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PTAS for the Euclidean Capacitated Vehicle Routing Problem in \(R^d\)

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Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem remaining NP-hard even in the Euclidean spaces of fixed dimension. Thirty years ago, in their celebrated paper, M. Haimovich and A. Rinnoy Kan proposed the first PTAS for the Planar Single Depot CVRP based on their Iterated Tour Partition heuristic. For decades, this result was extended by many authors to numerous useful modifications of the problem taking into account multiple depots, pick up and delivery options, time window restrictions, etc. But, to the best of our knowledge, almost none of these results go beyond the Euclidean plane. In this paper, we try to bridge this gap and propose an EPTAS for the Euclidean CVRP for any fixed dimension.

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Notes

  1. 1.

    A PTAS with time complexity \(f(1/\varepsilon )p(n)\) for some polynomial p.

  2. 2.

    Not necessarily distinct.

  3. 3.

    e.g. for \(\rho =O((\log \log n)^{1/d})\).

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Acknowledgments

This research was supported by Russian Science Foundation, project no. 14-11-00109.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Ural Federal University, Ekaterinburg, Russia

    Michael Khachay & Roman Dubinin

  3. Omsk State Technical University, Omsk, Russia

    Michael Khachay

Authors
  1. Michael Khachay
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  2. Roman Dubinin
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Corresponding author

Correspondence to Michael Khachay .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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Khachay, M., Dubinin, R. (2016). PTAS for the Euclidean Capacitated Vehicle Routing Problem in \(R^d\) . In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

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