Local Optima Networks for Continuous Fitness Landscapes

Abstract

Local Optima Networks (LONs) have been proposed as a coarsegrained model of discrete (combinatorial) fitness landscapes, where nodes are local optima and edges are search transitions based on an exploration search operator. This paper presents one of the first complex network analysis of continuous fitness landscapes. We use benchmark functions with well-known global structure, and an existing implementation of a Basin-Hopping algorithm to extract the networks. We also explore the impact of varying the Basin-Hopping perturbation step-size. Our results suggest that the landscape's connectivity pattern (global structure) strongly varies with the perturbation step-size, with extreme values of this parameter being detrimental to search and fragmenting the global structure. Our LON visualisations strikingly illustrate the landscape's global (funnel) structure, indicating that LONs serve as a tool for visualising high-dimensional functions.