2012/06/06 by Alexandre Chotard, Alexandre Adrien Chotard, Chotard, Alexandre Adrien +4 · 2 citations
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Metaheuristic Optimization Algorithms Research #Optimization and Search Problems #cs.LG
paper · pdf · doi:10.48550/arxiv.1206.1208
Parallel Problem Solving From Nature (2012)
openalex publication_date 2012/06/06 · arxiv created 2012/06/29 · arxiv updated 2012/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.