Towards population-based fitness landscape analysis using local optima networks

Abstract

A fitness landscape describes the interaction of a search domain, a cost function on designs drawn from the domain, and a neighbourhood function defining the adjacency of designs - - induced by the optimisation method used. Fitness landscapes can be represented in a compact form as Local Optima Networks (LONs). Although research has been conducted on LONs in continuous domains, the majority of work has focused on combinatorial landscapes. LONs are often used to understand the landscape encountered by population-based search heuristics, but are usually constructed via point-based search. This paper proposes the first construction of LONs by a population-based algorithm, applied to continuous optimisation problems. We construct LONs for three benchmark functions with well-known global structure using the widely used Nelder-Mead downhill simplex algorithm, and contrast these to the LONs from a point-based approach. We also investigate the sensitivity of the LON visualisation to the downhill simplex algorithm's hyperparameters, by varying the initial step size of the simplex and the step size for connectivity of optima. Our results suggest that large initial simplex sizes fragment the landscape structure, and exclude some local optima from the fitness landscape.