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

Jianlin Jiang (), Su Zhang (), Yibing Lv (), Xin Du () and Ziwei Yan ()
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Jianlin Jiang: Nanjing University of Aeronautics and Astronautics
Su Zhang: Nankai University
Yibing Lv: Yangtze University
Xin Du: Shanghai University
Ziwei Yan: Nanjing University of Aeronautics and Astronautics

Journal of Global Optimization, 2020, vol. 76, issue 4, No 8, 793-818

Abstract: 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.

Keywords: Multi-source Weber problem; Nonconvex; Location–allocation; ADMM; Gauge (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-019-00796-9

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