Abstract: This paper concerns a Vehicle Routing Problem with Simultaneous Pick-up and Delivery and Time-Windows（VRPSPDTW）. A binary mixed binary integer programming model is developed for the problem. To further improve the convergence speed and optimization capability of the artificial fish swarm algorithm, an Improved Global Artificial Fish Swarm Algorithm（IGAFSA） is proposed, and the parameters of the algorithm are also determined by experiments. In order to reduce computational complexity, during the course of the algorithm, the time windows constraint and the vehicle capacity constraint are allowed to violate. Computational results are reported from Wang and Chen’s benchmark and compared with the results from Artificial Fish Swarm Algorithm（AFSA） and Parallel Simulated Annealing（P-SA） that minimizes the Number of Vehicles（NV） and the total Travel Distance（TD）, which demonstrate the effectiveness of the IGAFSA algorithm. The results show that the IGAFSA which obtains the NV and TD solutions is better than AFSA, and its TD solutions are better than P-SA too.

Key words: global artificial fish swarm algorithm, combinational optimization, Vehicle Routing Problem with Simultaneous Pick-up and Delivery and Time-Windows（VRPSPDTW）, reverse logistic

摘要： 研究带时间窗的同时送取货车辆路径规划问题（VRPSPDTW），并建立0-1混合整数规划模型。为进一步提高人工鱼群算法的寻优能力和收敛速度，提出一种改进的全局人工鱼群算法，并通过实验确定算法参数。算法将模型中的时间窗和车载量两个强约束纳入适应度函数进行处理，降低算法计算复杂度。以最小化发车数（NV）和路由距离（TD）为优化目标，通过王与陈提供的VRPSPDTW算例与基本人工鱼群算法（AFSA）和并行模拟退火算法（P-SA）进行比较，验证了改进全局人工鱼群算法的有效性。实验结果显示：IGAFSA获得的NV和TD目标值均优于AFSA，TD目标值优于P-SA。

关键词: 全局人工鱼群算法, 组合优化, 带时间窗同时送取货车辆路径问题（VRPSPDTW）, 逆向物流