A study of NK landscapes' basins and local optima networks

Proceedings of the Genetic and Evolutionary Computation Conference Companion

2017

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Local optima networks are a compact representation of the global structure of a search space. They can be used for analysis and visualisation. This paper provides one of the rst analyses of program search spaces using local optima networks. These are generated by sampling the search space by recording the progress of an Iterated Local Search algorithm. Source code mutations in comparison and Boolean operators are considered. The search spaces of two small benchmark programs, the triangle and TCAS programs, are analysed and visualised. Results show a high level of neutrality, i.e. connected test-equivalent mutants. It is also generally relatively easy to nd a path from a random mutant to a mutant that passes all test cases. CCS CONCEPTS•Software and its engineering → Search-based software engineering; •Computing methodologies → Randomized search;

Section: Local Optima Networkmentioning

confidence: 99%

Modelling genetic improvement landscapes with local optima networks

Veerapen

Daolio

Proceedings of the Genetic and Evolutionary Computation Conference Companion

2017

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“…GECCO '16, July 20 -24, 2016, Denver, CO, USA Ochoa et al [24] propose to characterize funnels in combinatorial spaces using local optima networks (LONs, [22]). The idea of LONs was inspired by the study of energy landscapes [28], and it was found that energy landscapes often have a structure of multiple funnels as well [19].…”

Section: Introductionmentioning

confidence: 99%

Communities of Local Optima as Funnels in Fitness Landscapes

Herrmann

Proceedings of the Genetic and Evolutionary Computation Conference 2016

Rothlauf

2016

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We conduct an analysis of local optima networks extracted from fitness landscapes of the Kauffman NK model under iterated local search. Applying the Markov Cluster Algorithm for community detection to the local optima networks, we find that the landscapes consist of multiple clusters. This result complements recent findings in the literature that landscapes often decompose into multiple funnels, which increases their difficulty for iterated local search. Our results suggest that the number of clusters as well as the size of the cluster in which the global optimum is located are correlated to the search difficulty of landscapes. We conclude that clusters found by community detection in local optima networks offer a new way to characterize the multi-funnel structure of fitness landscapes.

“…This article uses the Local Optima Network (LON) model [15,16,14,18] in order to explore in more detail the structure of TSP landscapes near the global optimum. Local optima networks compress the whole search spaces into a graph having as vertices the local optima, and as edges transitions among them according to a given search operator.…”

Section: Introductionmentioning

confidence: 99%

The Multi-Funnel Structure of TSP Fitness Landscapes: A Visual Exploration

Lecture Notes in Computer Science

Veerapen

Whitley

et al. 2016

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Abstract. We use the Local Optima Network model to study the structure of symmetric TSP fitness landscapes. The 'big-valley' hypothesis holds that for TSP and other combinatorial problems, local optima are not randomly distributed, instead they tend to be clustered around the global optimum. However, a recent study has observed that, for solutions close in evaluation to the global optimum, this structure breaks down into multiple valleys, forming what has been called 'multiple funnels'. The multiple funnel concept implies that local optima are organised into clusters, so that a particular local optimum largely belongs to a particular funnel. Our study is the first to extract and visualise local optima networks for TSP and is based on a sampling methodology relying on the Chained Lin-Kernighan algorithm. We confirm the existence of multiple funnels on two selected TSP instances, finding additional funnels in a previously studied instance. Our results suggests that transitions among funnels are possible using operators such as 'double-bridge'. However, for consistently escaping sub-optimal funnels, more robust escaping mechanisms are required.