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

机译：规范下非凸约束多源Weber问题的基于ADMM的位置分配算法

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摘要

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.
机译：多源Weber问题（MSWP）是设施位置中的经典非凸和NP硬模型。解决MSWP的一种众所周知的方法是位置分配算法，该算法包括一个用于定位新设施的定位阶段和一个在每次迭代中分配客户的分配阶段。本文考虑了称为约束多源Weber问题（CMSWP）的MSWP的更一般，更实际的案例，即考虑到用于测量新设施的距离和位置约束的量规来定位多个设施。根据重构后所涉及的位置子问题的有利结构，乘数交替方向法（ADMM）型方法有助于在统一框架下解决不同距离度量下的这些子问题。提出了一种基于ADMM的CMSWP定位算法，并从理论上证明了其局部收敛性。报告了一些初步的数值结果，以验证所提出方法的有效性。

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    《Journal of Global Optimization》 |2020年第4期|793-818|共26页
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    Nanjing Univ Aeronaut & Astronaut Dept Math Coll Sci Nanjing 210016 Peoples R China|Yangtze Univ Sch Informat & Math Jingzhou 434023 Peoples R China;

    Nankai Univ Sch Business Tianjin 300071 Peoples R China;

    Yangtze Univ Sch Informat & Math Jingzhou 434023 Peoples R China;

    Shanghai Univ Sch Mech Engn & Automat Shanghai 200444 Peoples R China|Shanghai Univ Shanghai Key Lab Power Stn Automat Technol Shanghai 200444 Peoples R China;

    Nanjing Univ Aeronaut & Astronaut Dept Math Coll Sci Nanjing 210016 Peoples R China;

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  • 正文语种 eng
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  • 关键词

    Multi-source Weber problem; Nonconvex; Location-allocation; ADMM; Gauge;

    机译：多源韦伯问题;非凸位置分配;ADMM;测量;

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