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.

-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.

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]).