The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new optimal solution approaches are proposed. Two variants of the "Big Triangle Small Triangle" global optimization method, and a procedure based on intersection points between Apollonius circles. We also compared the results with a multi-start approach using the non-linear multi-purpose software SNOPT. Problems with 1,000 demand points are optimally solved in a fraction of a second of computer time.

中文翻译：

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令人讨厌的设施位置：加权需求点的情况

本文考虑的问题是需求点凸包中的加权讨厌设施位置。目标函数是最大化设施点和一组请求点之间的最小加权距离。提出了三种新的最优解方法。“大三角小三角”全局优化方法的两种变体，以及一种基于阿波罗尼乌斯圆之间交点的程序。我们还将结果与使用非线性多用途软件 SNOPT 的多开始方法进行了比较。具有 1,000 个请求点的问题可以在几分之一秒的计算机时间内得到最佳解决。