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Adaptive Large Neighborhood Search with a Constant-Time Feasibility Test for the Dial-a-Ride Problem

Author

Listed:
  • Timo Gschwind

    () (Johannes Gutenberg-University Mainz, Germany)

  • Michael Drexl

    () (Johannes Gutenberg-University Mainz, Germany and Deggendorf Institute of Technology)

Abstract

In the dial-a-ride problem (DARP), user-specified transport requests from origin to destination points have to be served by a fleet of homogeneous vehicles. The problem variant we consider aims at finding a set of minimum-cost routes satisfying constraints on vehicle capacity, time windows, maximum route duration, and maximum user ride times. We propose an adaptive large neighborhood search (ALNS) for its solution. The key novelty of the approach is an exact amortized constant-time algorithm for evaluating the feasibility of request insertions in the repair steps of the ALNS. In addition, we use two optional improvement techniques: a local-search based, intra-route improvement of routes of promising solutions using the Balas-Simonetti neighborhood, and the solution of a set-partitioning model over a subset of all routes generated during the search. With these techniques, the proposed algorithm outperforms the state-of-the-art methods in terms of solution quality. New best solutions are found for several benchmark instances.

Suggested Citation

  • Timo Gschwind & Michael Drexl, 2016. "Adaptive Large Neighborhood Search with a Constant-Time Feasibility Test for the Dial-a-Ride Problem," Working Papers 1624, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  • Handle: RePEc:jgu:wpaper:1624
    as

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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1624.pdf
    File Function: First version, 2016
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    References listed on IDEAS

    as
    1. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    2. Timo Gschwind & Stefan Irnich, 2015. "Effective Handling of Dynamic Time Windows and Its Application to Solving the Dial-a-Ride Problem," Transportation Science, INFORMS, vol. 49(2), pages 335-354, May.
    3. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    4. Gerardo Berbeglia & Gilles Pesant & Louis-Martin Rousseau, 2011. "Checking the Feasibility of Dial-a-Ride Instances Using Constraint Programming," Transportation Science, INFORMS, vol. 45(3), pages 399-412, August.
    5. Cordeau, Jean-François & Laporte, Gilbert, 2003. "A tabu search heuristic for the static multi-vehicle dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 579-594, July.
    6. Gschwind, Timo, 2015. "A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 60-71.
    7. Timo Gschwind, 2015. "Route Feasibility Testing and Forward Time Slack for the Synchronized Pickup and Delivery Problem," Working Papers 1503, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 22 May 2015.
    8. Lauri Häme & Harri Hakula, 2015. "A Maximum Cluster Algorithm for Checking the Feasibility of Dial-A-Ride Instances," Transportation Science, INFORMS, vol. 49(2), pages 295-310, May.
    9. Braekers, Kris & Caris, An & Janssens, Gerrit K., 2014. "Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 166-186.
    10. Yuan Qu & Jonathan F. Bard, 2015. "A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity," Transportation Science, INFORMS, vol. 49(2), pages 254-270, May.
    11. Kirchler, Dominik & Wolfler Calvo, Roberto, 2013. "A Granular Tabu Search algorithm for the Dial-a-Ride Problem," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 120-135.
    12. Renaud Masson & Fabien Lehuédé & Olivier Péton, 2013. "An Adaptive Large Neighborhood Search for the Pickup and Delivery Problem with Transfers," Transportation Science, INFORMS, vol. 47(3), pages 344-355, August.
    13. Jean-François Cordeau & Gilbert Laporte, 2007. "The dial-a-ride problem: models and algorithms," Annals of Operations Research, Springer, vol. 153(1), pages 29-46, September.
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    Cited by:

    1. repec:eee:transb:v:111:y:2018:i:c:p:395-421 is not listed on IDEAS
    2. Michael Drexl, 2018. "On Testing Capacity Constraints in Pickup-and-Delivery Problems with Trailers in Amortized Constant Time," Working Papers 1823, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    More about this item

    Keywords

    Dial-a-ride problem; Adaptive large neighborhood search; Feasibility testing;

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