With the intensification of market competition and fast development of science and technology, many enterprises have begun to realize the importance of logistic distribution vehicle routing problem under uncertainty environment, and begin to pay more attention to the research of this problem. In this paper, The traditional vehicle routing problem with time windows is expanded to the situation that the time window is replaced by fuzzy due time which can represent the preferences of the customers. After a simple description of fuzzy due time and the fuzzy vehicle routing problem, a multi-objective mathematical model for the problem is built. Then, an insertion heuristic-based hybrid genetic algorithm is proposed to this kind of problem. In this algorithm, the modified push-bump-throw procedure is employed to handle the fuzzy nature of the problem. Finally, an extensive computational analysis is presented, which identifies the tradeoffs between the different objectives, and the superiority of the genetic algorithm is proved through the comparison of the genetic algorithms with improved Solomon insert heuristic algorithm.
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