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The minmax regret inverse maximum weight problem

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  • Nguyen, Kien Trung
  • Hung, Nguyen Thanh

Abstract

Let a ground set E and a prespecified element be given. We address the problem of modifying the weight of each element in E at minimum cost so that the weight of the prespecified element become the maximum one in the perturbed set. Moreover, as modifying costs are usually uncertain in many real life situations, we measure the robustness by taking into account the minmax regret inverse maximum weight problem on E. In order to solve the problem, we first prove that there are exactly two scenarios that lead to the maximum regret of the cost function. Based on the convexity of the objective function, we develop a combinatorial algorithm that solves the corresponding problem in linear time.

Suggested Citation

  • Nguyen, Kien Trung & Hung, Nguyen Thanh, 2021. "The minmax regret inverse maximum weight problem," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321004173
    DOI: 10.1016/j.amc.2021.126328
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    1. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    2. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    3. Xiaoguang Yang & Jianzhong Zhang, 2007. "Some inverse min-max network problems under weighted l 1 and l ∞ norms with bound constraints on changes," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 123-135, February.
    4. Cai Mao-Cheng & Yanjun Li, 1997. "Inverse Matroid Intersection Problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 235-243, June.
    5. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
    6. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    7. Cai, Mao-Cheng & Duin, C.W. & Yang, Xiaoguang & Zhang, Jianzhong, 2008. "The partial inverse minimum spanning tree problem when weight increase is forbidden," European Journal of Operational Research, Elsevier, vol. 188(2), pages 348-353, July.
    8. Gassner, Elisabeth, 2009. "Up- and downgrading the 1-center in a network," European Journal of Operational Research, Elsevier, vol. 198(2), pages 370-377, October.
    9. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.
    10. Kien Trung Nguyen, 2016. "Inverse 1-Median Problem on Block Graphs with Variable Vertex Weights," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 944-957, March.
    11. Zhao Zhang & Shuangshuang Li & Hong-Jian Lai & Ding-Zhu Du, 2016. "Algorithms for the partial inverse matroid problem in which weights can only be increased," Journal of Global Optimization, Springer, vol. 65(4), pages 801-811, August.
    12. Behrooz Alizadeh & Rainer Burkard, 2013. "A linear time algorithm for inverse obnoxious center location problems on networks," 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. 21(3), pages 585-594, September.
    13. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    14. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    15. Kien Trung Nguyen & Huong Nguyen-Thu & Nguyen Thanh Hung, 2018. "On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 147-159, October.
    16. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
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