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A fast solution method for the time-dependent orienteering problem

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  • Verbeeck, C.
  • Sörensen, K.
  • Aghezzaf, E.-H.
  • Vansteenwegen, P.

Abstract

This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4% with an average computation time of 0.5seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings.

Suggested Citation

  • Verbeeck, C. & Sörensen, K. & Aghezzaf, E.-H. & Vansteenwegen, P., 2014. "A fast solution method for the time-dependent orienteering problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 419-432.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:419-432
    DOI: 10.1016/j.ejor.2013.11.038
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    2. Visser, T.R. & Spliet, R., 2017. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Econometric Institute Research Papers EI2017-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    4. Zhao, Yanlu & Alfandari, Laurent, 2020. "Design of diversified package tours for the digital travel industry : A branch-cut-and-price approach," European Journal of Operational Research, Elsevier, vol. 285(3), pages 825-843.
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    7. Merve Kayacı Çodur & Mustafa Yılmaz, 2020. "A time-dependent hierarchical Chinese postman problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 337-366, March.
    8. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    9. Krzysztof Ostrowski & Joanna Karbowska-Chilinska & Jolanta Koszelew & Pawel Zabielski, 2017. "Evolution-inspired local improvement algorithm solving orienteering problem," Annals of Operations Research, Springer, vol. 253(1), pages 519-543, June.
    10. Cédric Verbeeck & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "The time-dependent orienteering problem with time windows: a fast ant colony system," Annals of Operations Research, Springer, vol. 254(1), pages 481-505, July.
    11. Yu, Qinxiao & Fang, Kan & Zhu, Ning & Ma, Shoufeng, 2019. "A matheuristic approach to the orienteering problem with service time dependent profits," European Journal of Operational Research, Elsevier, vol. 273(2), pages 488-503.
    12. Thomas R. Visser & Remy Spliet, 2020. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Transportation Science, INFORMS, vol. 54(4), pages 1091-1112, July.
    13. Mei, Yi & Salim, Flora D. & Li, Xiaodong, 2016. "Efficient meta-heuristics for the Multi-Objective Time-Dependent Orienteering Problem," European Journal of Operational Research, Elsevier, vol. 254(2), pages 443-457.
    14. 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.
    15. Zheng, Weimin & Liao, Zhixue & Qin, Jing, 2017. "Using a four-step heuristic algorithm to design personalized day tour route within a tourist attraction," Tourism Management, Elsevier, vol. 62(C), pages 335-349.
    16. Bian, Zheyong & Liu, Xiang, 2018. "A real-time adjustment strategy for the operational level stochastic orienteering problem: A simulation-aided optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 246-266.
    17. Sun, Peng & Veelenturf, Lucas P. & Dabia, Said & Van Woensel, Tom, 2018. "The time-dependent capacitated profitable tour problem with time windows and precedence constraints," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1058-1073.
    18. Morin, Michael & Abi-Zeid, Irène & Quimper, Claude-Guy, 2023. "Ant colony optimization for path planning in search and rescue operations," European Journal of Operational Research, Elsevier, vol. 305(1), pages 53-63.

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