Diversity Preservation in Evolutionary Algorithms
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Transcript of Diversity Preservation in Evolutionary Algorithms
Diversity Preservation in Evolutionary Algorithms
Jiří Kubalík
Intelligent Data Analysis Group
Department of Cybernetics
CTU Prague
Diversity Preservation in EAs2
EAs and Premature ConvergenceEAs and Premature Convergence Evolutionary cycle Homogeneous
population
Premature convergence - as the population gets homogeneous, only a little new can be evolved and EA converges to suboptimal solution.
Causes of premature convergence: improper representation and genetic operators, improper
selection pressure, insufficient population size, deception
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GA with Limited ConvergenceGA with Limited Convergence (GALCO)(GALCO)
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
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GALCOGALCO:: Algorithm Algorithm
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
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GALCO: replace_with_mask GALCO: replace_with_mask
Mask – vector of integer counters; stores a number of 1s for each bit of the representation
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Static Test ProblemsStatic Test Problems
Multimodal problem Deceptive problem
Hierarchical problem Royal Road Problem
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GALCO: Finding Optimal cGALCO: Finding Optimal c
multimodal
hierarchicalroyal road
deceptive
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GALCO: Comparison with SGAGALCO: Comparison with SGA
multimodal
hierarchicalroyal road
deceptive
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GALCO: Multimodal Optimization GALCO: Multimodal Optimization
Initial population SIGA
with replace_with_mask without
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GALCO: Multimodal Optimization GALCO: Multimodal Optimization (cnd.)(cnd.)
Initial population GALCO SGA
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GA with GA with Real-coded Binary Rep.Real-coded Binary Rep.
Motivation using redundant representation, where many different
genotypes map to the same phenotype would increase the explorative power of the EA and decrease the probability of getting stuck in a local optimum
Realization real coded binary representation
Effect population can not converge to the homogeneous state so that
the premature convergence can not take place
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Pseudo-binary representation – binary gene values coded by real numbers from the interval 0.0, 1.0
Example:
ch1 = [0.92 0.07 0.23 0.62]
ch2 = [0.65 0.19 0.41 0.86]
interpretation(ch1)=interpretation(ch2)=[1001]
Gene strength – gene’s stability measure The closer the real value is to 0.5 the weaker the gene is „one-valued genes“: 0.92 > 0.86 > 0.65 > 0.62 „zero-valued genes“: 0.07 > 0.19 > 0.23 > 0.41
GARB: Representation GARB: Representation
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GARB: Gene-strength AdaptationGARB: Gene-strength Adaptation
Every offspring gene is adjusted depending on its interpretation the relative frequency of ones at given position in the
population
Vector P[] stores the population statisticEx.: P[0.82 0.17 0.35 0.68]
82% of ones at the first position, 17% of ones at the second position, 35% of ones at the third position, 68% of ones at the fourth position.
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GARB: Gene-strength Adaptation GARB: Gene-strength Adaptation cnd.cnd.
Zero-valued gene:gene’ = gene + c*(1.0-P[i]) weakeninggene’ = gene – c*P[i] strengthening
One-valued genegene’ = gene + c*(1.0-P[i]) strengtheninggene’ = gene – c*P[i] weakening
c stands for a maximal gene-adaptation step: c (0.0,0.2
Gene value interpreted with above-average frequency at given position in the chromosome is weakened, the other one is strengthened.
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GARB: Gene-Strength Adaptation GARB: Gene-Strength Adaptation cnd.cnd.
Effect if some allele begines to prevail in the population,
1. the corresponding genes are weakened in subsequent generations,
2. at some point they are moved to the other side of the threshold 0.5,
3. so that they change their interpretation and the frequency of the allele decreases.
frequency of a given allele is controled by contradictory pressures
the convergence to optimal solution pressure and the population diversity preservation pressure
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GARB: Boosting-up the GARB: Boosting-up the ExploitationExploitation
Genotype of promising solutions should be stabilized for subsequent generations in order to disable rapid changes in their genotype
interpretation Newly generated solutions that are better than their parents
all genes are rescaled (strengthened) - zero-valued genes are set to be close to 0.0 and one-valued genes are set to be close to 1.0
Ex.:
ch = (0.71, 0.45, 0.18, 0.57)
ch’= (0.97, 0.03, 0.02, 0.99)
Effect Genes survive with uchanged interpretation through more
generations.
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GARB: AlgorithmGARB: Algorithm
1 begin2 initialize(OldPop)3 repeat4 calculate P[] from OldPop5 repeat6 select Parents from OldPop7 generate Children8 adjust Children genes9 evaluate Children10 if Child is better than Parents11 then rescale Child12 insert Children to NewPop13 until NewPop is completed14 switch OldPop and NewPop15 until termination condition16 end
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GARB: Results on Static ProblemsGARB: Results on Static Problems
0 100 200 300 400 5001300
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f itness ev aluations (x1000)
fitn
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GARBSGA
deceptive
F101
0 100 200 300 400 500500
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f itness ev aluations (x1000)
fitn
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GARBSGA
hierarchical
0 100 200 300 400 500-955
-900
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f itness ev aluations (x1000)
fitne
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GARBSGA
multimodal
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Single Gene Diversity MonitoringSingle Gene Diversity Monitoring
F101H
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rch
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rob
lem
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GARB: Tracking Moving OptimumGARB: Tracking Moving Optimum
Moving optimum Population diversity
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GARB: Results onGARB: Results on KnapsackKnapsack PProblrobleemm
Oscillating Knapsack Problem 14 objects, wi=2i, i=0,...,13
f(x)=1/(1+|target - wixi|)
Target oscillates between two values 12643 and 2837, which differ in 9 bits
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GARB: RecoveringGARB: Recovering from Homog. from Homog. StateState
DF3 Knapsack problem