基于数据驱动的鲁棒最小成本共识模型  

A Data-driven-based Robust Minimum-cost Consensus Model

作　　者：韩烨帆 纪颖 屈绍建 HAN Yefan;JI Ying;QU Shaojian(Business School,Shanghai University,Shanghai 200444,China;School of Management Science and Engineering,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]上海大学管理学院,上海200444 [2]南京信息工程大学管理工程学院,江苏南京210044

出　　处：《运筹与管理》2023年第9期36-42,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(72171149,72171123);上海市哲学社会科学基金项目(2020BGL010)。

摘　　要：针对权重的随机性和模糊性影响聚合算子质量,从而导致最优决策产生巨大变动的问题,本文构造了不确定集合刻画决策者权重的不确定性,并运用数据驱动鲁棒优化方法建立了最小成本共识模型。首先,利用核密度估计(KDE)方法从历史数据中获取不确定权重的概率密度函数,以构造具有置信水平的不确定性区间,并控制聚合算子中不确定权重的波动范围。其次,分别在三种形状的集合(包括盒子集、椭球集和多面体集)下定义柔性不确定集合I和柔性不确定集合II,建立了六个不确定环境下的数据驱动鲁棒成本共识模型。最后,从碳配额分配问题中抽象出一个群体决策问题,估计政府为各企业分配额度的概率密度函数,构造基于置信水平的区间以处理偏差造成的不确定性,证明了所提出的模型的有效性和适用性。结果表明:(1)利用数据驱动方法遍历权重的历史数据,能够有效提高聚合算子的质量;(2)政府可以根据对风险的偏好程度选择合适的不确定集合以制定决策;(3)新提出的模型能够在一定程度上降低数据分析结果的鲁棒性代价。The quality and reliability of the composite indicator are directly influenced by the aggregation of indi-vidual preference information.Even slight perturbations in the aggregation weights may result in the selection of unreasonable solutions,leading to economic and social losses.Therefore,it is crucial to determine the aggrega-tion weights of decision-makers(DMs)appropriately.Robust optimization(RO)methods have gained signifi-cant attention due to their ability to generate uncertainty-immune solutions.However,these methods typically construct uncertainty sets based on experience,which in troduces certain conservatism to the model results.In contrast,data-driven RO methods construct uncertainty sets based on uncertain observations,allowing for a reasonable balance between conservatism and robustness in decision outcomes.Consequently,it is necessary to develop a model that can efectively manage the uncertainty associated with aggregation weights using the data-driven RO methods.To tackle the uncertainty and randomness of DMs’aggregation weights,a series of data-driven robust mini-mum-cost consensus models is proposed in this paper.Firstly,a min imum-cost consensus model with consensus constraints is introduced as the foundation of the study.This model ensures that DMs achieve an acceptable level of consistency.Secondly,a kernel density estimation(KDE)method is used to derive probability density func-tions of uncertain weights based on historical data.These functions are utilized to construct uncertainty intervals with confidence levels,enabling control over the perturbation range of uncertain weights in the aggregation opera-tor.Subsequently,two types of flexible uncertainty sets,namely flexible uncertainty set Ⅰ and flexible uncertainty set Ⅱ,are defined.These sets correspond to the set of three different shapes,including the box set,ellipsoidal set,and polyhedral set.By employing these uncertainty sets,the data-driven robust minimum-cost consensus models are developed to address six different uncertain env

关 键 词：群体决策 最小成本共识模型 聚合算子 数据驱动鲁棒优化 置信水平 

分 类 号：C934[经济管理—管理学]