3 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