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Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty

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  • Raith, Andrea
  • Schmidt, Marie
  • Schöbel, Anita
  • Thom, Lisa

Abstract

In this paper, we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an existing algorithm for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation.

Suggested Citation

  • Raith, Andrea & Schmidt, Marie & Schöbel, Anita & Thom, Lisa, 2018. "Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty," European Journal of Operational Research, Elsevier, vol. 267(2), pages 628-642.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:628-642
    DOI: 10.1016/j.ejor.2017.12.018
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    References listed on IDEAS

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    Cited by:

    1. Majid Askarifard & Hamidreza Abbasianjahromi & Mehran Sepehri & Ehsanollah Zeighami, 2021. "A robust multi-objective optimization model for project scheduling considering risk and sustainable development criteria," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(8), pages 11494-11524, August.
    2. Yong Wang & Qin Li & Xiangyang Guan & Jianxin Fan & Yong Liu & Haizhong Wang, 2020. "Collaboration and Resource Sharing in the Multidepot Multiperiod Vehicle Routing Problem with Pickups and Deliveries," Sustainability, MDPI, vol. 12(15), pages 1-33, July.
    3. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    4. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    5. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    6. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    7. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.
    8. Schmidt, M. & Schöbel, Anita & Thom, Lisa, 2019. "Min-ordering and max-ordering scalarization methods for multi-objective robust optimization," European Journal of Operational Research, Elsevier, vol. 275(2), pages 446-459.

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