Computationally Efficient Local Optima Network Construction

The codebase for this paper is available at https://github.com/fieldsend/local_optima_networksThere 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.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/N017846/1]. The author would like to thank Sébastien Vérel and Gabriela Ochoa for providing inspirational invited talks on LONs at the University of Exeter during this grant, and also Ozgur Akman, Khulood Alyahya and Kevin Doherty

Insights into the feature selection problem using local optima networks

The binary feature selection problem is investigated in this paper. Feature selection fitness landscape analysis is done, which allows for a better understanding of the behaviour of feature selection algorithms. Local optima networks are employed as a tool to visualise and characterise the fitness landscapes of the feature selection problem in the context of classification. An analysis of the fitness landscape global structure is provided, based on seven real-world datasets with up to 17 features. Formation of neutral global optima plateaus are shown to indicate the existence of irrelevant features in the datasets. Removal of irrelevant features resulted in a reduction of neutrality and the ratio of local optima to the size of the search space, resulting in improved performance of genetic algorithm search in finding the global optimum

Visualising the Landscape of Multi-Objective Problems using Local Optima Networks

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe codebase for this paper is available at https://github.com/fieldsend/mo_lonsLocal optima networks (LONs) represent the landscape of optimisation problems. In a LON, graph vertices represent local optima in the search domain, their radii the basin sizes, and directed edges between vertices the ability to transit from one basin to another (with the edge width denoting how easy this is). Recently, a network construction approach inspired by LONs has been proposed for multi-objective problems which uses an undirected graph, representing mutually non-dominating solutions and neighbouring links, but not basin sizes. In contrast, here we introduce two formulations for multi/many-objective problems which are analogous to the traditional LON, using dominance-based hill-climbing to characterise the search domain. Each vertex represents a set of locally optimal solutions, with basins and ease of transition between them shown. These LONs vary depending on whether a point-based (dominance neutral optima) or set-based (Pareto local optima) representation is used to define mode construction. We illustrate these alternative formulations on some illustrative problems.We discuss some of the underlying computational issues in constructing LONs in a multiobjective as opposed to uni-objective problem domain, along with the inherent issue of neutrality — as each a vertex in these graphs almost invariably represents a set in our proposed constructs.Engineering and Physical Sciences Research Council (EPSRC