This article introduces an extension of Vehicle Routing Problem with Time Window (VRPTW) called Vehicle Routing Problem with Time Window Considering Service Time Customization (VRPTW-STC). This problem considers total service time as a problem objective. We give out the mathematical model of VRPTW-STC and an ant-based heuristic algorithm to solve it. The algorithm that we apply to this problem is called Multi-Ant System with Local Search (MAS-LS). It combines MAS algorithm with four kinds of local search operators. And, a customer selection heuristic is designed to help find customers that can be added extra service time. Finally, we test performance of MAS-LS on selected Solomon's benchmarks and Homberger's benchmarks. Comparison algorithms include ant-based heuristics, population-based heuristics and variable neighborhood search heuristics. Computation experiment results show that MAS-LS has a good and robust performance of finding solutions with lower travelling distance in most tested instances.

中文翻译：

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基于多蚂蚁系统的混合启发式算法解决服务时间定制的车辆路径问题

本文介绍了带时间窗的车辆路径问题（VRPTW）的扩展，称为考虑服务时间定制的带时间窗的车辆路径问题（VRPTW-STC）。该问题将总服务时间视为问题目标。我们给出了VRPTW-STC的数学模型和基于蚂蚁的启发式算法来解决它。我们应用于此问题的算法称为具有本地搜索的多蚂蚁系统（MAS-LS）。它将MAS算法与四种局部搜索算子相结合。而且，客户选择启发式旨在帮助找到可以增加额外服务时间的客户。最后，我们在选定的 Solomon 基准和 Homberger 基准上测试了 MAS-LS 的性能。比较算法包括基于蚂蚁的启发式算法、基于群体的启发式算法和可变邻域搜索启发式算法。计算实验结果表明，在大多数测试实例中，MAS-LS 具有良好且鲁棒的寻找移动距离较短的解的性能。