基于Prim-DMGA算法的闭环供应链网络鲁棒优化研究

针对不确定环境下的闭环供应链网络优化问题，在需求不确定及设施中断风险的条件下，基于鲁棒对等优化方法建立了一种以闭环供应链网络总成本最小为目标的鲁棒优化模型，以解决供应链网络中的不确定性问题，并提出了Prim-DMGA。首先基于Prim算法得到高质量的初始种群，其次让路径规划方案和设施选址方案在两层自适应GA的不断反馈中达到最优。实验结果表明，Prim-DMGA得到的目标函数值优于单层Prim-MGA与传统GA,且在求解大规模算例时，求解结果优于CPLEX软件。研究结论表明，Prim-DMGA能以较少的计算时间获得质量更优的解，鲁棒优化模型可以有效减少不确定因素带来的不利影响，提高闭环供应链网络的鲁棒性能。

Robust optimization of closed-loop supply chain network based on Prim-DMGA algorithm

This article proposed a robust peer-to-peer optimization method in the context of uncertain environments to address the uncertainty in closed-loop supply chain networks while considering demand uncertainty and facility disruption risk. This article formulated a robust optimization model to minimize the total cost of the closed-loop supply chain network. Additionally, this article proposed a Prim-DMGA that firstly identified high-quality initial solutions using the Prim algorithm and then optimized the routing and facility selection solutions in a two-layer adaptive GA feedback loop. The experimental results demonstrate that the Prim-DMGA generates better objective function values than the single-layer Prim-MGA and traditional GA with less computational time. Further, the results obtained from the algorithm are superior to those obtained by using the CPLEX software in solving large-scale scenarios. This article concludes that the proposed robust optimization model effectively reduces the adverse effects caused by uncertainty and improves the robustness of closed-loop supply chain networks. Moreover, the Prim-DMGA generates better solutions with less computational time.