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Inverse Maximum Flow Problem Under the Combination of the Weighted l\(_2\) Norm and the Weighted Hamming Distance

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Abstract

The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal. The modification cost is measured by different norms, such as \(l_1, l_2, l_\infty \) norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse maximum flow problem under the combination of the weighted \(l_2\) norm and the weighted Hamming distance, i.e., the modification cost is fixed in a given interval and depends on the modification out of the given interval. We present a combinatorial algorithm which can be finished in O(nm) to solve it due to the minimum cut of the residual network.

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Acknowledgements

The authors wish to thank the anonymous referees whose valuable comments allowed us to improve the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China

    Long-Cheng Liu & Han Gao

  2. School of Mathematics and Computer, Wuyi University, Wuyishan, 354300, Fujian, China

    Chao Li

Authors
  1. Long-Cheng Liu
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  2. Han Gao
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  3. Chao Li
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Corresponding author

Correspondence to Long-Cheng Liu.

Additional information

This research is supported by the Fundamental Research Funds for the Central Universities (No. 20720190068) and the China Scholarship Council (No. 201706315073).

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Liu, LC., Gao, H. & Li, C. Inverse Maximum Flow Problem Under the Combination of the Weighted l\(_2\) Norm and the Weighted Hamming Distance. J. Oper. Res. Soc. China 9, 465–474 (2021). https://doi.org/10.1007/s40305-019-00273-w

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  • DOI: https://doi.org/10.1007/s40305-019-00273-w

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