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University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Mutation at Evolution StrategyMutation at Evolution Strategy
by
Guido Moritz
SoftComputingMethods 2006
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Target of Evolution Strategy Target of Evolution Strategy
Find a solution for BlackBoxProblems (no explicit solution) wich is exactly enough.
INPUT OUTPUT
EXAMPLE: FIND AN INPUT WHERE THE OUTPUT IS MAXIMUM
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Target of Evolution StrategyTarget of Evolution Strategy
Regler Strecke
Stellgröße y Regelgröße xSollwert w
Störgröße z
P I D
Proportionalanteil
Integralanteil
Differentialanteil
x (t)
AktionReaktion
Regelgröße
by Ingo Rechenberg
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Evolution Strategy – how toEvolution Strategy – how to
• Genererating new elements by recombination/variation of existing elements
• Choose good and bad elements (because of difference between OUTPUTS)
• Take good ones for next generation (recombination/variation) - > creating new INPUTS
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Evolution Strategy – how toEvolution Strategy – how to
• Creating elements randomly• Select parents (by random)• Recombination of parents• Mutation• Choose because of fitness• Generating new generation
Xneu=Xalt+∂*N(0,σ)
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Mutation – how toMutation – how to
• Changing a value by f.e. adding or substracting a small normal distributed (avarage=0) value with a standard variance (dt. standartabweichung)
• How big changing-decided by ∂ and standart variance of N()
• Xneu=Xalt+∂*N(0,σ)
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Mutation – how toMutation – how to
GALTONs Nailboard(Nails vertical of wall)
by Ingo Rechenberg
Leakage=distance between nails
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Selfadapting Leakage (StepSize) - Selfadapting Leakage (StepSize) - WhyWhy
∆x1
∆h1
∆x2∆h2
∆x1=∆x2BUT
∆h1!=∆h2
∆
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Rechenberg 1/5 RuleRechenberg 1/5 Rule
If 1/5 of mutations are better (better fitness) decrease leakage!
If sucess<1/5∂= ∂*1,5;
Else if (sucess>1/5) ∂= ∂/1,5;
Else ∂= ∂;
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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ProblemsProblems
• Rechenbergs Rule is static and depends not on problem itself (maybe only local optimum)
Schwefel enhanced Rechenbergs Rule (∂ takes part at evolution): σ neu := σ alt e^N(0,Δ)⋅
xneu := xalt + ∂ *N(0, ∂ σ neu)• σ can addapt itself to problem• Δ-factor how strong is selfadapting of leakage
http://www.evocomp.de/themen/evolutionsstrategien/evostrat.html
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Random NumbersRandom Numbers
• Constant allocated (same chance)• Gauß allocated
University of Rostock Institute of Applied Microelectronics and Computer Engineering
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Random NumbersRandom Numbers
• Take quadratic values– Gaußnarrow/higher– Constandbigger values
• Group numbers– Constand getting closer to avarage
• Effect of both (quadrativ&group)– Difference between values and avarage is
getting smaller