Distributionally Robust Chance Constrained Optimization Model for the Minimum Cost Consensus

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.