考虑负效应的垃圾回收两级选址-路径模型与算法

针对生活垃圾中转站和焚烧站的选址-路径问题（LRP），考虑经济目标和垃圾设施的负面影响，设计了与风向和距离有关的负效应分段函数，构建了两级多目标选址-路径（2E-MOLRP）模型，并提出了鲸鱼优化算法（WOA）和模拟退火（SA）算法结合的非支配算法WOA-SA。首先，结合随机方法与Clarke和Wright(CW)节约算法优化初始种群；其次，采用非线性动态惯性权重系数调整收敛速度；然后，设计WOA-SA的并行结构来增强全局搜索能力；最后，使用非支配排序法得到帕累托解集。对Prins和Barreto等35个基准案例以及天津市模拟案例进行分析。结果表明，WOA-SA可以找到20个基准案例的已知最优解（BKS），且对Prins和Barreto案例的求解结果与BSK差距的平均值分别为0.37%和0.08%，具有很好的收敛性和稳定性。将所提模型和算法应用于实例，给决策者提供了三种不同方案的负效应值及经济成本的方案，以支持不同偏好决策者选择，从而减少垃圾回收物流成本和设施对环境的负面影响。

Two-echelon location-routing model and algorithm for waste recycling considering obnoxious effect

With regard to the Location-Routing Problem （LRP） of domestic waste transfer stations and incineration stations， by considering the economic objective and the obnoxious effect of waste facilities， a piecewise function of obnoxious effect related to wind direction and distance was designed， a Two-Echelon Multi-Objective LRP （2E-MOLRP） model was formulated， and a non-dominated algorithm combining Whale Optimization Algorithm （WOA） and Simulated Annealing （SA） algorithm was proposed， namely WOA-SA. Firstly， the random method and Clarke and Wright （CW） saving algorithm were used to optimize the initial population. Secondly， a nonlinear dynamic inertia weight coefficient was adopted to adjust the convergence speed of the WOA-SA. Thirdly， the global optimization ability was enhanced by designing the parallel structure of WOA-SA. Finally， the Pareto solution set was obtained by using the non-dominated sorting method. The analysis was carried out on 35 benchmark cases such as Prins and Barreto as well as a simulated case of Tianjin. The results show that the WOA-SA can find the Best Known Solution （BKS） of 20 benchmark cases， and has the mean values of the difference between the solution results and the BKSs of 0.37% and 0.08% on Prins and Barreto cases， which proves the good convergence and stability of the WOA-SA. The proposed model and algorithm were applied to the instance， and provided three schemes with different obnoxious effect values and economic costs for decision makers with different decision preferences. Therefore， the cost of waste recycling and the obnoxious effect of facilities on environment were reduced.