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Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems

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  • Sebastián Muñoz-Herrera

    (Departamento de Ingeniería Industrial, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepcion 4090541, Chile
    Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Santiago 7941169, Chile
    These authors contributed equally to this work.)

  • Karol Suchan

    (Escuela de Informática y Telecomunicaciones, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441, Santiago 8370191, Chile
    Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland
    These authors contributed equally to this work.
    Current address: Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441, Santiago 8370191, Chile.)

Abstract

Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem’s constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.

Suggested Citation

  • Sebastián Muñoz-Herrera & Karol Suchan, 2022. "Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4644-:d:997026
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    References listed on IDEAS

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    1. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    2. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    3. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.
    4. Liming Zheng & Shiqi Luo, 2022. "Adaptive Differential Evolution Algorithm Based on Fitness Landscape Characteristic," Mathematics, MDPI, vol. 10(9), pages 1-33, May.
    5. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    6. Van Breedam, Alex, 1995. "Improvement heuristics for the Vehicle Routing Problem based on simulated annealing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 480-490, November.
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    Cited by:

    1. Kai Huang & Michael Xu, 2023. "Optimization Models for the Vehicle Routing Problem under Disruptions," Mathematics, MDPI, vol. 11(16), pages 1-21, August.

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