带时间窗车辆路径问题的随机构造启发式算法：聚焦Regret-k
Randomized Constructive Heuristics for the VRPTW: A Focus on Regret-k
浏览论文内容
中文总结 AI 辅助
研究带时间窗车辆路径问题，在随机多起点框架下探讨三种经典构造启发式算法，提出对Regret-k的新颖随机化，研究其与局部搜索和蚁群优化结合的影响，通过实验突出解质量与计算成本权衡，为混合方法研究迈出初步步伐。
中文摘要 AI 辅助
带时间窗车辆路径问题（VRPTW）要求车队在严格时间窗内服务客户并最小化总行驶时间。构造启发式算法是生成解决方案的基础，常作为元启发式算法的起点。本文在随机多起点框架下研究三种经典构造启发式算法——最近邻、最佳插入和Regret-k，该框架虽有确定性应用，但随机应用探索较少。提出对Regret-k进行新颖随机化，分离‘选择哪个客户插入’和‘插入位置’决策，按后悔值概率选择以保留启发式算法的前瞻性并注入多起点方法所需的多样性。还研究将这些贪婪随机构造与局部搜索和蚁群优化相结合的影响。实验遵循DIMACS 2021惯例，在Solomon和Gehring & Homberger基准测试（100 - 1000个客户）上进行，与最佳已知解和最先进的混合遗传搜索求解器比较，关键组件用现代C++实现并通过pybind11绑定到Python。据我们所知，Regret-k的随机化从未被研究过；分析突出了解决方案质量和计算成本之间的权衡，为MAMUT项目中时变VRPTW的混合方法（蚁群优化、迭代局部搜索、分支定价）迈出了初步步伐。
英文摘要
The Vehicle Routing Problem with Time Windows (VRPTW) requires a fleet of capacitated vehicles to serve customers within strict time windows while minimizing total travel time. Constructive heuristics are fundamental for generating solutions and commonly serve as starting points for metaheuristics such as Iterated Local Search (ILS), Genetic Algorithms, and Ant Colony Optimization (ACO). This work studies three classical constructive heuristics - Nearest Neighbor, Best Insertion, and Regret-k - within a randomized, multi-start framework, a setting that remains largely under-explored despite their well-established deterministic use. We address how to effectively randomize these heuristics and, in particular, propose a novel randomization of Regret-k by separating the ''who'' (which customer to insert next) and ''where'' (insertion position) decisions, applying a probabilistic selection proportional to the regret value to preserve the heuristic's foresight while injecting the diversity needed for a multi-start approach. We further study the impact of combining these greedy randomized constructions with Local Search and ACO. Experiments follow the DIMACS 2021 conventions (integer, truncated Euclidean distances) on the Solomon and Gehring \& Homberger benchmarks (100--1000 customers), comparing against the Best-Known Solutions and the state-of-the-art Hybrid Genetic Search solver, with all critical components implemented in modern C++ and bound to Python via pybind11. To the best of our knowledge, the randomization of Regret-k has never been examined; our analysis highlights the trade-off between solution quality and computational cost, providing a preliminary step toward hybrid methods (ACO, ILS, Branch-and-Price) for the Time-Dependent VRPTW within the MAMUT project.
