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Evolution Strategy: Mutations and Self-Adaptation in Black-Box Problem Solving

This work by Guido Moritz outlines the principles of Evolution Strategies (ES) aimed at optimizing black-box problems where explicit solutions are unavailable. It discusses generating new input through recombination and mutation of existing elements, along with the selection process based on fitness. Key concepts include the adaptation of mutation parameters via Rechenberg's 1/5 rule, which governs mutation step sizes based on success rates. The study emphasizes the importance of self-adaptation in finding optimal solutions, particularly through the enhancement of traditional rules for dynamic problem characteristics.

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Evolution Strategy: Mutations and Self-Adaptation in Black-Box Problem Solving

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  1. Mutation at Evolution Strategy • by • Guido Moritz • SoftComputingMethods 2006

  2. 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

  3. Target of Evolution Strategy Aktion Integralanteil Reaktion Differentialanteil Proportionalanteil I P D x(t) Regelgröße by Ingo Rechenberg

  4. 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

  5. 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)

  6. 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)

  7. Mutation – how to GALTONs Nailboard (Nails vertical of wall) Leakage=distance between nails by Ingo Rechenberg

  8. Selfadapting Leakage (StepSize) - Why ∆x2 ∆h2 ∆x1 ∆ ∆x1=∆x2 BUT ∆h1!=∆h2 ∆h1

  9. 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 • ∂= ∂;

  10. 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

  11. Random Numbers • Constant allocated (same chance) • Gauß allocated

  12. 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 getting smaller

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