The aim of this work is to locate a semi-obnoxious facility, i.e. to minimize the distances to a given set of customers in order to save transportation costs on the one hand and to avoid undesirable interactions with other facilities within the region by maximizing the distances to the corresponding facilities on the other hand. Hence, the goal is to satisfy economic and environmental issues simultaneously. Due to the contradicting character of these goals, we obtain a non-convex objective function. We assume that distances can be measured by rectilinear distances and exploit the structure of this norm to obtain a very efficient dual pair of algorithms.

中文翻译：

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在曼哈顿距离的特殊情况下定位半令人讨厌的设施

这项工作的目的是找到一个半令人讨厌的设施，即最大程度地减少与给定客户群的距离，以便一方面节省运输成本，并通过最大化距离来避免与该区域内其他设施的不良相互作用另一方面到相应的设施。因此，目标是同时满足经济和环境问题。由于这些目标的矛盾性，我们获得了非凸目标函数。我们假设可以通过直线距离来测量距离，并利用该范数的结构来获得非常有效的双对算法。