This paper addresses an open vehicle routing problem with predetermined time windows under uncertain travel times (OVRP-UT). A novel light-robust-optimization model is proposed by integrating the goal programming formulations with set-based descriptions of the problem data, which can enable as many customers as possible to meet their demands within a group of predetermined time windows. An effective memetic algorithm (MA) is presented for solving the OVRP-UT model. We design a heuristic-based initialization mechanism to generate an initial population with a high level of quality and diversity. We design a timely-vertices based crossover operator and mutation operator to give birth to the offspring with high quality and good structure built in the search process. We provide a hybrid selection mechanism and a population updating strategy to remain the diversity of the population. We develop a self-adapted crossover and mutation rate to help the MA suit the different phases during the search process. A comprehensive simulation experiment based on the 320 benchmark instances demonstrates the effectiveness of the proposed algorithm.

本文解决了在不确定的行驶时间（OVRP-UT）下具有预定时间窗的开放式车辆路径问题。通过将目标编程公式与问题数据的基于集合的描述集成在一起，提出了一种新颖的鲁棒优化模型，该模型可以使尽可能多的客户在一组预定的时间窗口内满足他们的需求。提出了一种有效的模因算法（MA），用于求解OVRP-UT模型。我们设计了一种基于启发式的初始化机制，以生成具有较高质量和多样性的初始种群。我们设计了一个基于及时顶点的交叉算子和变异算子，以在搜索过程中生成具有高质量和良好结构的后代。我们提供了一种混合选择机制和种群更新策略，以保持种群的多样性。我们开发了一种自适应的交叉和突变率，以帮助MA在搜索过程中适应不同的阶段。基于320个基准实例的综合仿真实验证明了该算法的有效性。