A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach
A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach
复制标题
测量下最近距离约束多源定位问题的启发式算法：变分不等式方法
DOI：
10.1155/2013/624398
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发表时间：
2013-10
影响因子：
--
通讯作者：
Xiao-xing Zhu
中科院分区：
文献类型：
--
作者：
Jian-lin Jiang;Saeed Assani;Kun Cheng;Xiao-xing Zhu
本文考虑了空间中多个设施的位置，旨在最小化设施与区域客户之间的加权距离之和，其中设施与区域客户之间的邻近度通过最近距离来评估。由于设施通常被允许位于某些限制区域，因此我们问题的设施受到了一些位置限制。此外，由于在实际情况中有时会违反距离的对称性，因此本文采用量规代替常用的标准来测量对称和非对称距离。本着库珀算法（Cooper，1964）的精神，提出了一种新的位置分配启发式算法来解决这个问题。在选址阶段，将具有区域需求的单源子问题重新表述为等效的线性变分不等式（LVI），然后采用投影收缩（PC）方法来寻找设施的最佳位置，而在分配阶段，根据最近中心重分类（NCR）将区域客户分配给设施。在温和的假设下证明了所提出算法的收敛性。一些初步的数值结果表明了新算法的有效性。
This paper considers the locations of multiple facilities in the space , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facilities are usually allowed to be sited in certain restricted areas, some locational constraints are imposed to the facilities of our problem. In addition, since the symmetry of distances is sometimes violated in practical situations, the gauge is employed in this paper instead of the frequently used norms for measuring both the symmetric and asymmetric distances. In the spirit of the Cooper algorithm (Cooper, 1964), a new location-allocation heuristic algorithm is proposed to solve this problem. In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). The convergence of the proposed algorithm is proved under mild assumptions. Some preliminary numerical results are reported to show the effectiveness of the new algorithm.
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影响因子：
5.4
作者：
LOVE, RF;MORRIS, JG
通讯作者：
MORRIS, JG
基于 Barzilai-Borwein 的启发式算法，用于根据区域需求定位多个设施
影响因子：
2.2
作者：
Jianlin Jiang;Xiaoming Yuan
通讯作者：
Xiaoming Yuan
影响因子：
1.9
作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
通讯作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
DOI：
10.1016/j.amc.2013.01.067
发表时间：
2013-03
期刊：
Appl. Math. Comput.
影响因子：
--
作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
通讯作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
DOI：
10.1007/b97543
发表时间：
2003
期刊：
--
影响因子：
--
作者：
F. Facchinei;J. Pang
通讯作者：
F. Facchinei;J. Pang