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Efficient Cluster-Based Heuristics for the Team Orienteering Problem with Time Windows

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  • Damianos Gavalas

    (Department of Product & Systems Design Engineering, University of the Aegean, Syros, 84100, Greece and Computer Technology Institute and Press, “Diophantus” (CTI), Patras, Greece)

  • Charalampos Konstantopoulos

    (Department of Informatics, University of Piraeus, Karaoli & Dimitriou 80 Piraeus, 18534, Greece and Computer Technology Institute and Press, “Diophantus” (CTI), Patras, Greece)

  • Konstantinos Mastakas

    (School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Heroon Polytechniou 9 Zografou, 15780, Greece and Computer Technology Institute and Press, “Diophantus” (CTI), Patras, Greece)

  • Grammati Pantziou

    (Department of Informatics and Computer Engineering, University of West Attica, Agiou Spyridonos Aigaleo, 12243, Greece and Computer Technology Institute and Press, “Diophantus” (CTI), Patras, Greece)

Abstract

In the Team Orienteering Problem with Time Windows (TOPTW), a variant of the Vehicle Routing Problem with Profits, a set of locations is given, each associated with a profit, a visiting time and a time window. The aim is to maximize the overall profit collected by a number of routes, while the duration of each route must not exceed a given time budget. TOPTW is NP-hard and is typically used to model the Tourist Trip Design Problem. The latter deals with deriving near optimal multiple-day tours for tourists visiting a destination with several points of interest (POIs). The most efficient known heuristic approach to TOPTW which yields the best solution quality versus execution time, is based on Iterated Local Search (ILS). However, the ILS algorithm treats each node separately, hence it tends to overlook highly profitable areas of nodes situated far from the current solution, considering them too time-expensive to visit. We propose two cluster-based extensions to ILS addressing the aforementioned weakness by grouping nodes on separate clusters (based on geographical criteria), thereby making visits to such nodes more attractive. Our approaches improve ILS with respect to solutions quality and execution time as evidenced by experimental tests exercised on both existing and new TTDP-oriented benchmark instances.

Suggested Citation

  • Damianos Gavalas & Charalampos Konstantopoulos & Konstantinos Mastakas & Grammati Pantziou, 2019. "Efficient Cluster-Based Heuristics for the Team Orienteering Problem with Time Windows," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-44, February.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:01:n:s0217595919500015
    DOI: 10.1142/S0217595919500015
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    References listed on IDEAS

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    1. Hu, Qian & Lim, Andrew, 2014. "An iterative three-component heuristic for the team orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 232(2), pages 276-286.
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    6. Bruce L. Golden & Larry Levy & Rakesh Vohra, 1987. "The orienteering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 307-318, June.
    7. Labadie, Nacima & Mansini, Renata & Melechovský, Jan & Wolfler Calvo, Roberto, 2012. "The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search," European Journal of Operational Research, Elsevier, vol. 220(1), pages 15-27.
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    1. Ruiz-Meza, José & Montoya-Torres, Jairo R., 2022. "A systematic literature review for the tourist trip design problem: Extensions, solution techniques and future research lines," Operations Research Perspectives, Elsevier, vol. 9(C).

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