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Heuristic Approaches for the Probabilistic Traveling Salesman Problem

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Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

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Abstract

The Probabilistic Traveling Salesman Problem (PTSP) is a variant of the classical Traveling Salesman Problem (TSP) where each city has a given probability requiring a visit. We aim for an a-priori tour including every city that minimizes the expected length over all realizations. In this paper we consider different heuristic approaches for the PTSP. First we analyze various popular construction heuristics for the classical TSP applied on the PTSP: nearest neighbor, farthest insertion, nearest insertion, radial sorting and space filling curve. Then we investigate their extensions to the PTSP: almost nearest neighbor, probabilistic farthest insertion, probabilistic nearest insertion. To improve the constructed solutions we use existing 2-opt and 1-shift neighborhood structures for which exact delta evaluation formulations exist. These are embedded within a Variable Neighborhood Descent framework into a Variable Neighborhood Search. Computational results indicate that this approach is competitive to already existing heuristic algorithms and able to find good solutions in low runtime.

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Acknowledgments

The authors thank Dennis Weyland for providing the source code of his EACS for better comparison.

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Authors and Affiliations

  1. Institute of Computer Graphics and Algorithms, TU Wien, Favoritenstraße 9-11/1861, 1040, Vienna, Austria

    Christoph Weiler, Benjamin Biesinger & Günther R. Raidl

  2. Mobility Department - Dynamic Transportation Systems, AIT Austrian Institute of Technology, Giefinggasse 2, 1210, Vienna, Austria

    Bin Hu

Authors
  1. Christoph Weiler
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  2. Benjamin Biesinger
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  3. Bin Hu
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  4. Günther R. Raidl
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Corresponding author

Correspondence to Benjamin Biesinger .

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Editors and Affiliations

  1. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Weiler, C., Biesinger, B., Hu, B., Raidl, G.R. (2015). Heuristic Approaches for the Probabilistic Traveling Salesman Problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_43

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  • DOI: https://doi.org/10.1007/978-3-319-27340-2_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

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