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Deep Infeasibility Exploration Method for Vehicle Routing Problems

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Evolutionary Computation in Combinatorial Optimization (EvoCOP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13222))

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Abstract

We describe a new method for the vehicle routing problems with constraints. Instead of trying to improve the typical metaheuristics used to efficiently solve vehicle routing problems, like large neighborhood search, iterated local search, or evolutionary algorithms, we allow them to explore the deeply infeasible regions of the search space in a controlled way. The key idea is to find solutions better in terms of the objective function even at the cost of violation of constraints, and then try to restore feasibility of the obtained solutions at a minimum cost. Furthermore, in order to preserve the best feasible solutions, we maintain two diversified pools of solutions, the main pool and the temporary working pool. The main pool stores the best diversified (almost) feasible solutions, while the working pool is used to generate new solutions and is periodically refilled with disturbed solutions from the main pool. We demonstrate our method on the vehicle routing problems, with variants respecting time, vehicle capacity and fleet limitation constraints. Our method provided a large number of new best-known solutions on well-known benchmark datasets. Although our method is designed for the family of vehicle routing problems, its concept is fairly general and it could potentially be applied to other NP-hard problems with constraints.

This work has been partially supported by the Polish National Centre for Research and Development (projects POIR.01.01.01-00-0222/16, POIR.01.01.01-00-0012/19).

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Acknowledgments

The authors would like to thank Krzysztof Krawiec for valuable comments on the paper.

The computing time for the reported experiments was provided to us by the generosity of Poznan Supercomputing and Networking Center, which had awarded us a computational grant to access its Eagle cluster. (Poznan Supercomputing and Networking Center, computing grant 358 (https://wiki.man.poznan.pl/hpc/index.php?title=Eagle)).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238, Lodz, Poland

    Piotr Beling, Piotr Cybula, Marek Rogalski & Piotr Sielski

  2. Faculty of Computing, Poznan University of Technology, Piotrowo 3, 60-965, Poznan, Poland

    Andrzej Jaszkiewicz

  3. Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology, Stefanowskiego 18/22, 90-924, Lodz, Poland

    Przemysław Pełka

  4. Emapa S.A., Ciolka 12, 01-402, Warsaw, Poland

    Piotr Cybula & Przemysław Pełka

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  1. Piotr Beling
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Correspondence to Piotr Cybula .

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Editors and Affiliations

  1. Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Leslie Pérez Cáceres

  2. Université du Littoral Côte d’Opale, Calais, France

    Sébastien Verel

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Beling, P., Cybula, P., Jaszkiewicz, A., Pełka, P., Rogalski, M., Sielski, P. (2022). Deep Infeasibility Exploration Method for Vehicle Routing Problems. In: Pérez Cáceres, L., Verel, S. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2022. Lecture Notes in Computer Science, vol 13222. Springer, Cham. https://doi.org/10.1007/978-3-031-04148-8_5

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  • DOI: https://doi.org/10.1007/978-3-031-04148-8_5

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