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

van Hemert, Jano I; Urquhart, Neil B

Abstract

We introduce 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.

Citation

van Hemert, J. I., & Urquhart, N. B. (2004). Phase transition properties of clustered travelling salesman problem instances generated with evolutionary computation.

• Conference Name: Parallel Problem Solving From Nature (PPSN) VIII
• Start Date: Sep 18, 2004
• End Date: Sep 22, 2004
• Publication Date: Sep 1, 2004
• Deposit Date: Jul 21, 2008
• Peer Reviewed: Peer Reviewed
• Pages: 151-160
• ISBN: 3540230920
• Keywords: Constraint theory; Evolutionary computing; Random processes; Clusters; Optimization; Sampling methods
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/1755