带有升级的诱导P-中位问题的元启发式算法
Metaheuristic algorithms for the induced P-median problem with upgrades
AI总结：
本文提出了一种基于GRASP的元启发式算法，用于解决带有升级的诱导P-中位问题，通过改进执行效率和解决复杂实例的能力，展示了优于传统数学规划模型的性能。
摘要：
设施选址问题（FLPs）是一类具有重大社会影响的优化问题。自20世纪60年代以来，这类问题一直是研究的焦点，经典方法包括韦伯问题和p-中位问题。目前，这些问题的更复杂变种正在被研究。特别是，诱导p-中位问题带升级（IpMU）代表了经典p-中位问题的一种变种，其中运输成本和时间作为输入图中的不同度量被分离。此外，该问题包含一个预算，允许放松图成本，从而减少边的成本，从而改善指定中位数与客户之间的相关路线。在本研究中，提出了一种基于贪心随机自适应搜索程序（GRASP）的元启发式算法。定义了一个两阶段解决方案，分别研究中位问题和升级问题。在该方法中，分析了一组更先进的实例，以确保与先前提案的公平比较。此外，研究了实例的特性以评估其复杂性。获得的结果在与基于数学规划模型的现有状态相比时很有希望。对于更难的实例，执行时间平均提高了两个数量级，且在超过99%的测试实例中获得了最佳已知结果。
英文摘要：
Facility location problems (FLPs) are a family of optimisation problems with significant social impact. This class of problems has been the subject of study since the 1960s, with classical approaches including the Weber problem and the p-Median problem. Currently, more complex variations of these problems are being investigated. In particular, the Induced p-Median Problem with Upgrades (IpMU) represents a variation of the classical p-Median problem, where the concepts of transport cost and time are separated as distinct metrics in the input graph of the problem. Furthermore, the problem includes a budget which allows one to relax the graph costs, reducing the cost of the edges, thus improving the associated routes between the designated medians and the customers. In this study, a metaheuristic algorithm, based on the Greedy Randomized Adaptive Search Procedure (GRASP), is proposed. A two-phase resolution scheme is defined, studying the median problem and the upgrading problem independently. In this approach, a larger set of state-of-the-art instances was analysed to ensure a fair comparison with previous proposals. In addition, the characteristics of the instances were studied to assess their complexity. The results obtained are promising when compared to the state-of-the-art, which is based entirely on mathematical programming models. The execution time was improved on average by two orders of magnitude for the harder instances, and the best known result was obtained in more than 99% of the tested instances.
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