In many real-world settings, problem instances that need to be solved are quite similar, and knowledge from previous optimization runs can potentially be utilized. We explore this for the Traveling Salesperson problem with time windows (TSPTW), which often arises in settings where the travel-time matrix is fixed but time-window constraints change across related tasks. Existing TSPTW studies, however, have not systematically compared solving such task sequences independently with sequential transfer from previously solved tasks. We address this gap using a multi-task benchmark in which each base instance is expanded into five related tasks under two environments: partial time-window expansion and swap-additive time reassignment. We compare a standard from-scratch protocol with an iterative protocol that initializes each task from the best tour of the previous task, using the popular local search approaches LNS, VNS, and LKH-3 under a common penalized-score objective. Our experimental results show that the iterative protocol is consistently superior in the progressive-relaxation setting and generally competitive under swap-additive changes, with improvements increasing on more difficult instances.

翻译：在诸多现实场景中，待求解的问题实例往往具有高度相似性，因此先前优化运行中获得的知识可以被有效利用。本文针对带时窗约束的旅行商问题（TSPTW）展开研究——该问题常见于旅行时间矩阵固定但相关任务间时窗约束会发生变化的应用场景中。然而，现有TSPTW研究尚未系统比较过独立求解任务序列与通过顺序迁移从已求解任务中获取知识的两种策略。为解决这一研究空白，我们构建了一个多任务基准测试，其中每个基础实例在两种环境下扩展为五个相关任务：部分时窗扩展与交换-累加时间重分配。我们采用标准的从头求解协议与迭代协议进行对比——后者利用前一个任务的最优路径初始化当前任务，并采用主流局部搜索方法LNS、VNS和LKH-3，在统一的惩罚得分目标下进行评估。实验结果表明，在渐进松弛场景中迭代协议始终表现更优，而在交换-累加变化下也具有普遍竞争力，且随着实例难度增加，改进效果更为显著。