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Comparison of Genetic Operators for the Multiobjective Pickup and Delivery Problem

Author

Listed:
  • Connor Little

    (School of Computing, Queen’s University, Kingston, ON K7L 3N6, Canada)

  • Salimur Choudhury

    (School of Computing, Queen’s University, Kingston, ON K7L 3N6, Canada)

  • Ting Hu

    (School of Computing, Queen’s University, Kingston, ON K7L 3N6, Canada)

  • Kai Salomaa

    (School of Computing, Queen’s University, Kingston, ON K7L 3N6, Canada)

Abstract

The pickup and delivery problem is a pertinent problem in our interconnected world. Being able to move goods and people efficiently can lead to decreases in costs, emissions, and time. In this work, we create a genetic algorithm to solve the multiobjective capacitated pickup and delivery problem, adapting commonly used benchmarks. The objective is to minimize total distance travelled and the number of vehicles utilized. Based on NSGA-II, we explore how different inter-route and intraroute mutations affect the final solution. We introduce 6 inter-route operations and 16 intraroute operations and calculate the hypervolume measured to directly compare their impact. We also introduce two different crossover operators that are specialized for this problem. Our methodology was able to find optimal results in 23% of the instances in the first benchmark and in most other instances, it was able to generate a Pareto front within at most one vehicle and +20% of the best-known distance. With multiple solutions, it allows users to choose the routes that best suit their needs.

Suggested Citation

  • Connor Little & Salimur Choudhury & Ting Hu & Kai Salomaa, 2022. "Comparison of Genetic Operators for the Multiobjective Pickup and Delivery Problem," Mathematics, MDPI, vol. 10(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4308-:d:975479
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    References listed on IDEAS

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    1. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    2. Francesco Carrabs & Jean-François Cordeau & Gilbert Laporte, 2007. "Variable Neighborhood Search for the Pickup and Delivery Traveling Salesman Problem with LIFO Loading," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 618-632, November.
    3. Guiliang Gong & Qianwang Deng & Xuran Gong & Like Zhang & Haibin Wang & He Xie, 2018. "A Bee Evolutionary Algorithm for Multiobjective Vehicle Routing Problem with Simultaneous Pickup and Delivery," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-21, June.
    4. Yanik, Seda & Bozkaya, Burcin & deKervenoael, Ronan, 2014. "A new VRPPD model and a hybrid heuristic solution approach for e-tailing," European Journal of Operational Research, Elsevier, vol. 236(3), pages 879-890.
    5. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
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    Cited by:

    1. Abdellah Chehri & Francois Rivest, 2023. "Editorial for the Special Issue “Advances in Machine Learning and Mathematical Modeling for Optimization Problems”," Mathematics, MDPI, vol. 11(8), pages 1-5, April.

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