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Robust balanced optimization

Author

Listed:
  • Annette M. C. Ficker

    (KU Leuven)

  • Frits C. R. Spieksma

    (Eindhoven University of Technology)

  • Gerhard J. Woeginger

    (RWTH Aachen)

Abstract

An instance of a balanced optimization problem with vector costs consists of a ground set X, a cost-vector for every element of X, and a system of feasible subsets over X. The goal is to find a feasible subset that minimizes the so-called imbalance of values in every coordinate of the underlying vector costs. Balanced optimization problems with vector costs are equivalent to the robust optimization version of balanced optimization problems under the min-max criterion. We regard these problems as a family of optimization problems; one particular member of this family is the known balanced assignment problem. We investigate the complexity and approximability of robust balanced optimization problems in a fairly general setting. We identify a large family of problems that admit a 2-approximation in polynomial time, and we show that for many problems in this family this approximation factor 2 is best-possible (unless P = NP). We pay special attention to the balanced assignment problem with vector costs and show that this problem is NP-hard even in the highly restricted case of sum costs. We conclude by performing computational experiments for this problem.

Suggested Citation

  • Annette M. C. Ficker & Frits C. R. Spieksma & Gerhard J. Woeginger, 2018. "Robust balanced optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 239-266, September.
    • Handle: RePEc:spr:eurjco:v:6:y:2018:i:3:d:10.1007_s13675-018-0093-y
    DOI: 10.1007/s13675-018-0093-y
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    References listed on IDEAS

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    1. Kinable, Joris & Smeulders, Bart & Delcour, Eline & Spieksma, Frits C.R., 2017. "Exact algorithms for the Equitable Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 475-485.
    2. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    3. Aharon Ben-Tal & Boaz Golany & Arkadi Nemirovski & Jean-Philippe Vial, 2005. "Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 248-271, February.
    4. Chungmok Lee & Kyungsik Lee & Kyungchul Park & Sungsoo Park, 2012. "Technical Note---Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations," Operations Research, INFORMS, vol. 60(3), pages 604-610, June.
    5. Poss, Michael, 2014. "Robust combinatorial optimization with variable cost uncertainty," European Journal of Operational Research, Elsevier, vol. 237(3), pages 836-845.
    6. Ahuja, Ravindra K., 1997. "The balanced linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 29-38, August.
    7. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    8. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    9. Gorissen, Bram L. & Yanıkoğlu, İhsan & den Hertog, Dick, 2015. "A practical guide to robust optimization," Omega, Elsevier, vol. 53(C), pages 124-137.
    10. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    11. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    1. Arie M. C. A. Koster & Michael Poss, 2018. "Special issue on: robust combinatorial optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 207-209, September.

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