Abstract: The Vehicle Routing Problem with Fuzzy Time Windows is addressed. A multi-objective mathematical model is designed with the objectives of logistics cost and average customer satisfaction. Based on Pareto dominance theory, a multi-objective tabu search algorithm is proposed to solve multi-objective optimization problems. Moreover, a dynamic programming method is embedded in the algorithm to optimize the customer satisfaction, which simplifies the original problem into tight path optimization sub-problems with the use of phasing. While fuzzy time windows are in piecewise linear and nonlinear convex membership function forms, customer beginning service time is optimized by proposed limited iteration subgradient algorithm and median iteration subgradient algorithm, respectively. Computational experiments on Solomon’s benchmark not only verify that the dynamic programming is more effective than projected subgradient methods to optimize the service level, but also show the advantages of the proposed multi-objective tabu search approach when compared with the well-known NSGA-II method.

Key words: vehicle routing problem, fuzzy time windows, dynamic programming, multi-objective tabu search, Pareto optimization

摘要： 为优化具有模糊时间窗的车辆路径问题，以物流配送成本和顾客平均满意度为目标，建立了多目标数学规划模型。基于Pareto占优的理论给出了求解多目标优化问题的并行多目标禁忌搜索算法，算法中嵌入同时优化顾客满意度的动态规划方法，运用阶段划分，把原问题分解为关于紧路径的优化子问题。对模糊时间窗为线性分段函数形式和非线性凹函数形式的隶属度函数，分别提出了次梯度有限迭代算法和次梯度中值迭代算法来优化顾客的最优开始服务时间。通过Solomon的标准算例，与次梯度投影算法的比较验证了动态规划方法优化服务水平的有效性，与主流的NSGA-II算法的对比实验表明了该研究提出的多目标禁忌搜索算法的优越性。

关键词: 车辆路径问题, 模糊时间窗, 动态规划, 多目标禁忌搜索, Pareto最优