讨厌设施平面p-中位数问题
The obnoxious facilities planar p-median problem
摘要：
在本文中，我们提出了平面讨厌的p-中位数问题。在p-median问题中，目标是为设施点找到p个位置，使需求点与其最近设施点之间的距离加权和最小化。在令人讨厌的版本中，我们添加了约束，每个设施必须位于至少有一定的距离，从一组部分的需求点，因为他们产生滋扰影响这些需求点。由此产生的问题是非常非凸和传统的非线性求解器，如SNOPT是没有效率的。提出并验证了一种基于Voronoi图的有效解方法。我们还构造了有效的边界的测试问题，以帮助规划者在作出位置的决定。
英文摘要：
In this paper we propose the planar obnoxious p-median problem. In the p-median problem the objective is to find p locations for facilities that minimize the weighted sum of distances between demand points and their closest facility. In the obnoxious version we add constraints that each facility must be located at least a certain distance from a partial set of demand points because they generate nuisance affecting these demand points. The resulting problem is extremely non-convex and traditional non-linear solvers such as SNOPT are not efficient. An efficient solution method based on Voronoi diagrams is proposed and tested. We also constructed the efficient frontiers of the test problems to assist the planers in making location decisions.
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