Mutation at Evolution Strategy Mutation at Evolution Strategy

Mutation at Evolution Strategy Mutation at Evolution Strategy

by

Guido Moritz

SoftComputingMethods 2006

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

Target of Evolution Strategy Target of Evolution Strategy

Regler Strecke

Stellgröße y Regelgröße x

Sollwert w

Störgröße z

P I D

Proportional anteil

Integralant

eil Differentiala nteil

x(t)

Aktion Reaktion

Regelgr

öße by Ingo Rechenberg

Evolution Strategy – how to Evolution 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

Evolution Strategy – how to Evolution 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)

Mutation – how to Mutation – 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)

Mutation – how to Mutation – how to

GALTONs Nailboard (Nails vertical of wall)

by Ingo Rechenberg

Leakage=distance between nails

Selfadapting Leakage (StepSize) - Selfadapting Leakage (StepSize) -

Why Why

∆x1

∆h1

∆x2

∆h2

∆x1=∆x2 BUT

∆h1!=∆h2

∆

Rechenberg 1/5 Rule Rechenberg 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

∂= ∂;

Problems Problems

• 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

Random Numbers Random Numbers

• Constant allocated (same chance)

• Gauß allocated

Random Numbers Random Numbers

• Take quadratic values – Gaußnarrow/higher

– Constandbigger values

• Group numbers

– Constand  getting closer to avarage

• Effect of both (quadrativ&group)

– Difference between values and avarage is