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DOI: 10.4230/LIPIcs.ESA.2024.91

Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm

Authors: Zipei Nie and Hang Zhou

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

We study the unit-demand capacitated vehicle routing problem in the random setting of the Euclidean plane. The objective is to visit n random terminals in a square using a set of tours of minimum total length, such that each tour visits the depot and at most k terminals. We design an algorithm combining the classical sweep heuristic and the framework for the Euclidean traveling salesman problem due to Arora [J. ACM 1998] and Mitchell [SICOMP 1999]. We show that our algorithm is a polynomial-time approximation of ratio at most 1.55 asymptotically almost surely. This improves on the prior ratio of 1.915 due to Mathieu and Zhou [RSA 2022]. In addition, we conjecture that, for any ε > 0, our algorithm is a (1+ε)-approximation asymptotically almost surely.

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Zipei Nie and Hang Zhou. Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 91:1-91:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{nie_et_al:LIPIcs.ESA.2024.91,
  author =	{Nie, Zipei and Zhou, Hang},
  title =	{{Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{91:1--91:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.91},
  URN =		{urn:nbn:de:0030-drops-211627},
  doi =		{10.4230/LIPIcs.ESA.2024.91},
  annote =	{Keywords: capacitated vehicle routing, approximation algorithm, combinatorial optimization}
}

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Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm

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