带时间窗的快递包装回收车辆路径优化研究

为解决大量快递包装给社会环境带来的一系列问题，优化快递包装及回收车辆路径，降低回收成本，提高客户满意度是快递包装回收的关键。考虑到快递包装回收的现状，提出在回收过程中设置软时间窗来反映顾客的满意度。建立了运输成本、处理成本、回收成本、时间惩罚成本等成本最小化的数学模型。采用改进的遗传算法对模型求解，提出运用2点交叉法改进交叉算子，加快种群的寻优速度，同时提出2点互异改进变异算子，增加种群的多样性，并对算法的种群规模、变异概率、运输成本等进行了灵敏度分析。运用Matlab软件对算例进行仿真，在有无时间窗条件下，验证了该设计的快递包装回收路径模型和算法的有效性。

Research on vehicle routing optimization of express package-recycling with time window

In order to solve a series of problems brought to the social environment by a large number of express packaging, it is the key to optimize the express package to recover the vehicle path, reduce the cost of recovery and improve the customer satisfaction. Considering the current situation of express packaging recycling, it is proposed to set up soft time windows to reflect customer satisfaction in the recovery process. The mathematical models of minimizing transportation cost, processing cost, recovery cost and time penalty cost are established. The improved genetic algorithm is used to solve the model. The two points cross method is used to improve the crossover operator and speed up the optimization of the population. At the same time, the two points are different to improve the mutation operator, and the diversity of the population is increased, and the sensitivity analysis is carried out on the population size, the mutation probability and the transport version of the algorithm. The Matlab software is used to simulate the example, and the time window is compared to verify the validity of the model and algorithm of the express package recovery path with time window.