摘要： 给出了分批配送的有时间窗车辆路径问题（BVRPTM）的数学模型。通过引入改进的路径可行化方法和MRC 交叉算子，构造了一种适于求解BVRPTM 的遗传算法。实验结果表明，该算法能有效地解决BVRPTM，并取得了较好的优化结果。

关键词: 分批配送的有时间窗车辆路径问题；遗传算法；交叉算子；数学模型

Abstract: This paper provides a mathematical model of batch vehicle routing problem with time windows(BVRPTM), and proposes a geneticalgorithm suitable for solving BVRPTM which is based on the improved routing scheme and the MRC crossover operator. As the experiments proved, when this algorithm is used for solving BVRPTM, it can obtain preferable results and solves this problem effectively

Key words: Batch vehicle routing problem with time windows; Genetic algorithm; Crossover operator; Mathematical model