Comparison of heuristics for the colourful travelling salesman problem

Authors:
J. Silberholz;A. Raiconi;R. Cerulli;M. Gentili;B. Golden;S. Chen
Affiliations:
Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA;Department of Mathematics, University of Salerno, P.te Don Melillo, 84084 Fisciano SA, Italy;Department of Mathematics, University of Salerno, P.te Don Melillo, 84084 Fisciano SA, Italy;Department of Mathematics, University of Salerno, P.te Don Melillo, 84084 Fisciano SA, Italy;R.H. Smith School of Business, University of Maryland, College Park, MD 20742, USA;College of Business, Murray State University, Murray, KY 42071, USA
Venue:
International Journal of Metaheuristics
Year:
2013

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Abstract

In the colourful travelling salesman problem CTSP, given a graph G with a not necessarily distinct label colour assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types. We propose two new heuristics based on the deconstruction of a Hamiltonian tour into subpaths and their reconstruction into a new tour, as well as an adaptation of an existing approach. Extensive experimentation shows the effectiveness of the proposed approaches.