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A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

机译：设施固定成本的带容量多源韦伯问题的基于交叉熵的启发式方法：连续位置问题的交叉熵

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摘要

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones.
机译：本文研究了设施固定成本下的容量有限的平面位置分配问题。考虑由生产和安装成本组成的基于区域的固定成本。首先提出了非线性混合整数公式。提出了一种具有新型密度函数的强大的三阶段交叉熵元启发式算法。在第一阶段，解决了覆盖位置问题，该覆盖位置问题为相关的随机问题提供了多元正态密度函数。在第二阶段获得考虑多项式密度函数的分配值。在第三阶段，解决了单一设施连续定位的问题。使用各种大小的几种实例来评估所提出的元启发式算法的性能。与优化器GAMS相比，我们的方法效果很好，该优化器用于为小型实例提供最佳解决方案，并为某些较大实例提供下限/上限。

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