The parallel row ordering problem (PROP) is concerned with arranging two groups of facilities along two parallel lines with the goal of minimizing the sum of the flow cost-weighted distances between the pairs of facilities. As the main result of this paper, we show that the insertion neighborhood for the PROP can be explored in optimal time Θ(n2) by providing an O(n2)-time procedure for performing this task, where n is the number of facilities. As a case study, we incorporate this procedure in a memetic algorithm (MA) for solving the PROP. We report on numerical experiments that we conducted with MA on PROP instances with up to 500 facilities. The experimental results demonstrate that the MA is superior to the adaptive iterated local search algorithm and the parallel hyper heuristic method, which are state-of-the-art for the PROP. Remarkably, our algorithm improved best known solutions for six largest instances in the literature. We conjecture that the time complexity of exploring the interchange neighborhood for the PROP is Θ(n2), exactly as in the case of insertion operation.

中文翻译：

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一种基于快速局部搜索的并行行排序问题模因算法


并行行排序问题 （PROP） 涉及沿两条平行线排列两组设施点，目的是最小化设施点对之间的流成本加权距离之和。作为本文的主要结果，我们表明可以通过提供执行此任务的 O（n2） 时间程序，在最佳时间 Θ（n2） 中探索 PROP 的插入邻域，其中 n 是设施点的数量。作为一个案例研究，我们将此过程纳入用于解决 PROP 的模因算法 （MA） 中。我们报告了我们使用 MA 在多达 500 个设施点的 PROP 实例上进行的数值实验。实验结果表明，MA 优于自适应迭代局部搜索算法和并行超启发式方法，这是 PROP 的最新技术。值得注意的是，我们的算法改进了文献中六个最大实例的已知解决方案。我们推测，探索 PROP 的交换邻域的时间复杂度为 Θ（n2），与插入操作的情况完全相同。