130 likes | 247 Views
Mutation at Evolution Strategy. by Guido Moritz SoftComputingMethods 2006. 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.
E N D
Mutation at Evolution Strategy • by • Guido Moritz • SoftComputingMethods 2006
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 Aktion Integralanteil Reaktion Differentialanteil Proportionalanteil I P D x(t) Regelgröße by Ingo Rechenberg
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 • 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 • 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 GALTONs Nailboard (Nails vertical of wall) Leakage=distance between nails by Ingo Rechenberg
Selfadapting Leakage (StepSize) - Why ∆x2 ∆h2 ∆x1 ∆ ∆x1=∆x2 BUT ∆h1!=∆h2 ∆h1
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 • 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, ∂ σneu) • σ can addapt itself to problem • Δ-factor how strong is selfadapting of leakage • http://www.evocomp.de/themen/evolutionsstrategien/evostrat.html
Random Numbers • Constant allocated (same chance) • Gauß allocated
Random 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