Elsevier

Information Processing Letters

Volume 104, Issue 6, 16 December 2007, Pages 216-219
Information Processing Letters

Simulated Annealing versus Metropolis for a TSP instance

https://doi.org/10.1016/j.ipl.2007.06.016Get rights and content

Abstract

In a recent paper [I. Wegener, Simulated Annealing beats Metropolis in combinatorial optimization, in: L. Caires, G.F. Italiano, L. Monteiro, C. Palamidessi, M. Yung (Eds.), Proc. ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 589–601] Wegener gave a first natural example of a combinatorial optimization problem where for certain instances a Simulated Annealing algorithm provably performs better than the Metropolis algorithm for any fixed temperature. Wegener's example deals with a special instance of the Minimum Spanning Tree problem. In this short note we show that Wegener's technique as well can be used to prove a similar result for another important problem in combinatorial optimization, namely the Traveling Salesman Problem. The main task is to construct a suitable TSP instance for which SA outperforms MA when using the well known 2-Opt local search heuristic.

References (4)

  • M. Jerrum et al.

    The Markov chain Monte Carlo method. An approach to approximate counting and integration

  • D.S. Johnson et al.

    The traveling salesman problem: A case study

There are more references available in the full text version of this article.

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    A long-standing open question is to determine which of those two algorithms would obtain better results on a given instance, that is, whether it exists a temperature value for which FTA outperforms SA under any cooling scheme (Jerrum et al., 1996). This question has been addressed in the literature mostly from a theoretical point of view without a conclusive answer (Cohn & Fielding, 1999; Jerrum et al., 1996; Meer, 2007; Mühlenbein & Zimmermann, 2000; Orosz & Jacobson, 2002; Wegener et al., 2005). In this work we take instead a different approach, performing extensive experiments to understand how these two simple SLS methods perform on different problems and instances.

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Partially supported by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778 and by the Danish Agency for Science, Technology and Innovation FNU. This publication only reflects the author's views.

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