Abstract: To overcome the deficiencies of the reverse logistics vehicle routing optimization study in the reasonable combination of vehicle sharing and multi-frequency recovery under smart recovery modes,a reverse logistics vehicle routing optimization scheme based on resource sharing and multi-frequency recovery was proposed.A bi-objective optimization model including the minimum reverse logistics operating costs and the minimum number of vehicles was established,and the logistics operating costs contained the vehicle transportation cost,the vehicle lease and maintenance cost,disposed cost of recycled products,the penalty cost of the time window violation and environmental externality benefit.A two-stage Clarke-Wright Self-learning Non-dominated Sorting Genetic Algorithm-Ⅱ (CW-SLNSGA-Ⅱ) was designed to solve the model.In the first stage of the algorithm,a Clarke-Wright (CW) savings algorithm and a sweep algorithm were combined to improve the quality of the initial solutions.In the second stage,a self-learning mechanism was embedded into the non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ),and then the occurrence probabilities of the mutation and crossover could vary according to the change of the fitness value.In addition,an elite iteration strategy was used to retain the individuals with better fitness value,which improved the search performance of the algorithm.The effectiveness of the algorithm was verified through the comparative analysis with the Multi-objective Ant Colony Optimization (MOACO),Multi-objective Whale Optimization Algorithm (MOWOA) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEAD).Finally,the proposed method was verified via a case study,and the ablation experiment of the proposed algorithm was conducted by combining the elite iteration strategy and the self-learning mechanism,the number of recycled vehicles and the operating costs of the reverse logistics were analyzed and discussed when the recycling center selected different capacities of recycled vehicles.The results showed that the proposed model and algorithm could reduce the operating costs of the reverse logistics and the number of vehicles,realize multi-frequency recovery and vehicle sharing scheduling effectively,so as to provide the decision reference and method support for the construction of the reverse logistics network and the smart city under smart recovery modes.

Key words: smart recovery modes, vehicle routing problem, resource sharing, clarke-wright self-learning non-dominated sorting genetic algorithm-Ⅱ, elite iteration

摘要： 针对智能回收模式下逆向物流车辆路径问题研究在多频次回收和车辆共享调度相结合方面存在的不足,提出了智能回收模式下基于多频次回收和车辆共享的逆向物流车辆路径优化策略。首先,构建了包含运输成本、车辆租赁与维修成本、回收品处理成本、违反时间窗惩罚成本和环境外部性收益的逆向物流运营成本最小化和回收车辆使用数最小化的双目标优化模型。其次,设计了一种两阶段CW-SLNSGA-Ⅱ算法对模型进行求解。该算法第一阶段将Clarke-Wright节约算法和Sweep扫描算法相结合生成初始解,第二阶段将自学习机制嵌入非支配排序遗传算法（NSGA-Ⅱ）中,使个体的交叉概率和变异概率可以根据适应度值的变化进行动态调整,并应用精英迭代策略保留了适应度值较优的个体,提高了算法的搜索性能。然后,通过与多目标蚁群算法（MOACO）、多目标鲸鱼优化算法（MOWOA）和基于分解的多目标进化算法（MOEAD）的对比分析,验证了算法的有效性。最后,通过实例对所提模型和算法进行了验证,并结合精英迭代策略和自学习机制对所提算法进行了消融实验研究,进而探讨了回收中心选择不同容量的回收车辆进行服务时车辆使用数与逆向物流运营成本的变化情况。研究结果表明,所提出的模型和算法可以有效降低逆向物流车辆调度成本和减少车辆使用数,并可实现多频次回收的车辆共享调度,进而为智能回收模式下的逆向物流网络构建和智慧城市建设提供理论支持和决策参考。

关键词: 智能回收模式, 车辆路径问题, 资源共享, CW-SLNSGA-Ⅱ算法, 精英迭代