Genetic Algorithm with Limited Convergence1

GAs and Premature GAs and Premature ConvergenceConvergence

Premature convergence - GAs converge too early to suboptimal solution as the population gets homogeneous, only a little new can

be evolved

Reasons for premature convergence:

improper selection pressure

insufficient population size

deception

improper representation and genetic operators

Genetic Algorithm with Limited Convergence2

Motivation and RealizationMotivation and Realization Motivation – to maintain a diversity of the evolved population

and extend the explorative power of the algorithm

Realization Convergence of the population is allowed up to specified extent Convergence at individual positions of the representation is

controlled Convergence rate – specifies a maximal difference in the frequency

of ones and zeroes in every column of the population ranges from 0 to PopSize/2

Principal condition – at any position of the representation neither ones nor zeroes can exceed the frequency constraint

Specific way of modifying the population genotype

Genetic Algorithm with Limited Convergence3

GALCO AlgorithmGALCO AlgorithmGALCO – Genetic Algorithms with Limited

Convergence

1. Generate initial population

2. Choose parents

3. Create offspring

4. if (offspring > parents)

then

replace parents with offspring

else{

find(replacement)

replace_with_mask(child1, replacement)

find(replacement)

replace_with_mask(child2, replacement)

}

5. if (not finished) then go to step 2

Genetic Algorithm with Limited Convergence4

Operator Operator replace_with_maskreplace_with_mask

Mask – vector of integer counters; stores a number of 1s for each bit of the representation

50

Genetic Algorithm with Limited Convergence5

Testovací úlohy - statickéTestovací úlohy - statické F101(x, y) Deceptive function

Hierarchická funkce

Royal Road Problem

Genetic Algorithm with Limited Convergence6

GALCO – vliv parametru CGALCO – vliv parametru C

Genetic Algorithm with Limited Convergence7

GALCO vs. SGAGALCO vs. SGA

Genetic Algorithm with Limited Convergence8

Multimodal Optimization Multimodal Optimization

Initial population SIGA

with replace_with_mask without replace_with_mask

Genetic Algorithm with Limited Convergence9

Multimodal Optimization Multimodal Optimization (cont.)(cont.)

Initial population GALCO SIGA