Evolution Strategies for Genetic Algorithms

Evolution Strategies is inspired by the theory of evolution by means of natural selection. Specically, the technique is inspired by macro-level or the species-level process of evolution (phenotype, hereditary, variation) and is not concerned with the genetic mechanisms of evolution (genome, chromosomes, genes, alleles).

The objective of the Evolution Strategies algorithm is to maximize the suitability of collection of candidate solutions in the context of an objective function from a domain. The objective was classically achieved through the adoption of dynamic variation, a surrogate for descent with modication, where the amount of variation was adapted dynamically with performance-based heuristics. Contemporary approaches co-adapt parameters that control the amount and bias of variation with the candidate solutions.

Instances of Evolution Strategies algorithms may be concisely described with a custom terminology in the form (μ; λ), where μ is number of candidate solutions in the parent generation, and λ is the number of candidate solutions generated from the parent generation. In this configuration, the best μ are kept if λ > μ>1. In addition to the so-called comma-selection Evolution Strategies algorithm, a plus-selection variation may be defined (μ+ λ), where the best members of the union of the μ and λ generations compete based on objective fitness for a position in the next generation.

Evolution Strategies uses problem specic representations, such as real values for continuous function optimization. The ratio of μ to λ influences the amount of selection pressure (greediness) exerted by the algorithm.

A contemporary update to the algorithms notation includes a ρ as (μ/ρ; λ) that species the number of parents that will contribute to each new candidate solution using a recombination operator. A classical rule used to govern the amount of mutation (standard deviation used in mutation for continuous function optimization) was the 1/5 -rule, where the ratio of successful mutations should be 1/5 of all mutations. If it is greater the variance is increased, otherwise if the ratio is is less, the variance is decreased.

The comma-selection variation of the algorithm can be good for dynamic problem instances given its capability for continued exploration of the search space, whereas the plus-selection variation can be good for renement and convergence.