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Phase transition properties of clustered travelling salesman problem instances generated with evolutionary computation

TitlePhase transition properties of clustered travelling salesman problem instances generated with evolutionary computation
Publication TypeConference Paper
Year of Publication2004
Authorsvan Hemert, JI, Urquhart, NB
Conference NameLNCS
PublisherSpringer-Verlag
Conference LocationBirmingham, UK
EditorYao, X, Burke, E, Lozano, JA, Smith, J, Merelo-Guerv\'os, JJ, Bullinaria, JA, Rowe, J, n, PT\v, Schwefel, H-P
ISBN Number3-540-23092-0
Keywordsevolutionary computation; problem evolving; travelling salesman
Abstract

This paper introduces a generator that creates problem instances for the Euclidean symmetric travelling salesman problem. To fit real world problems, we look at maps consisting of clustered nodes. Uniform random sampling methods do not result in maps where the nodes are spread out to form identifiable clusters. To improve upon this, we propose an evolutionary algorithm that uses the layout of nodes on a map as its genotype. By optimising the spread until a set of constraints is satisfied, we are able to produce better clustered maps, in a more robust way. When varying the number of clusters in these maps and, when solving the Euclidean symmetric travelling salesman person using Chained Lin-Kernighan, we observe a phase transition in the form of an easy-hard-easy pattern.

URLhttp://www.vanhemert.co.uk/files/clustered-phase-transition-tsp.tar.gz
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