面向多车场多集合定向越野问题的变邻域搜索算法
Variable Neighborhood Search for the Multi-Depot Multiple Set Orienteering Problem
AI总结：
本文提出多车场多集合定向越野问题（mDmSOP），构建新的数学模型，采用变邻域搜索（VNS）元启发式算法求解，在GTSP基准算例上验证了其在鲁棒性、解质量和计算效率上的优势，且增加旅行者数可显著提升收益。
摘要：
本文提出了集合定向越野问题（Set Orienteering Problem, SOP）的一个变体——多车场多集合定向越野问题（multi-Depot multiple Set Orienteering Problem, mDmSOP）。该问题将节点划分为互斥的集合（簇），每个集合对应相应收益，只要访问集合内任意一个节点即可获得该集合的收益，是对SOP的推广。问题中使用数量为$t$（$t>1$）的多名旅行者，每名旅行者对应一个特定车场，核心目标是在预设预算内最大化从各集合中收集的总收益。本文为mDmSOP提出了一种新的数学建模方式，并采用变邻域搜索（Variable Neighborhood Search, VNS）元启发式算法，在广义旅行商问题（Generalized Traveling Salesman Problem, GTSP）基准的小规模、中规模和大规模算例上求解该问题。结果表明，VNS在鲁棒性和解的质量上更具优势，其所需计算时间少于使用GAMS 37.1.0和CPLEX求解数学模型的耗时。此外，增加旅行者数量可显著提升总收益。
英文摘要：
This paper introduces a variant of the Set Orienteering Problem (SOP), the multi-Depot multiple Set Orienteering Problem (mDmSOP). It generalizes the SOP by grouping nodes into mutually exclusive sets (clusters) with associated profits. Profit can be earned if any node within the set is visited. Multiple travelers, denoted by $t$ $(> 1)$, are employed, with each traveler linked to a specific depot. The primary objective of the problem is to maximize profit collection from the sets within a predefined budget. A novel formulation is introduced for the mDmSOP. The paper utilizes the Variable Neighborhood Search (VNS) meta-heuristic to solve the mDmSOP on small, medium, and large instances from the Generalized Traveling Salesman Problem (GTSP) benchmark. The results demonstrate the VNS's superiority in robustness and solution quality, as it requires less computational time than solving the mathematical formulation with GAMS 37.1.0 and CPLEX. Additionally, increasing the number of travelers leads to significant improvements in profits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
