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An ADMM-based location–allocation algorithm for nonconvex constrained multi-source Weber problem under gauge

  • S.I.: MOA 2018
  • Published:
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Abstract

Multi-source Weber problem (MSWP) is a classical nonconvex and NP-hard model in facility location. A well-known method for solving MSWP is the location–allocation algorithm which consists of a location phase to locate new facilities and an allocation phase to allocate customers at each iteration. This paper considers the more general and practical case of MSWP called the constrained multi-source Weber problem (CMSWP), i.e., locating multiple facilities with the consideration of the gauge for measuring distances and locational constraints on new facilities. According to the favorable structure of the involved location subproblems after reformulation, an alternating direction method of multipliers (ADMM) type method is contributed to solving these subproblems under different distance measures in a uniform framework. Then a new ADMM-based location–allocation algorithm is presented for CMSWP and its local convergence is theoretically proved. Some preliminary numerical results are reported to verify the effectiveness of proposed methods.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jianlin Jiang & Ziwei Yan

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

    Jianlin Jiang & Yibing Lv

  3. Business School, Nankai University, Tianjin, 300071, China

    Su Zhang

  4. School of Mechanical Engineering and Automation and Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200444, China

    Xin Du

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  1. Jianlin Jiang
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  2. Su Zhang
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  3. Yibing Lv
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  4. Xin Du
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Correspondence to Su Zhang.

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The first author was supported by National Natural Science Foundation of China No. 11571169. The second author was supported by National Natural Science Foundation of China No. 71772094.

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Jiang, J., Zhang, S., Lv, Y. et al. An ADMM-based location–allocation algorithm for nonconvex constrained multi-source Weber problem under gauge. J Glob Optim 76, 793–818 (2020). https://doi.org/10.1007/s10898-019-00796-9

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