Real Coding Crossover Survery (Amgad)

8/3/2019 Real Coding Crossover Survery (Amgad)

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Real coding Crossover survey

methodsAmgad. M. Mohammed

Department of operations research

Menofia University

For more information or interest research Area in Genetic Evolution and

Quantum Evolutionary algorithms. Dont hesitate please send mail

[email protected]


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Genetic Algorithms

An Example Genetic Algorithm

Procedure GA{

t = 0;

Initialize P(t);

Evaluate P(t);

While (Not Done)

{

Parents(t) = Select_Parents(P(t));

Offspring(t) = Procreate(Parents(t));

Evaluate(Offspring(t));P(t+1)= Select_Survivors(P(t),Offspring(t));

t = t + 1;

}


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Genetic Algorithms

Representation of Candidate Solutions

GAs on primarily two types of representations:

Binary-Coded

Real-Coded

Permutation Representations (TSP) each n occurs exactly once


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Genetic Algorithms:

Binary-Coded Representations

For Example, lets say that we are trying to optimize the

following function,

f(x) = x2

for 2 u x u 1

If we were to use binary-coded representations we would

first need to develop a mapping function form our

genotype representation (binary string) to our phenotype

representation (our CS). This can be done using thefollowing mapping function:

d(ub,lb,l,chrom) = (ub-lb) decode(chrom)/2l-1 + lb


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Genetic Algorithms:

Binary Coded Representations

Individual

Chromosome: 00101

Fitness = ?????

d(2,1,5,00101) = 1.16 f(1.16) = 1.35

Individual

Chromosome: 00101

Fitness = 1.35

The Fitness Assignment Process for Binary Coded

Chromosomes (ub=2, lb=1, l=5)


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Genetic Algorithms:

Real-Coded Representations

Individual

Chromosome: 1.16

Fitness = ?????

f(1.16) = 1.35

Individual

Chromosome: 1.16

Fitness = 1.35

The Fitness Assignment Process for Real Coded Chromosomes


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Genetic Algorithms:

Parent Selection Methods

An Example Genetic Algorithm

Procedure GA{

t = 0;

Initialize P(t);

Evaluate P(t);

While (Not Done)

{

Parents(t) = Select_Parents(P(t));

Offspring(t) = Procreate(Parents(t));

Evaluate(Offspring(t));P(t+1)= Select_Survivors(P(t),Offspring(t));

t = t + 1;

}


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Crossover OR Mutation

Exploration: Discovering promising areas in the

search space

Exploitation: Optimising within a promising area

Crossover is explorative, it makes a bigjump to

an area in search space

Mutation is exploitative, it creates random small

diversions, thereby staying near


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Cont


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1) Simulated Binary Crossover (SBX)

SBX was designed with respect to the one-point

crossover properties in binary-coded GA.

Average Property:

The average of the decoded parameter values is the same

before and after the crossover operation.

Spread Factor Property:

The probability of occurrence of spread factor 1 is more

likely than any other value.


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SBX cont..


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2) Arithmetical crossover


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Arithmetical crossover cont..

Arithmetic crossover is better when the set is convex ,

because I'm sure that Individuals will be feasible


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Arithmetical crossover cont..


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Arithmetical Crossover cont


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Other names and techniques for Arithmetic


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3) Heuristic crossover

which was applied to produce one offspring from A pair

of parents with a bias towards the better one


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4) Flat Crossover

in which an offspring was generated randomly between

the genes of the parents


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5) Blend Crossover (BLX-)


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Blend Crossover (BLX-) cont

If I measure distance between x1 & x2 and take half distance

Then subtract half distance from x1

And Add half distance to x2


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6) Laplace crossover

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Real Coding Crossover Survery (Amgad)