genetic algorithm selection

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Genetic Algorithm SelectionSchemes

By: Mohammed MazaidaSupervisor : Dr. Eyas Alqawasmah


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Genetic Algorithm SelctionSchemes2

1. Introduction

Genetic Algorithms (GA) are probabilistic searchalgorithms, based on the model of natural evolution.

GA follow the idea of SURVIVAL OF THE FITTEST-Better and better solutions evolve from previousgenerations until a near optimal solution is obtained .

In computer world, genetic material (chromosomes)is replaced by strings of bits and natural selectionreplaced by fitness function.


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2. Basic Genetic Algorithm

1. Starting with an initial random n population whichare suitable solutions for the problem.

2. Evaluate the fitness of each individual ( solution ) inthe population. The fitness is a metric to indicatehow good an individual represents a solution of the

problem3. New individuals are introduced by crossover

operation, where at least two individuals of ageneration are chosen as 'parents'. Their genomes

are combined to produce children.


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Basic Genetic Algorithm ,,,cont

4. Mutation operation is performed by replacing apart of the child with a random value.

5. Select two parent chromosomes from a populationaccording to their fitness (the better fitness, thebigger chance to be selected) The idea is to

choose the better parents.6. Loop from step 2 until the end condition is satisfied,

and return the best solution in current population,


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Basic Genetic Algorithm ,,,cont

Describe

Problem

Generate

Initial

Solutions

Test: is initial

solution good enough?Stop

Select parents

to reproduce

Apply crossover process

and create a set of offspring

Apply random mutation

Yes

No


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Selection schemescont

Selection schemes characterized by several terms such as :

selection intensity IP expected average fitness value ofthe population after applying a selection method .

Selection variance is the expected variance of the fitnessdistribution of the population after applying the selectionmethod to the normalized Gaussian distribution

Loss of diversity proportion of individuals of a populationthat is not selected during the selection phase[1]


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The Selection schemes ,,,cont

Commonly used selection schemes:

Proportionate reproduction. Tournament selection.

Truncation selection

Linear ranking selection.


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3.1 Proportional Selection

also known as roulette-wheel selection

Parents are selected according to their fitness. Thebetter , the more chances to be selected

Can be imagined as roulette wheel where areplaced all individuals, every has its place bigaccordingly to its fitness function.

Then a marble is thrown there and selects theindividual . individuals with bigger fitness will beselected more times.


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Proportional Selectioncont

This can be simulated by following algorithm.

[Sum] Calculate sum of all chromosome fitnesses in

population - sum S. [Select] Generate random number from interval

(0,S)- r.

[Loop] Go through the population and sum fitnesses

from 0 - sum s. When the sum s is greater then r,stop and return the chromosome where you are.

Of course, step 1 is performed only once for eachpopulation.


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individual i in the population, its probability of beingselected is

where N is the number of individuals in thepopulation.

The time complexity of the algorithm is O(N).

Selection intensity

where is the mean variance of the fitness values ofthe population before selection.


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roulette-wheel selection algorithm [2]


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3.2 Tournament selection

Choose some number of individuals ( t) (tournamentsize )randomly from the population and select the best

individual from this group as parent.

Repeat N time.

No sorting of population is needed

It has the time complexity O(N).


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Tournament selectioncont

Selection intensity

Selection variance:

This method is not very useful when we use largepopulation because we will need a lot of N time tosearch every time on new element from the selectedgroup randomly


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Tournament selection ...cont

Gaussian fitness distribution approximately leads again toGaussian distributions after tournament selection (from leftto right: initial distribution, t =2, t = 5, t = 10).[2]


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Tournament selection ...cont

Properties of tournament selection[1]


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3.3 Truncation selection

Individuals are sorted according to their fitness.

Only the individuals above the threshold T areselected as parents.

As a sorting of the population is required, truncationselection has a time complexity of O(N ln N).


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Truncation selectioncont

Selection intensity

Selection Variance:


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Truncation selection algorithm [2]


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Properties of truncation selection[1]


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3.4 Linear Ranking Selection

For ranking selection the individuals are sortedaccording their fitness values and the rank N is

assigned to the best individual and the rank 1 to theworst individual.

The probability for the individual to be selected givenby


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Linear Ranking Selectioncont

As a sorting of the population is required, it

has a time complexity of O(N log N). Selection intensity

Where /N is the probability of the worstindividual to be Selected


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Linear ranking selection algorithm[2]


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Properties of linear ranking[1]


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Gaussian fitness distribution and the resulting distributionsafter performing ranking selection with - = 0.5 and - = 0(from left to right).[2]


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Conclusion

A genetic algorithm conceptually a simulation ofsteps inspired by the biological processes of

evolution. Selection schemes are use to choose the

individuals in the population that will create offspringfor the next generation.

Proportionate reproduction, Tournament selection,

Truncation selection and Linear ranking selectionare examples of selection schemes Selection schemes are characterized by selection

intensity, selection variance and loss of diversity.


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Reference

1. http://www.geatbx.com/docu/algindex-02.html

2. Blickle,T.,& Thiele,L.(1995). A comparison of selection

schemes used in genetic algorithms. (TechnicalReportNo.11).Gloriastrasse35,CH-8092 Zurich: Swiss Federal Institute ofTechnology (ETH) Zurich, Computer Engineering andCommunications Networks Lab(TIK).

3. Stuart Russell & Peter Norvig. Artificial Intelligence: A ModernApproach. 2 Edition / 2003

4. http://www.talkorigins.org/faqs/genalg/genalg.html5. BradL.Miller & DavidE.Goldberg (1996). Genetic Algorithms,

Selection Schemes, and the Varying effects of Noise.
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