中文摘要：

针对战场物资配送中带硬时间窗车辆路径问题的多重模糊性，基于模糊可信性理论建立了多目标模糊期望值模型，提出了一种改进的约束多目标粒子群优化算法。算法采用基于相位空间思想的实数编码方式，提出了带优秀不可行解动态记忆机制的非支配解构造方法，基于自适应栅格和拥挤距离的混合多样性策略维护非支配解集，改进了个体向导更新方式，提高了算法的收敛性能，同时引入局部搜索和变异算子避免算法早熟。仿真实验表明了模型的合理性和算法的有效性。

英文摘要：

Aiming at the multiple fuzzy characteristics of vehicle routing problem with hard time.windows in battlefield resources distribution, a multi-objective fuzzy expected model is designed based on the fuzzy credibility theory, and an improved constrained multi-objective particle swarm optimization is proposed. The algorithm puts forward a particle encoding technique according to phase space, and designs a non-dominated solutions con- structing method which can store excellent infeasible solutions. In order to improve the convergence performance, a hybrid diversity strategy based on adaptive grids and crowding distance is used to maintenance the nondominated solutions, and the individual guide updating mechanism is improved. Meanwhile, local search and mutation operators are introduced to avoid the algorithm premature convergence. The rationality of the proposed model and effectiveness of the algorithm are verified by computational experiments.