Abstract

As a solution method that not only considers the probability distribution information of data, but also ensures that the results are not too conservative, more and more researches have been made on the distributionally robust optimization method. Based on the minimum cost consensus model, this paper proposes a new minimum cost consensus model with distributionally robust chance constraints (DRO-MCC). Firstly, Conditional Value-at-Risk (CVaR) is used to approximate the chance constraints in the cost model. Secondly, when the information of the first and second moments of random variables affecting the unit adjustment cost are known, the min-max problem is obtained based on the moment method and dual theory, and a tractable semidefinite programming problem can be easily processed through further transformation. Finally, in order to evaluate the robustness of the proposed model, the results of different parameters are compared, and the DRO-MCC is compared with the robust optimization model (RO-MCC) and the minimum cost consensus model (MCC). The example proves that MCC is too optimistic and RO-MCC is too conservative. In contrast, DRO-MCC overcomes the conservatism of robust optimization and considers the probability information of data, so the result is more ideal.

中文翻译：

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最小成本共识的分布鲁棒机会约束优化模型

摘要

作为一种既考虑数据的概率分布信息，又保证结果不太保守的解决方法，对分布鲁棒性优化方法的研究越来越多。基于最小成本共识模型，本文提出了一种具有分布鲁棒机会约束（DRO-MCC）的新的最小成本共识模型。首先，条件风险值（CVaR）用于近似成本模型中的机会约束。其次，当知道影响单位调整成本的随机变量的第一矩和第二矩的信息时，基于矩量法和对偶理论就可以得到最小-最大问题，并且可以通过进一步简单地解决难处理的半定规划问题转型。最后，为了评估所提出模型的鲁棒性，比较了不同参数的结果，并将DRO-MCC与鲁棒优化模型（RO-MCC）和最小成本共识模型（MCC）进行了比较。该示例证明，MCC过于乐观，而RO-MCC过于保守。相比之下，DRO-MCC克服了鲁棒优化的保守性，并考虑了数据的概率信息，因此结果更加理想。