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A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows

Author

Listed:
  • Sébastien Mouthuy

    (Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • Florence Massen

    (Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • Yves Deville

    (Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • Pascal Van Hentenryck

    (NICTA and the Australian National University, Canberra ACT 0200, Australia)

Abstract

This paper considers the vehicle routing problem with soft time windows, a challenging routing problem where customers' time windows may be violated at a certain cost. The vehicle routing problem with soft time windows has a lexicographic objective function, aimed at minimizing first the number of routes, then the number of violated time windows, and finally the total routing distance. We present a multistage very large-scale neighborhood search for this problem. Each stage corresponds to a variable neighborhood descent over a parameterizable very large-scale neighborhood. These neighborhoods contain an exponential number of neighbors, as opposed to classical local search neighborhoods. Often, searching very large-scale neighborhoods can produce local optima of a higher quality than polynomial-sized neighborhoods can. Furthermore, we use a sophisticated heuristic to determine service start times allowing us to minimize the number of violated time windows. We test our approach on a number of different problem types, and compare the results to the relevant state of the art. The experimental results show that our algorithm improves best known solutions on 53% of the most studied instances. Many of these improvements stem from a reduction of the number of vehicles, a critical objective in vehicle routing problems.

Suggested Citation

  • Sébastien Mouthuy & Florence Massen & Yves Deville & Pascal Van Hentenryck, 2015. "A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows," Transportation Science, INFORMS, vol. 49(2), pages 223-238, May.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:223-238
    DOI: 10.1287/trsc.2014.0558
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    References listed on IDEAS

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    2. Kuhn, Heinrich & Schubert, Daniel & Holzapfel, Andreas, 2021. "Integrated order batching and vehicle routing operations in grocery retail – A General Adaptive Large Neighborhood Search algorithm," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1003-1021.

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