Iterative patching and the asymmetric traveling salesman problem

Authors:
Marcel Turkensteen;Diptesh Ghosh;Boris Goldengorin;Gerard Sierksma
Affiliations:
Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;P&QM Area, Indian Institute of Management, Ahmedabad, India;Faculty of Economics, University of Groningen, The Netherlands;Faculty of Economics, University of Groningen, The Netherlands
Venue:
Discrete Optimization
Year:
2006

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Abstract

Although Branch-and-Bound (BnB) methods are among the most widely used techniques for solving hard problems, it is still a challenge to make these methods smarter. In this paper, we investigate iterative patching, a technique in which a fixed patching procedure is applied at each node of the BnB search tree for the Asymmetric Traveling Salesman Problem. Computational experiments show that iterative patching results in general in search trees that are smaller than the classical BnB trees, and that solution times are lower for usual random and sparse instances. Furthermore, it turns out that, on average, iterative patching with the Contract-or-Patch procedure of Glover, Gutin, Yeo and Zverovich (2001) and the Karp-Steele procedure are the fastest, and that 'iterative' Modified Karp-Steele patching generates the smallest search trees.