基于改进的RNGA算法求解两阶段分布鲁棒优化群体共识模型

Solving a Two-Stage Distributionally Robust Optimization Group Consensus Model Based on an Improved RNGA Algorithm

摘要: 作为一种既考虑数据的概率分布信息，又能保证结果不会过于保守的求解方法，分布鲁棒优化方法的研究越来越多。本文在最小成本共识模型的基础上，提出一种考虑风险成本的两阶段分布鲁棒最小成本共识模型。首先，考虑到风险的不确定性，使用CVaR来对第二阶段风险成本进行刻画。其次，通过Wasserstein距离定义一个包含经验分布周围所有分布可能的不确定集。针对问题中的风险度量部分给模型造成难以求解的后果，给出一种改进的RNGA算法来对模型进行更好地求解。最后，为了评价所提模型的鲁棒性，将TSDRO-MCCM-CVaR与SP-MCCM进行了比较。案例分析证明，SP-MCCM结果过于乐观，性能不理想，而本文提出的模型的解决方案更加鲁棒。既有更好的性能，又有足够的抗风险性。

Abstract: As a solution method that considers the probability distribution information of the data while ensuring that the results are not too conservative, distributionally robust optimization methods are increasingly studied. In this paper, based on the least-cost consensus model, a two-stage distributionally robust least-cost consensus model that considers the cost of risk is proposed. First, CVaR is used to characterize the second-stage risk cost considering the uncertainty of risk. Secondly, an uncertainty set containing all possible distributions around the empirical distribution is defined by Wasserstein distance. To address the consequences of the risk measure part of the problem that makes the model difficult to solve, an improved RNGA algorithm is given to solve the model better. Finally, to evaluate the robustness of the proposed model, TSDRO-MCCM-CVaR is compared with SP-MCCM. The case study proves that the SP-MCCM results are too optimistic and the performance is not satisfactory, while the solution of the model proposed in this paper is more robust. It has both better performance and sufficient risk resistance.