A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand
A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand
复制标题
基于 Barzilai-Borwein 的启发式算法，用于根据区域需求定位多个设施
DOI：
10.1007/s10589-010-9392-9
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发表时间：
2011-01
影响因子：
2.2
通讯作者：
Xiaoming Yuan
中科院分区：
文献类型：
--
作者：
Jianlin Jiang;Xiaoming Yuan
我们对平面上多个设施的位置感兴趣，目的是最小化这些设施和区域客户之间的加权距离之和，其中设施和区域客户之间的距离由该设施到需求区域的最远距离来评估。通过应用著名的位置分配启发式算法，解决这一问题的主要任务是解决一系列约束韦伯问题（CWPs）。本文通过开发经典Barzilai-Borwein （BB）梯度方法的一种变体来求解减少的CWPs，重点介绍了该主题的计算贡献。因此，提出了一种混合库珀型方法来解决所考虑的问题。初步的数值结果验证了新方法的明显有效性。
We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.