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A Branch and Bound-Based Algorithm for the Weak Linear Bilevel Programming Problems

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Wuhan University Journal of Natural Sciences

Abstract

Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first (upper level) objective function being minimized over the solution set mapping of the second (lower level) optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm.

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Authors and Affiliations

  1. School of Management, Huaibei Normal University, Huaibei, Anhui, 235000, China

    June Liu & Yue Zheng

  2. School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, 434023, China

    Yunfei Hong

Authors
  1. June Liu
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  2. Yunfei Hong
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  3. Yue Zheng
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Corresponding author

Correspondence to Yunfei Hong.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (11501233), and the Natural Science Research Project of Universities of Anhui Province (KJ2018A0390)

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Liu, J., Hong, Y. & Zheng, Y. A Branch and Bound-Based Algorithm for the Weak Linear Bilevel Programming Problems. Wuhan Univ. J. Nat. Sci. 23, 480–486 (2018). https://doi.org/10.1007/s11859-018-1352-8

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  • DOI: https://doi.org/10.1007/s11859-018-1352-8

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