5 research outputs found
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