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A Simulation-Based Algorithm for the Probabilistic Traveling Salesman Problem

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EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII

Part of the book series: Studies in Computational Intelligence ((SCI,volume 662))

Abstract

The probabilistic traveling salesman problem (PTSP) is a variation of the classic TSP and one of the most significant stochastic network and routing problems. Designing effective and efficient algorithms for solving PTSP is a really challenging task, since in PTSP, the computational complexity associated with the combinatorial explosion of potential solution is exacerbated by the stochastic element in the data. In general, researchers use two types of techniques in their search algorithms for PTSP: analytical computation and empirical estimation. The analytical computation approach computes the cost  f(\(\pi \)) of an a priori tour \(\pi \) using a closed-form expression. Empirical estimation simply estimates the cost through Monte Carlo simulation. This paper describes a simulation-based algorithm that constructs the solution attractor of local search for the PTSP and then finds the best a priori tour within the solution attractor. More specifically, our algorithm first uses a simple multi-start local search process to find a set of locally optimal a priori tours through Monte Carlo simulation and stores these tours in a matrix. Then, the algorithm uses an exhausted search process to find all tours contained in the solution attractor and identifies a globally optimal a priori tour \(\pi \) through Monte Carlo simulation.

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Authors and Affiliations

  1. University of Michigan, 303 E. Kearsley Street, Flint, MI, 48502, USA

    Weiqi Li

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  1. Weiqi Li
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Editors and Affiliations

  1. Leiden Institute of Advanced Com. Sci., Leiden University Leiden Institute of Advanced Com. Sci., CA Leiden, The Netherlands

    Michael Emmerich

  2. Leiden Institute of Advanced Com. Sci., Leiden University Leiden Institute of Advanced Com. Sci., CA Leiden, The Netherlands

    André Deutz

  3. Depto. de Ingeniería Eléctrica, CINVESTAV-IPN Depto. de Ingeniería Eléctrica, México, D.F., Mexico

    Oliver Schütze

  4. University of Bordeaux, Université Bordeaux Victoire , Bordeaux Cedex, France

    Pierrick Legrand

  5. Luxembourg Centre for Systems Biomedicin, University of Luxembourg Luxembourg Centre for Systems Biomedicin, Belval, Luxembourg

    Emilia Tantar

  6. Computer Science & Comm. Research Unit, University of Luxembourg Computer Science & Comm. Research Unit, Luxembourg, Luxembourg

    Alexandru-Adrian Tantar

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Li, W. (2017). A Simulation-Based Algorithm for the Probabilistic Traveling Salesman Problem. In: Emmerich, M., Deutz, A., Schütze, O., Legrand, P., Tantar, E., Tantar, AA. (eds) EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII. Studies in Computational Intelligence, vol 662. Springer, Cham. https://doi.org/10.1007/978-3-319-49325-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-49325-1_8

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