In this paper we address the multiple obnoxious facility location problem. In this problem p facilities need to be spread within the unit square in such a way that they are far enough from each other and that their minimal distance from n communities, with known positions within the unit square, is maximized. The problem has a combinatorial component, related to the key observation made in Drezner (Omega 87:105–116, 2019) about the role played by Voronoi points. We propose a new approach, which exploits both the combinatorial component of the problem and, through continuous local optimizations, also its continuous component. We also propose techniques to limit the impact on computation times of the number n of communities. The approach turns out to be quite competitive and is able to return 24 new best known solutions with respect to the best results reported in Kalczynski (Optim Lett 16:1153–1166, 2022).

在本文中，我们解决了多个令人讨厌的设施位置问题。在这个问题中，p 个设施需要以这样的方式分布在单位正方形内：它们彼此之间足够远，并且它们与单位正方形内已知位置的n 个社区的最小距离最大化。该问题具有组合成分，与 Drezner (Omega 87:105–116, 2019) 中关于 Voronoi 点所扮演的角色的关键观察相关。我们提出了一种新方法，它既利用问题的组合部分，又通过连续局部优化，利用其连续部分。我们还提出了限制社区数量n对计算时间影响的技术。事实证明，该方法非常有竞争力，并且能够返回 24 个新的最著名的解决方案，与 Kalczynski 报告的最佳结果相比（Optim Lett 16:1153–1166, 2022）。