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

Author

Listed:
  • Jianlin Jiang

    (Nanjing University of Aeronautics and Astronautics
    Yangtze University)

  • Su Zhang

    (Nankai University)

  • Yibing Lv

    (Yangtze University)

  • Xin Du

    (Shanghai University)

  • Ziwei Yan

    (Nanjing University of Aeronautics and Astronautics)

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.

Suggested Citation

  • Jianlin Jiang & Su Zhang & Yibing Lv & Xin Du & Ziwei Yan, 2020. "An ADMM-based location–allocation algorithm for nonconvex constrained multi-source Weber problem under gauge," Journal of Global Optimization, Springer, vol. 76(4), pages 793-818, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00796-9
    DOI: 10.1007/s10898-019-00796-9
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    References listed on IDEAS

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    1. Ya-Feng Liu & Xin Liu & Shiqian Ma, 2019. "On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 632-650, May.
    2. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    3. Jack Brimberg & Robert F. Love, 1993. "Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp Distances," Operations Research, INFORMS, vol. 41(6), pages 1153-1163, December.
    4. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    5. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    6. Robert F. Love & James G. Morris, 1979. "Mathematical Models of Road Travel Distances," Management Science, INFORMS, vol. 25(2), pages 130-139, February.
    7. Emilio Carrizosa & Eduardo Conde & Manuel Muñoz-Márquez & Justo Puerto, 1997. "Simpson Points in Planar Problems with Locational Constraints. The Polyhedral-Gauge Case," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 291-300, May.
    8. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    9. Lawrence M. Ostresh, 1978. "On the Convergence of a Class of Iterative Methods for Solving the Weber Location Problem," Operations Research, INFORMS, vol. 26(4), pages 597-609, August.
    10. Jiang, Jian-Lin & Yuan, Xiao-Ming, 2008. "A heuristic algorithm for constrained multi-source Weber problem - The variational inequality approach," European Journal of Operational Research, Elsevier, vol. 187(2), pages 357-370, June.
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    Cited by:

    1. Jianlin Jiang & Liyun Ling & Yan Gu & Su Zhang & Yibing Lv, 2023. "Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 362-389, January.
    2. Yan Gu & Jianlin Jiang & Shun Zhang, 2023. "Distributionally robust Weber problem with uncertain demand," Computational Optimization and Applications, Springer, vol. 85(3), pages 705-752, July.

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