Computationally Efficient Local Optima Network Construction

Abstract

There has been an increasing amount of research on the visualisation of search landscapes through the use of exact and approximate local optima networks (LONs). Although there are many papers available describing the construction of a LON, there is a dearth of code released to support the general practitioner constructing a LON for their problem. Furthermore, a naive implementation of the algorithms described in work on LONs will lead to inefficient and costly code, due to the possibility of repeatedly reevaluating neighbourhood members, and partially overlapping greedy paths. Here we discuss algorithms for the efficient computation of both exact and approximate LONs, and provide open source code online. We also provide some empirical illustrations of the reduction in the number of recursive greedy calls, and quality function calls that can be obtained on NK model landscapes, and discretised versions of the IEEE CEC 2013 niching competition tests functions, using the developed framework compared to naive implementations. In many instances multiple order of magnitude improvements are observed.