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Computing compatible tours for the traveling salesman problem

Fortini, M and Letchford, A N and Lodi, A and Wenger, K M (2011) Computing compatible tours for the traveling salesman problem. Mathematical Programming Computation, 3 (1). pp. 59-78.

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    Abstract

    We consider the following natural heuristic for the Symmetric Traveling Salesman Problem: solve the subtour relaxation, yielding a solution x*, and then find the best tour x-bar that is 'compatible' with x*, where compatible means that every subtour elimination constraint that is satisfied at equality at x* is also satisfied at equality at x-bar. We prove that finding the best compatible tour is NP-hard and show that the tour can have a cost approaching 5/3 that of the optimal tour. We then describe a branch-and-cut algorithm for computing the best compatible tour, and present extensive computational results for TSPLIB instances. It turns out that, in practice, the tour is usually of very good quality. Moreover, the computational effort for computing the compatible tour is considerably smaller than that of solving the full problem with the best available software, i.e., Concorde.

    Item Type: Article
    Journal or Publication Title: Mathematical Programming Computation
    Uncontrolled Keywords: traveling salesman problem ; heuristics ; branch-and-cut
    Subjects: H Social Sciences > HB Economic Theory
    Departments: Lancaster University Management School > Management Science
    ID Code: 45768
    Deposited By: ep_importer_pure
    Deposited On: 11 Jul 2011 19:37
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Apr 2014 22:36
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/45768

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