Piecewise Linear Topology, Evolutionary Algorithms, and Optimization Problems

2012/06/28 by Andrew Clark, Clark, Andrew
Computer Science · Engineering · Mathematics · #Artificial Immune Systems Applications #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #General Topology (math.GN) #I.6.1 #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #Optimization and Control (math.OC) #cs.NE #math.GN #math.OC

paper · pdf · doi:10.48550/arxiv.1206.6722

PDF from Word docx, 11 pages, no figures

arxiv created 2012/06/28 · openalex publication_date 2012/06/28 · arxiv updated 2012/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to its less-than-global view. We show that moving the investigation into topological space improves our understanding of why EAs work.

Related

• Influence of Topological Features on Spatially-Structured Evolutionary Algorithms Dynamics
• Evolutionary algorithms
• Spontaneous organization leads to robustness in evolutionary algorithms
• Schemata Evolution and Building Blocks
• Analysis of the Effective Degrees of Freedom in Genetic Algorithms