带时间窗物流配送车辆路径问题的蝙蝠算法

带时间窗车辆路径问题（Vehicle Routing Problem with Time Windows，VRPTW）是一个重要而实际的研究课题，该问题在有能力约束模型的基础上增加了时间约束，要求配送系统总费用最低。蝙蝠算法（Bat Algorithm，BA）是一种新型的智能优化算法，目前尚未被应用到求解VRPTW问题中。根据VRPTW问题的数学模型及其具体特征，重新设计了BA的操作算子，给出了求解VRPTW问题的改进蝙蝠算法，并通过仿真实例和与其他算法进行比较的方式，验证了蝙蝠算法在VRPTW问题中的求解性能，拓展了蝙蝠算法的应用领域。

Bat algorithm for vehicle routing problem of logistics distribution with time windows

Vehicle Routing Problem with Time Windows（VRPTW） is an important and practical research project, which adds the time constraints into the mathematical model based on the capacity constraints with requirements of the lowest total cost in distribution system. Bat Algorithm（BA） is a new intelligent optimization algorithm, which has not yet been applied to VRPTW. Based on the mathematical model and specific features of VRPTW, this paper redesigns the operators of BA and proposes an improved bat algorithm for solving it. Furthermore, the results show that bat algorithm can effectively and feasibly solve VRPTW in logistics distribution through simulation examples and comparisons with other algorithms. The research results also expand the application field of BA.