Cumulative Step-size Adaptation on Linear Functions

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies the CSA-ES on composites of strictly increasing functions with affine linear functions through the investigation of its underlying Markov chains. Rigorous results on the change and the variation of the step size are derived with and without cumulation. The step-size diverges geometrically fast in most cases. Furthermore, the influence of the cumulation parameter is studied.Comment: arXiv admin note: substantial text overlap with arXiv:1206.120

Cumulative Step-size Adaptation on Linear Functions: Technical Report

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies the CSA-ES on composites of strictly increasing with affine linear functions through the investigation of its underlying Markov chains. Rigorous results on the change and the variation of the step size are derived with and without cumulation. The step-size diverges geometrically fast in most cases. Furthermore, the influence of the cumulation parameter is studied.Comment: Parallel Problem Solving From Nature (2012

Cumulative Step-size Adaptation on Linear Functions: Technical Report

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies the CSA-ES on composites of strictly increasing with affine linear functions through the investigation of its underlying Markov chains. Rigorous results on the change and the variation of the step size are derived with and without cumulation. The step-size diverges geometrically fast in most cases. Furthermore, the influence of the cumulation parameter is studied

Self-adaptation in evolution strategies

In this thesis, an analysis of self-adaptative evolution strategies (ES) is provided. Evolution strategies are population-based search heuristics usually applied in continuous search spaces which ultilize the evolutionary principles of recombination, mutation, and selection. Self-Adaptation in evolution strategies usually aims at steering the mutation process. The mutation process depends on several parameters, most notably, on the mutation strength. In a sense, this parameter controls the spread of the population due to random mutation. The mutation strength has to be varied during the optimization process: A mutation strength that was advantageous in the beginning of the run, for instance, when the ES was far away from the optimizer, may become unsuitable when the ES is close to optimizer. Self-Adaptation is one of the means applied. In short, self-adaptation means that the adaptation of the mutation strength is left to the ES itself. The mutation strength becomes a part of an individual’s genome and is also subject to recombination and mutation. Provided that the resulting offspring has a sufficiently “good” fitness, it is selected into the parent population. Two types of evolution strategies are considered in this thesis: The (1,lambda)-ES with one parent and lambda offspring and intermediate ES with a parental population with mu individuals. The latter ES-type applies intermediate recombination in the creation of the offspring. Furthermore, the analysis is restricted to two types of fitness functions: the sphere model and ridge functions. The thesis uses a dynamic systems approach, the evolution equations first introduced by Hans-Georg Beyer, and analyzes the mean value dynamics of the ES