License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.43
URN: urn:nbn:de:0030-drops-154769
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15476/
Mathieu, Claire ;
Zhou, Hang
Probabilistic Analysis of Euclidean Capacitated Vehicle Routing
Abstract
We give a probabilistic analysis of the unit-demand Euclidean capacitated vehicle routing problem in the random setting, where the input distribution consists of n unit-demand customers modeled as independent, identically distributed uniform random points in the two-dimensional plane. The objective is to visit every customer using a set of routes of minimum total length, such that each route visits at most k customers, where k is the capacity of a vehicle. All of the following results are in the random setting and hold asymptotically almost surely.
The best known polynomial-time approximation for this problem is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the ITP algorithm is near-optimal when k is either o(√n) or ω(√n), and they asked whether the ITP algorithm was "also effective in the intermediate range". In this work, we show that when k = √n, the ITP algorithm is at best a (1+c₀)-approximation for some positive constant c₀.
On the other hand, the approximation ratio of the ITP algorithm was known to be at most 0.995+α due to Bompadre, Dror, and Orlin, where α is the approximation ratio of an algorithm for the traveling salesman problem. In this work, we improve the upper bound on the approximation ratio of the ITP algorithm to 0.915+α. Our analysis is based on a new lower bound on the optimal cost for the metric capacitated vehicle routing problem, which may be of independent interest.
BibTeX - Entry
@InProceedings{mathieu_et_al:LIPIcs.ISAAC.2021.43,
author = {Mathieu, Claire and Zhou, Hang},
title = {{Probabilistic Analysis of Euclidean Capacitated Vehicle Routing}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {43:1--43:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-214-3},
ISSN = {1868-8969},
year = {2021},
volume = {212},
editor = {Ahn, Hee-Kap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15476},
URN = {urn:nbn:de:0030-drops-154769},
doi = {10.4230/LIPIcs.ISAAC.2021.43},
annote = {Keywords: capacitated vehicle routing, iterated tour partitioning, probabilistic analysis, approximation algorithms}
}
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Keywords: |
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capacitated vehicle routing, iterated tour partitioning, probabilistic analysis, approximation algorithms |
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Collection: |
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32nd International Symposium on Algorithms and Computation (ISAAC 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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30.11.2021 |
