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

  • Jianlin Jiang
  • Su ZhangEmail author
  • Yibing Lv
  • Xin Du
  • Ziwei Yan
S.I.: MOA 2018

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 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Information and MathematicsYangtze UniversityJingzhouChina
  3. 3.Business SchoolNankai UniversityTianjinChina
  4. 4.School of Mechanical Engineering and Automation and Shanghai Key Laboratory of Power Station Automation TechnologyShanghai UniversityShanghaiChina

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