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The lower bounded inverse optimal value problem on minimum spanning tree under unit \(l_{\infty }\) norm

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Abstract

We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit \(l_{\infty }\) norm. Given an edge weighted connected undirected network \(G=(V,E,\varvec{w})\), a spanning tree \(T^0\), a lower bound vector \(\varvec{l}\) and a value K, we aim to find a new weight vector \(\bar{\varvec{w}}\) respecting the lower bound such that \(T^0\) is a minimum spanning tree under the vector \(\bar{\varvec{w}}\) with weight K, and the objective is to minimize the modification cost under unit \(l_{\infty }\) norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop a strongly polynomial time algorithm with running time O(|V||E|). Finally, we give an example to demonstrate the algorithm and present the numerical experiments.

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Acknowledgements

Research is supported by National Natural Science Foundation of China (11471073,11901153), Chinese Universities Scientific Fund (2018B44014) and the Natural Science Foundation of Jiangsu Province, China (20170298). The work of P.M. Pardalos was conducted within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE).

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Authors and Affiliations

  1. College of Science, Hohai University, Nanjing, 210098, China

    Binwu Zhang & Yan Liu

  2. Institute of Intelligent Optimization and Control, Hohai University, Nanjing, 210098, China

    Binwu Zhang & Yan Liu

  3. School of Mathematics, Southeast University, Nanjing, 210096, China

    Xiucui Guan, Hui Wang & Qiao Zhang

  4. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  5. LATNA, Higher School of Economics, Moscow, Russia

    Panos M. Pardalos

  6. School of Business Administration, Hohai University, Changzhou, 213022, China

    Shuyi Chen

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  1. Binwu Zhang
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  2. Xiucui Guan
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  4. Hui Wang
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  5. Qiao Zhang
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  6. Yan Liu
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Correspondence to Xiucui Guan.

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Zhang, B., Guan, X., Pardalos, P.M. et al. The lower bounded inverse optimal value problem on minimum spanning tree under unit \(l_{\infty }\) norm. J Glob Optim 79, 757–777 (2021). https://doi.org/10.1007/s10898-020-00947-3

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