Constrained Optimisation with the Fuzzy Clustering Evolution Strategy
In previously published work ,,  we have demonstrated that, by using a variant of the fuzzy clustering algorithm to provide multiple parent selection within the well-known Evolution Strategy paradigm, the Fuzzy Clustering Evolution Strategy (FCES) can help to preserve population diversity and maintain high convergence rates in fitness landscapes with “difficult” topological characteristics.
This paper describes an adaptation of the FCES to handle constrained optimisation problems. The constraint-handling method employed here is a version of the Behavioral Memory algorithm  which was chosen because of its minimal problem dependent a priori knowledge requirements and simplicity of implementation. An important requirement of this method is a search algorithm which enables a thorough exploration of the entire feasible region, even when this is not a connected domain. Schoenauer and Xanthakis  used a fitness sharing algorithm to achieve this, and here we demonstrate that our fuzzy-clustering approach is capable of promoting the required search characteristics without adversely affecting the rapid convergence for which the (μ,λ)- Evolution Strategy is renowned.
KeywordsFuzzy Cluster Fitness Landscape Bump Function Constraint Surface High Convergence Rate
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