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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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Proportional Selectioncont
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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Proportional Selectioncont
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 selectioncont
Truncation selection algorithm [2]
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Truncation selectioncont
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 Selectioncont
Linear ranking selection algorithm[2]
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Linear Ranking Selectioncont
Properties of linear ranking[1]
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Linear Ranking Selectioncont
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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