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An Approximate Solution of the Travelling Salesman Problem Based on the Metropolis Simulation with Annealing

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Topics in Statistical Simulation

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 114))

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Abstract

The symmetric traveling salesman problem is studied and its approximate solution is proposed. The algorithm is based on the simulation of dynamic fields according to Metropolis method with annealing. The choice of the optimal annealing coefficient is discussed. Peculiarities of the proposed algorithm consist of: (i) good initial approximation choice, (ii) simulation of the separate parts of path, (iii) path self-crossings deletion, (iv) visual control of the intermediate results. Four examples with the paths close to the optimal ones are presented. As a criterion the normalized path length is used.

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Acknowledgements

The work is supported by Russian Foundation of Basic Researches (grant 11.01.00769-a).

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    Tatiana M. Tovstik

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  1. Tatiana M. Tovstik
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Correspondence to Tatiana M. Tovstik .

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Editors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    V.B. Melas

  2. University of Bologna, Rimini, Italy

    Stefania Mignani

  3. University of Bologna, Rimini, Italy

    Paola Monari

  4. University of Padova, Padova, Italy

    Luigi Salmaso

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Tovstik, T.M. (2014). An Approximate Solution of the Travelling Salesman Problem Based on the Metropolis Simulation with Annealing. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_48

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