Abstract The obnoxious p-median problem (OpM) is to determine a set of opened facilities such that the sum of distances between each client and the opened facilities is maximized. OpM is a general model that has a wide range of practical applications. However the problem is computationally challenging because it is known to be NP-hard. In this work, we propose an effective parallel iterative solution-based tabu search algorithm to solve OpM. The proposed algorithm combines a delete-add compound move instead of a typical time-consuming swap move to improve neighborhood exploration, a solution-based tabu search procedure to strictly prevent visited solutions from being revisited, a perturbation scheme similar to the shaking phase of variable neighborhood search for diversification, and a parallel strategy of leveraging multiple processors of a computer. Experimental results on 144 benchmark instances demonstrate that the proposed algorithm is able to find new lower bounds for 7 instances and match the best known results for the other instances. Further experimental analysis sheds light on the key ingredients to the performance of the proposed algorithm. The code of our PISTS algorithm is publicly available to facilitate future comparative studies.

中文翻译：

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基于并行迭代解法的禁忌搜索令人讨厌的 p 中值问题

摘要 讨厌的 p 中值问题 (OpM) 是确定一组已打开的设施，以使每个客户端与已打开设施之间的距离总和最大化。OpM 是一种通用模型，具有广泛的实际应用。然而，该问题在计算上具有挑战性，因为已知它是 NP 难的。在这项工作中，我们提出了一种有效的基于并行迭代解决方案的禁忌搜索算法来解决 OpM。所提出的算法结合了删除-添加复合移动而不是典型的耗时的交换移动来改进邻域探索，一种基于解决方案的禁忌搜索程序，以严格防止访问的解决方案被重新访问，一种类似于变量振动阶段的扰动方案邻里搜索多样化，以及利用计算机的多个处理器的并行策略。在 144 个基准实​​例上的实验结果表明，所提出的算法能够为 7 个实例找到新的下限，并匹配其他实例的最佳已知结果。进一步的实验分析揭示了所提出算法的性能的关键因素。我们的 PISTS 算法的代码是公开的，以方便未来的比较研究。