卡车无人机协同配送作为一种新型的物流配送模式,被广泛应用在最后一公里配送中。本研究针对柔性时间窗下的多卡车多无人机协同配送路径问题,根据物流企业的具体需求,建立了一个最小化运输成本、最小化客户不满意度的多目标优化模型。针对该模型的优化问题,提出一种基于目标空间分解的改进MOEA/D算法(An Improved MOEA/D Algorithm Based on Objective Space Decomposition, MOEA/D-OSD)。通过目标空间分解策略、交配亲本选择策略、子种群更新策略等多种策略提高种群多样性,通过结合多个交叉和变异算子来加速算法的收敛,并针对具体问题特征设计染色体编码、解码方式以及遗传算子。最后,通过一组基准实例对算法性能进行评估,验证了该算法解决卡车无人机协同路径问题的有效性。The collaboration of trucks and drones for delivery has emerged as a new logistics model widely applied in last-mile delivery. This study addresses the multi-truck, multi-drone collaborative delivery routing problem under flexible time windows. Based on the specific needs of logistics companies, a multi-objective optimization model is established to minimize transportation costs and customer dissatisfaction. To solve this model, an improved MOEA/D algorithm based on objective space decomposition (MOEA/D-OSD) is proposed. This approach enhances population diversity through various strategies, including objective space decomposition, parent selection for mating, and subspace updating. Additionally, it accelerates algorithm convergence by combining multiple crossover and mutation operators while designing chromosome encoding, decoding methods, and genetic operators tailored to the specific problem characteristics. Finally, the algorithm’s performance is evaluated through a set of benchmark instances, demonstrating its effectiveness in solving the truck-drone collaborative routing problem.
