.
Therefore, fitter individuals have a higher chance of mating and propagating their features
to the next generation. Therefore, such a selection strategy applies a selection pressure to
the more fit individuals in the population, evolving better individuals over time.
Consider a circular wheel. The wheel is divided into n pies, where n is the number of
individuals in the population. Each individual gets a portion of the circle which is
proportional to its fitness value.
Two implementations of fitness proportionate selection are possible –
Roulette Wheel Selection
In a roulette wheel selection, the circular wheel is divided as described before. A fixed
point is chosen on the wheel circumference as shown and the wheel is rotated. The region
of the wheel which comes in front of the fixed point is chosen as the parent. For the second
parent, the same process is repeated.
6. GA – Parent Selection

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It is clear that a fitter individual has a greater pie on the wheel and therefore a greater
chance of landing in front of the fixed point when the wheel is rotated. Therefore, the
probability of choosing an individual depends directly on its fitness.
Implementation wise, we use the following steps –
 Calculate S = the sum of a finesses.
 Generate a random number between 0 and S.
 Starting from the top of the population, keep adding the finesses to the partial
sum P, till P<S.
 The individual for which P exceeds S is the chosen individual.
Stochastic Universal Sampling (SUS)
Stochastic Universal Sampling is quite similar to Roulette wheel selection, however instead
of having just one fixed point, we have multiple fixed points as shown in the following
image. Therefore, all the parents are chosen in just one spin of the wheel. Also, such a
setup encourages the highly fit individuals to be chosen at least once.

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It is to be noted that fitness proportionate selection methods don’t work for cases where
the fitness can take a negative value.

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TournamentSelection
In K-Way tournament selection, we select K individuals from the population at random and
select the best out of these to become a parent. The same process is repeated for selecting
the next parent. Tournament Selection is also extremely popular in literature as it can even
work with negative fitness values.
RankSelection
Rank Selection also works with negative fitness values and is mostly used when the
individuals in the population have very close fitness values (this happens usually at the
end of the run). This leads to each individual having an almost equal share of the pie (like
in case of fitness proportionate selection) as shown in the following image and hence each
individual no matter how fit relative to each other has an approximately same probability
of getting selected as a parent. This in turn leads to a loss in the selection pressure towards
fitter individuals, making the GA to make poor parent selections in such situations.

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In this, we remove the concept of a fitness value while selecting a parent. However, every
individual in the population is ranked according to their fitness. The selection of the parents
depends on the rank of each individual and not the fitness. The higher ranked individuals
are preferred more than the lower ranked ones.
RandomSelection
In this strategy we randomly select parents from the existing population. There is no
selection pressure towards fitter individuals and therefore this strategy is usually avoided.

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In this chapter, we will discuss about what a Crossover Operator is along with its other
modules, their uses and benefits.
IntroductiontoCrossover
The crossover operator is analogous to reproduction and biological crossover. In this more
than one parent is selected and one or more off-springs are produced using the genetic
material of the parents. Crossover is usually applied in a GA with a high probability – 𝒑 𝒄.
CrossoverOperators
In this section we will discuss some of the most popularly used crossover operators. It is
to be noted that these crossover operators are very generic and the GA Designer might
choose to implement a problem-specific crossover operator as well.
One Point Crossover
In this one-point crossover, a random crossover point is selected and the tails of its two
parents are swapped to get new off-springs.
Multi Point Crossover
Multi point crossover is a generalization of the one-point crossover wherein alternating
segments are swapped to get new off-springs.
7. GA – Crossover

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Uniform Crossover
In a uniform crossover, we don’t divide the chromosome into segments, rather we treat
each gene separately. In this, we essentially flip a coin for each chromosome to decide
whether or not it’ll be included in the off-spring. We can also bias the coin to one parent,
to have more genetic material in the child from that parent.
Whole Arithmetic Recombination
This is commonly used for integer representations and works by taking the weighted
average of the two parents by using the following formulae –
 Child1 = α.x + (1-α).y
 Child2 = α.y + (1-α).x
Obviously, if α=0.5, then both the children will be identical as shown in the following image.

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Davis’ Order Crossover (OX1)
OX1 is used for permutation based crossovers with the intention of transmitting
information about relative ordering to the off-springs. It works as follows –
 Create two random crossover points in the parent and copy the segment between
them from the first parent to the first offspring.
 Now, starting from the second crossover point in the second parent, copy the
remaining unused numbers from the second parent to the first child, wrapping
around the list.
 Repeat for the second child with the parent’s role reversed.
There exist a lot of other crossovers like Partially Mapped Crossover (PMX), Order based
crossover (OX2), Shuffle Crossover, Ring Crossover, etc.

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IntroductiontoMutation
In simple terms, mutation may be defined as a small random tweak in the chromosome,
to get a new solution. It is used to maintain and introduce diversity in the genetic
population and is usually applied with a low probability – 𝒑 𝒎. If the probability is very high,
the GA gets reduced to a random search.
Mutation is the part of the GA which is related to the “exploration” of the search space. It
has been observed that mutation is essential to the convergence of the GA while crossover
is not.
MutationOperators
In this section, we describe some of the most commonly used mutation operators. Like the
crossover operators, this is not an exhaustive list and the GA designer might find a
combination of these approaches or a problem-specific mutation operator more useful.
Bit Flip Mutation
In this bit flip mutation, we select one or more random bits and flip them. This is used for
binary encoded GAs.
Random Resetting
Random Resetting is an extension of the bit flip for the integer representation. In this, a
random value from the set of permissible values is assigned to a randomly chosen gene.
Swap Mutation
In swap mutation, we select two positions on the chromosome at random, and interchange
the values. This is common in permutation based encodings.
8. GA – Mutation

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Scramble Mutation
Scramble mutation is also popular with permutation representations. In this, from the
entire chromosome, a subset of genes is chosen and their values are scrambled or shuffled
randomly.
Inversion Mutation
In inversion mutation, we select a subset of genes like in scramble mutation, but instead
of shuffling the subset, we merely invert the entire string in the subset.

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The Survivor Selection Policy determines which individuals are to be kicked out and which
are to be kept in the next generation. It is crucial as it should ensure that the fitter
individuals are not kicked out of the population, while at the same time diversity should
be maintained in the population.
Some GAs employ Elitism. In simple terms, it means the current fittest member of the
population is always propagated to the next generation. Therefore, under no circumstance
can the fittest member of the current population be replaced.
The easiest policy is to kick random members out of the population, but such an approach
frequently has convergence issues, therefore the following strategies are widely used.
AgeBasedSelection
In Age-Based Selection, we don’t have a notion of a fitness. It is based on the premise
that each individual is allowed in the population for a finite generation where it is allowed
to reproduce, after that, it is kicked out of the population no matter how good its fitness
is.
For instance, in the following example, the age is the number of generations for which the
individual has been in the population. The oldest members of the population i.e. P4 and P7
are kicked out of the population and the ages of the rest of the members are incremented
by one.
9. GA – Survivor Selection

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FitnessBasedSelection
In this fitness based selection, the children tend to replace the least fit individuals in the
population. The selection of the least fit individuals may be done using a variation of any
of the selection policies described before – tournament selection, fitness proportionate
selection, etc.
For example, in the following image, the children replace the least fit individuals P1 and
P10 of the population. It is to be noted that since P1 and P9 have the same fitness value,
the decision to remove which individual from the population is arbitrary.

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The termination condition of a Genetic Algorithm is important in determining when a GA
run will end. It has been observed that initially, the GA progresses very fast with better
solutions coming in every few iterations, but this tends to saturate in the later stages
where the improvements are very small. We usually want a termination condition such
that our solution is close to the optimal, at the end of the run.
Usually, we keep one of the following termination conditions –
 When there has been no improvement in the population for X iterations.
 When we reach an absolute number of generations.
 When the objective function value has reached a certain pre-defined value.
For example, in a genetic algorithm we keep a counter which keeps track of the generations
for which there has been no improvement in the population. Initially, we set this counter
to zero. Each time we don’t generate off-springs which are better than the individuals in
the population, we increment the counter.
However, if the fitness any of the off-springs is better, then we reset the counter to zero.
The algorithm terminates when the counter reaches a predetermined value.
Like other parameters of a GA, the termination condition is also highly problem specific
and the GA designer should try out various options to see what suits his particular problem
the best.
10. GA – Termination Condition

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Till now in this tutorial, whatever we have discussed corresponds to the Darwinian model
of evolution – natural selection and genetic variation through recombination and mutation.
In nature, only the information contained in the individual’s genotype can be transmitted
to the next generation. This is the approach which we have been following in the tutorial
so far.
However, other models of lifetime adaptation – Lamarckian Model and Baldwinian
Model also do exist. It is to be noted that whichever model is the best, is open for debate
and the results obtained by researchers show that the choice of lifetime adaptation is highly
problem specific.
Often, we hybridize a GA with local search – like in Memetic Algorithms. In such cases,
one might choose do go with either Lamarckian or Baldwinian Model to decide what to do
with individuals generated after the local search.
LamarckianModel
The Lamarckian Model essentially says that the traits which an individual acquires in
his/her lifetime can be passed on to its offspring. It is named after French biologist Jean-
Baptiste Lamarck.
Even though, natural biology has completely disregarded Lamarckism as we all know that
only the information in the genotype can be transmitted. However, from a computation
view point, it has been shown that adopting the Lamarckian model gives good results for
some of the problems.
In the Lamarckian model, a local search operator examines the neighborhood (acquiring
new traits), and if a better chromosome is found, it becomes the offspring.
BaldwinianModel
The Baldwinian model is an intermediate idea named after James Mark Baldwin (1896). In
the Baldwin model, the chromosomes can encode a tendency of learning beneficial
behaviors. This means, that unlike the Lamarckian model, we don’t transmit the acquired
traits to the next generation, and neither do we completely ignore the acquired traits like
in the Darwinian Model.
The Baldwin Model is in the middle of these two extremes, wherein the tendency of an
individual to acquire certain traits is encoded rather than the traits themselves.
In this Baldwinian Model, a local search operator examines the neighborhood (acquiring
new traits), and if a better chromosome is found, it only assigns the improved fitness to
the chromosome and does not modify the chromosome itself. The change in fitness
signifies the chromosomes capability to “acquire the trait”, even though it is not passed
directly to the future generations.
11. GA – Models of Lifetime Adaptation

Genetic Algorithms
28
GAs are very general in nature, and just applying them to any optimization problem
wouldn’t give good results. In this section, we describe a few points which would help and
assist a GA designer or GA implementer in their work.
Introduce problem-specific domain knowledge
It has been observed that the more problem-specific domain knowledge we incorporate
into the GA; the better objective values we get. Adding problem specific information can
be done by either using problem specific crossover or mutation operators, custom
representations, etc.
The following image shows Michalewicz’s (1990) view of the EA –
Reduce Crowding
Crowding happens when a highly fit chromosome gets to reproduce a lot, and in a few
generations, the entire population is filled with similar solutions having similar fitness.
This reduces diversity which is a very crucial element to ensure the success of a GA.
There are numerous ways to limit crowding. Some of them are –
12. GA – Effective Implementation

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29
 Mutation to introduce diversity.
 Switching to rank selection and tournament selection which have more
selection pressure than fitness proportionate selection for individuals with
similar fitness.
 Fitness Sharing – In this an individual’s fitness is reduced if the population
already contains similar individuals.
Randomization Helps!
It has been experimentally observed that the best solutions are driven by randomized
chromosomes as they impart diversity to the population. The GA implementer should be
careful to keep sufficient amount of randomization and diversity in the population for the
best results.
Hybridize GA with Local Search
Local search refers to checking the solutions in the neighborhood of a given solution to
look for better objective values.
It may be sometimes useful to hybridize the GA with local search. The following image
shows the various places in which local search can be introduced in a GA.

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30
Variation of parameters and techniques
In genetic algorithms, there is no “one size fits all” or a magic formula which works for all
problems. Even after the initial GA is ready, it takes a lot of time and effort to play around
with the parameters like population size, mutation and crossover probability etc. to find
the ones which suit the particular problem.

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31
In this section, we introduce some advanced topics in Genetic Algorithms. A reader looking
for just an introduction to GAs may choose to skip this section.
ConstrainedOptimizationProblems
Constrained Optimization Problems are those optimization problems in which we have to
maximize or minimize a given objective function value that is subject to certain constraints.
Therefore, not all results in the solution space are feasible, and the solution space contains
feasible regions as shown in the following image.
In such a scenario, crossover and mutation operators might give us solutions which are
infeasible. Therefore, additional mechanisms have to be employed in the GA when dealing
with constrained Optimization Problems.
13. GA – Advanced Topics

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32
Some of the most common methods are –
 Using penalty functions which reduces the fitness of infeasible solutions,
preferably so that the fitness is reduced in proportion with the number of constraints
violated or the distance from the feasible region.
 Using repair functions which take an infeasible solution and modify it so that the
violated constraints get satisfied.
 Not allowing infeasible solutions to enter into the population at all.
 Use a special representation or decoder functions that ensures feasibility of
the solutions.
BasicTheoreticalBackground
In this section, we will discuss about the Schema and NFL theorem along with the
building block hypothesis.
Schema Theorem
Researchers have been trying to figure out the mathematics behind the working of genetic
algorithms, and Holland’s Schema Theorem is a step in that direction. Over the year’s
various improvements and suggestions have been done to the Schema Theorem to make
it more general.
In this section, we don’t delve into the mathematics of the Schema Theorem, rather we
try to develop a basic understanding of what the Schema Theorem is. The basic
terminology to know are as follows –
 A Schema is a “template”. Formally, it is a string over the alphabet = {0,1,*},
where * is don’t care and can take any value.
Therefore, *10*1 could mean 01001, 01011, 11001, or 11011
Geometrically, a schema is a hyper-plane in the solution search space.
 Order of a schema is the number of specified fixed positions in a gene.

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33
 Defining length is the distance between the two furthest fixed symbols in the
gene.
The schema theorem states that this schema with above average fitness, short defining
length and lower order is more likely to survive crossover and mutation.
Building Block Hypothesis
Building Blocks are low order, low defining length schemata with the above given average
fitness. The building block hypothesis says that such building blocks serve as a foundation
for the GAs success and adaptation in GAs as it progresses by successively identifying and
recombining such “building blocks”.
No Free Lunch (NFL) Theorem
Wolpert and Macready in 1997 published a paper titled "No Free Lunch Theorems for
Optimization." It essentially states that if we average over the space of all possible
problems, then all non-revisiting black box algorithms will exhibit the same performance.
It means that the more we understand a problem, our GA becomes more problem specific
and gives better performance, but it makes up for that by performing poorly for other
problems.
GABasedMachineLearning
Genetic Algorithms also find application in Machine Learning. Classifier systems are a
form of genetics-based machine learning (GBML) system that are frequently used in
the field of machine learning. GBML methods are a niche approach to machine learning.

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34
There are two categories of GBML systems –
 The Pittsburg Approach – In this approach, one chromosome encoded one
solution, and so fitness is assigned to solutions.
 The Michigan Approach – one solution is typically represented by many
chromosomes and so fitness is assigned to partial solutions.
It should be kept in mind that the standard issue like crossover, mutation, Lamarckian or
Darwinian, etc. are also present in the GBML systems

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35
Genetic Algorithms are primarily used in optimization problems of various kinds, but they
are frequently used in other application areas as well.
In this section, we list some of the areas in which Genetic Algorithms are frequently used.
These are –
 Optimization - Genetic Algorithms are most commonly used in optimization
problems wherein we have to maximize or minimize a given objective function value
under a given set of constraints. The approach to solve Optimization problems has
been highlighted throughout the tutorial.
 Economics – GAs are also used to characterize various economic models like the
cobweb model, game theory equilibrium resolution, asset pricing, etc.
 Neural Networks – GAs are also used to train neural networks, particularly
recurrent neural networks.
 Parallelization – GAs also have very good parallel capabilities, and prove to be
very effective means in solving certain problems, and also provide a good area for
research.
 Image Processing – GAs are used for various digital image processing (DIP) tasks
as well like dense pixel matching.
 Vehicle routing problems - With multiple soft time windows, multiple depots and
a heterogeneous fleet.
 Scheduling applications – GAs are used to solve various scheduling problems as
well, particularly the time tabling problem.
 Machine Learning – as already discussed, genetics based machine learning
(GBML) is a niche area in machine learning.
 Robot Trajectory Generation – GAs have been used to plan the path which a
robot arm takes by moving from one point to another.
 Parametric Design of Aircraft – GAs have been used to design aircrafts by
varying the parameters and evolving better solutions.
 DNA Analysis – GAs have been used to determine the structure of DNA using
spectrometric data about the sample.
 Multimodal Optimization – GAs are obviously very good approaches for
multimodal optimization in which we have to find multiple optimum solutions.
 Traveling salesman problem and its applications – GAs have been used to
solve the TSP, which is a well-known combinatorial problem using novel crossover
and packing strategies.
14. GA – Application Areas

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The following books can be referred to further enhance the reader’s knowledge of
Genetic Algorithms, and Evolutionary Computation in general:
 Genetic Algorithms in Search, Optimization and Machine Learning by David E.
Goldberg.
 Genetic Algorithms + Data Structures = Evolutionary Programs by Zbigniew
Michalewicz.
 Practical Genetic Algorithms by Randy L. Haupt and Sue Ellen Haupt.
 Multi Objective Optimization using Evolutionary Algorithms by Kalyanmoy Deb.
15. GA – Further Readings

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