The multiple obnoxious facilities location problem is an extremely non-convex optimization problem with millions of local optima. It is a very challenging problem. We improved the best known solution for 33 out of 76 test instances. We believe that the results of many instances reported here are still not optimal and thus better objective function values exist. We challenge the optimization community to design procedures that will further improve some of the results reported here. Optimality can be proven for a small number of new facilities. Proving optimality for a large number of facilities would be an achievement.

中文翻译：

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极不凸优化问题：多个令人讨厌的设施位置的情况

多个令人讨厌的设施位置问题是具有数百万个局部最优解的极非凸优化问题。这是一个非常具有挑战性的问题。我们为76个测试实例中的33个改进了最著名的解决方案。我们认为这里报告的许多实例的结果仍然不是最佳的，因此存在更好的目标函数值。我们向优化社区提出挑战，要求其设计程序以进一步改善此处报告的某些结果。少数新设施可以证明其最优性。证明大量设施的最优性将是一项成就。