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The Set Orienteering Problem

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  • Archetti, Claudia
  • Carrabs, Francesco
  • Cerulli, Raffaele

Abstract

In this paper, we study the Set Orienteering Problem which is a generalization of the Orienteering Problem where customers are grouped in clusters and a profit is associated with each cluster. The profit of a cluster is collected only if at least one customer from the cluster is visited. A single vehicle is available to collect the profit and the objective is to find the vehicle route that maximizes the profit collected and such that the route duration does not exceed a given threshold. We propose a mathematical formulation of the problem and a matheuristic algorithm. Computational tests are made on instances derived from benchmark instances for the Generalized Traveling Salesman Problem with up 1084 vertices. Results show that the matheuristic produces robust and high-quality solutions in a short computing time.

Suggested Citation

  • Archetti, Claudia & Carrabs, Francesco & Cerulli, Raffaele, 2018. "The Set Orienteering Problem," European Journal of Operational Research, Elsevier, vol. 267(1), pages 264-272.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:1:p:264-272
    DOI: 10.1016/j.ejor.2017.11.009
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    References listed on IDEAS

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    1. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    2. Angelelli, E. & Archetti, C. & Vindigni, M., 2014. "The Clustered Orienteering Problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 404-414.
    3. Gunawan, Aldy & Lau, Hoong Chuin & Vansteenwegen, Pieter, 2016. "Orienteering Problem: A survey of recent variants, solution approaches and applications," European Journal of Operational Research, Elsevier, vol. 255(2), pages 315-332.
    4. Walton Pereira Coutinho & Roberto Quirino do Nascimento & Artur Alves Pessoa & Anand Subramanian, 2016. "A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 752-765, November.
    5. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
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    Citations

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    Cited by:

    1. Katharina Glock & Anne Meyer, 2020. "Mission Planning for Emergency Rapid Mapping with Drones," Transportation Science, INFORMS, vol. 54(2), pages 534-560, March.
    2. Glock, Katharina & Meyer, Anne, 2023. "Spatial coverage in routing and path planning problems," European Journal of Operational Research, Elsevier, vol. 305(1), pages 1-20.
    3. Shih-Wei Lin & Sirui Guo & Wen-Jie Wu, 2024. "Applying the Simulated Annealing Algorithm to the Set Orienteering Problem with Mandatory Visits," Mathematics, MDPI, vol. 12(19), pages 1-24, October.
    4. Wu, Qinghua & He, Mu & Hao, Jin-Kao & Lu, Yongliang, 2024. "An effective hybrid evolutionary algorithm for the clustered orienteering problem," European Journal of Operational Research, Elsevier, vol. 313(2), pages 418-434.
    5. Qian, Qiuchen & Wang, Yanran & Boyle, David, 2024. "On solving close enough orienteering problems with overlapped neighborhoods," European Journal of Operational Research, Elsevier, vol. 318(2), pages 369-387.
    6. Archetti, C. & Carrabs, F. & Cerulli, R. & Laureana, F., 2024. "A new formulation and a branch-and-cut algorithm for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 314(2), pages 446-465.
    7. Yang, Yu & Yan, Chiwei & Cao, Yufeng & Roberti, Roberto, 2023. "Planning robust drone-truck delivery routes under road traffic uncertainty," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1145-1160.
    8. Miranda, Pablo A. & Blazquez, Carola A. & Obreque, Carlos & Maturana-Ross, Javier & Gutierrez-Jarpa, Gabriel, 2018. "The bi-objective insular traveling salesman problem with maritime and ground transportation costs," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1014-1036.
    9. Pěnička, Robert & Faigl, Jan & Saska, Martin, 2019. "Variable Neighborhood Search for the Set Orienteering Problem and its application to other Orienteering Problem variants," European Journal of Operational Research, Elsevier, vol. 276(3), pages 816-825.
    10. Dontas, Michael & Sideris, Georgios & Manousakis, Eleftherios G. & Zachariadis, Emmanouil E., 2023. "An adaptive memory matheuristic for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1010-1023.
    11. Carrabs, Francesco, 2021. "A biased random-key genetic algorithm for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 292(3), pages 830-854.

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