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Evolution Strategies

Evolution Strategies. Originally developed in Germany in the early 60s with Rechenberg and Schwefel being the main contributors. Main ideas include:

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Evolution Strategies

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  1. Evolution Strategies • Originally developed in Germany in the early 60s with Rechenberg and Schwefel being the main contributors. Main ideas include: • floating point representation with standard derivation: (x,) where x is a vector in n-dimensional space and  is the standard derivation that influeces how solutions are changed: x’= x + N(0, ). • mutation is the sole operator. • in most approaches  is changed dynamically (e.g. using Rechenberg’s 1/5 Rule). • employs a two-member evolution strategy. • Was later generalized to support multi-membered evolution strategies: • employs: uniform crossover and averaging crossover. • each member of the population has the same chance to reproduce (selection doesn’t consider fitness). • weakest individual is eliminated to keep a constant population size.

  2. -ES and -ESs. • developed by H.P. Schwefel: 2-member population ((1+1)-ES) is generalized to multi-membered populations. 2 approaches are supported • ()-ES: •  individuals produceoffsprings • the population consisting ofindividuals (the old generation and the parents) is reduced to  using selection. • relies on replacement • ()-ESs: • lifetime of individuals is limited to one generation. •  individual produce  offsprings ( > ) with the best  surviving. • generates the new generation from the scratch • Moreover, the standard deviation undergoes evolution.

  3. Evolutionsstrategie and GAs • Differences ES and trad. GAs : • real-code (ES) vs. binary string representation (GA) • selection is performed implicitly by removing unfit individual deterministically (ES); GAs employ a stoachastic selection process, and does not rely on removal.. • selection after recombination (ES); selection before recombination (GA). • different handling of constraints: ES supports un-equalities as a part of the problem specification, and disqualifies illegal offspring; moreover, ES adjusts control parameters if illegal offspring occur too frequently. GAs, on the other hand, employ penalty functions. • mutation is less important for traditional GAs; crossover is less important for ESs. • Some scientists, e.g. Fogel, claim that ES and GAs are not fundamentally different (see also Hoffmeister’s paper [141]).

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