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An efficient and scalable approach to hub location problems based on contraction
Computers & Industrial Engineering ( IF 7.9 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.cie.2020.106955
Sebastian Wandelt , Weibin Dai , Jun Zhang , Qiuhong Zhao , Xiaoqian Sun

Abstract Solving the vast majority of hub location problems is NP-hard, implying that optimally solving large-scale instances (with hundreds of nodes) with exact solution techniques is extremely difficult. While heuristics have been developed which scale up to hundreds of nodes for specific problem types, these techniques do not scale up for further larger instances (with thousands of nodes) or intriguing problem variants. In this paper, we propose EHLC (Efficient Hub Location by Contraction), which exploits the idea of efficiently computing hub locations on a reduced network instance, so-called contracted network. The obtained solutions are rewritten back to the original network, followed by a final optimization step. A rich set of computational experiments on instances with up to 5000 nodes and different problem types, i.e., USApHMPC, CSApHMPC, USApHMPI, UMApHMPC, CMApHMPC, and UMApHMPI shows that EHLC outperforms the existing solution techniques by orders of magnitude regarding execution time, while achieving solutions with identical gaps for almost all datasets and parameter combinations. For large enough datasets or complex hub location problems, EHLC has a speedup of over 20 times (such as GA, GVNS for USApHMPI on URAND1000 and Benders for UMApHMPI on TR40), compared to non-contracted methods. Given the same time limit, EHLC provides final solutions with similar or better qualities for most instances, such as EHLC_GVNS and NC_GVNS reach the optimal solutions for most instances.

中文翻译:

基于收缩的枢纽位置问题的有效且可扩展的方法

摘要 解决绝大多数枢纽位置问题是 NP-hard 问题,这意味着使用精确求解技术优化解决大规模实例(具有数百个节点)是极其困难的。虽然已经开发出可以针对特定问题类型扩展到数百个节点的启发式方法,但这些技术并没有扩展到更大的实例(具有数千个节点)或有趣的问题变体。在本文中,我们提出了 EHLC(Efficient Hub Location by Contraction),它利用了在减少的网络实例(即所谓的收缩网络)上有效计算集线器位置的想法。将获得的解决方案重写回原始网络,然后进行最后的优化步骤。在多达 5000 个节点和不同问题类型的实例上进行了丰富的计算实验,即 USApHMPC、CSApHMPC、USApHMPI、UMApHMPC、CMApHMPC 和 UMApHMPI 表明,EHLC 在执行时间方面在数量级上优于现有解决方案技术,同时为几乎所有数据集和参数组合实现了具有相同间隙的解决方案。对于足够大的数据集或复杂的枢纽位置问题,与非契约方法相比,EHLC 具有超过 20 倍的加速(例如 GA、GVNS 用于 URAND1000 上的 USApHMPI 和 Benders 用于 TR40 上的 UMApHMPI)。在相同的时间限制下,EHLC 为大多数实例提供具有相似或更好质量的最终解决方案,例如 EHLC_GVNS 和 NC_GVNS 达到大多数实例的最佳解决方案。同时为几乎所有数据集和参数组合实现具有相同间隙的解决方案。对于足够大的数据集或复杂的枢纽位置问题,与非契约方法相比,EHLC 具有超过 20 倍的加速(例如 GA、GVNS 用于 URAND1000 上的 USApHMPI 和 Benders 用于 TR40 上的 UMApHMPI)。在相同的时间限制下,EHLC 为大多数实例提供具有相似或更好质量的最终解决方案,例如 EHLC_GVNS 和 NC_GVNS 达到大多数实例的最佳解决方案。同时为几乎所有数据集和参数组合实现具有相同间隙的解决方案。对于足够大的数据集或复杂的枢纽位置问题,与非契约方法相比,EHLC 具有超过 20 倍的加速(例如 GA、GVNS 用于 URAND1000 上的 USApHMPI 和 Benders 用于 TR40 上的 UMApHMPI)。在相同的时间限制下,EHLC 为大多数实例提供具有相似或更好质量的最终解决方案,例如 EHLC_GVNS 和 NC_GVNS 达到大多数实例的最佳解决方案。
更新日期:2021-01-01
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