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Proportion-based robust optimization and team orienteering problem with interval data

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  • Ke, Liangjun
  • Xu, Zongben
  • Feng, Zuren
  • Shang, Ke
  • Qian, Xueming

Abstract

In this paper, a proportion-based robust optimization approach is developed to deal with uncertain combinatorial optimization problems. This approach assumes that a certain proportion of uncertain coefficients in each solution are allowed to change and optimizes a deterministic model so as to achieve a trade-off between optimality and feasibility when the coefficients change. We apply this approach on team orienteering problem with interval data (TOPID), a variant of vehicle routing problem, which has not yet been studied before. A branch and price algorithm is proposed to solve the robust counterpart by using two novel dominance relations. Finally, numerical study is performed. The results show the usefulness of the proposed robust optimization approach and the effectiveness of our algorithm.

Suggested Citation

  • Ke, Liangjun & Xu, Zongben & Feng, Zuren & Shang, Ke & Qian, Xueming, 2013. "Proportion-based robust optimization and team orienteering problem with interval data," European Journal of Operational Research, Elsevier, vol. 226(1), pages 19-31.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:19-31
    DOI: 10.1016/j.ejor.2012.10.038
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    References listed on IDEAS

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    1. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    2. Chao, I-Ming & Golden, Bruce L. & Wasil, Edward A., 1996. "The team orienteering problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 464-474, February.
    3. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    4. Vansteenwegen, Pieter & Souffriau, Wouter & Berghe, Greet Vanden & Oudheusden, Dirk Van, 2009. "A guided local search metaheuristic for the team orienteering problem," European Journal of Operational Research, Elsevier, vol. 196(1), pages 118-127, July.
    5. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    6. 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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    Cited by:

    1. 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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