关键词: 数学模型, 遗传算法, 有时间窗的车辆路径问题, 交叉算子, 群体多样性

Abstract: We state a universal mathematical model of vehicle routing problem with time windows，which can satisfy numerous practical requirements and transform into other typical combination optimal problems by setting different parameters．An improved genetic algorithm (IGA) is proposed based on the novel crossover operator．IGA avoids effectively the common defects of early convergence and the diversity of population in traditional genetic algorithm.This algorithm can find the optimal or nearly optimal solution to the vehicle routing problem with time windows effectively，which is proved bya number of experiments.

Key words: mathematical model, genetic algorithm, vehicle routing problem with time windows, crossover operator, population diversity, early convergence