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A mathematical method for solving multi-depot vehicle routing problem

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Abstract

Because logistics companies usually have multiple depots to serve their many dispersed customers, multi-depot vehicle routing problem (MDVRP) has gained significant research attention. To solve an MDVRP model, this paper develops a hybrid ant colony optimization based on a polygonal circumcenter (BPC-HACO). Furthermore, because ACO has been found to fall easily into the local optimum, simulated annealing and three local optimization operations are introduced to encourage the ACO to improve the algorithm’s optimization ability. Finally, MDVRP benchmarks and data sets of other papers are employed to verify the effectiveness of the BPC-HACO in solving MDVRP (In 23 instances, BPC-HACO finds 14 BSKs, and 3 results are better than the BSKs), MDVRP with distance constraints (Compared to other papers, the route length is reduced by an average of 17.94%) and dynamic MDVRP (In 10 instances, BPC-HACO finds 3 BSKs, and 2 results are better than the BSKs). Finally, fitness landscape analysis has been applied to analyze the structural features of MDVRP to choose the most appropriate algorithm for MDVRP.

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Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

National Natural Science Foundation of China [Grant No. 72074198, 71874165, 71573237]; the National Social Science Fund of China [Grant No. 21AZD074]; Young Talents Foundation of The Central Propaganda Department [Grant No. 2020084007]; the Research Foundation of Philosophy and Social sciences of Ministry of Education of China [Grant No. 20JHQ094]; Soft science research project of technological innovation in Hubei Province [Grant No. 2019ADC154]; Young Talents Foundation of The Central Propaganda Department; Hubei Provincial Natural Science Foundation of China [Grant No. 2020CFB822].

Funding

National Natural Science Foundation of China [grant numbers 72074198, 71874165, 71573237]; the National Social Science Fund of China [grant numbers 21AZD074]; Young Talents Foundation of The Central Propaganda Department [grant number 2020084007].

Author information

Authors and Affiliations

  1. School of Economics and Management, China University of Geosciences, Wuhan, People’s Republic of China

    Fang wan, Haixiang Guo, Wenwen Pan & Jundong Hou

  2. Mineral Resource Strategy and Policy Research Center of China University of Geosciences, Wuhan, People’s Republic of China

    Haixiang Guo & Jundong Hou

  3. School of Management, Xi’an University of Finance and Economics, Xi’an, China

    Haixiang Guo & Shengli Chen

Authors
  1. Fang wan
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  2. Haixiang Guo
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  3. Wenwen Pan
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  4. Jundong Hou
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  5. Shengli Chen
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Contributions

WF contributed to conceptualization, methodology, software, visualization, investigation, and writing—original draft. GH was involved in funding acquisition, project administration, writing—review and editing, supervision, and data curation. PW contributed to data curation, writing—review and editing, supervision, and validation. HJ and CS were involved in writing—review and editing and supervision.

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Correspondence to Fang wan.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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On behalf of my co-authors, I would like to declare that the work described was original research that has not been published previously and is not under consideration for publication elsewhere, in whole or in part.

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wan, F., Guo, H., Pan, W. et al. A mathematical method for solving multi-depot vehicle routing problem. Soft Comput 27, 15699–15717 (2023). https://doi.org/10.1007/s00500-023-08811-8

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