Abstract: This paper proposes an adaptive brain storm optimization（ABSO） for the vehicle routing problem with simultaneous pickup-delivery and time windows（VRPSPDTW）, a path optimization mathematical model is constructed to minimize the total expenditure of vehicle use cost and vehicle travel distance cost. In the global search stage, expand the search area with multiple penalties, as well as use clustering and three path search strategies for global search. In the local search stage, ues six kinds of damage-repair operators as candidate sets, and then design an adaptive dynamic selection neighborhood search mechanism to enhance local search efficiency. Based on the standard test data set and practical cases, the experimental results show the ABSO algorithm can obtain all the currently known optimal solution for the small-scale standard test example. For the large-scale standard test example, compared with the genetic algorithm, parallel-simulated annealing algorithm, and discrete cuckoo search, the experimental calculation results of the algorithm in this paper have an improvement of 7.52%-12.03%. For practical cases, the proposed algorithm shows its superiority in terms of convergence speed and optimization ability. The experimental calculation results verify the effectiveness of the proposed ABSO algorithm to solve the VRPSPDTW.

Key words: vehicle routing problem, simultaneous pickup-delivery, time windows, brain storm optimization, adaptive large neighborhood search

摘要： 针对带时间窗的同时取送货车辆路径问题（vehicle routing problem with simultaneous pickup-delivery and time windows，VRPSPDTW），构建了以车辆使用成本、车辆行驶距离成本总支出最小化的路径优化数学模型，提出自适应头脑风暴算法（adaptive brain storm optimization，ABSO）进行求解。全局搜索阶段，采用多项惩罚方式扩大搜索区域，并使用聚类及三种路径搜索策略进行全局搜索；局部搜索阶段，将六种破坏-修复算子作为备选集合，进而设计自适应动态选择邻域搜索机制，增强局部搜索效能。选取测试数据集和实际案例对算法性能进行测试，实验结果表明针对小规模标准算例，所提算法全部取得了当前已知最优解；对于大规模标准算例，通过与遗传算法、并行模拟退火算法、离散布谷鸟算法对比，所提算法实验计算结果有7.52%~12.03%的提升；对于实际案例，所提算法在收敛速度和寻优能力方面均展示出优越性，充分验证了所提算法对解决VRPSPDTW问题的有效性。

关键词: 车辆路径问题, 同时取送货, 时间窗, 头脑风暴算法, 自适应大邻域搜索