Distributionally Robust Chance Constrained Optimization Model for the Minimum Cost Consensus
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Distributionally Robust Chance Constrained Optimization Model for the Minimum Cost Consensus Yefan Han1 • Shaojian Qu1 • Zhong Wu1
Received: 20 July 2019 / Revised: 26 September 2019 / Accepted: 19 December 2019 Ó Taiwan Fuzzy Systems Association 2020
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 DROMCC 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. Keywords Distributionally robust optimization Group decision-making Consensus CVaR
& Shaojian Qu [email protected] 1
University of Shanghai for Science and Technology, Shanghai 200093, China
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The minimum cost consensus model based on distributionally robust chance constraints is proposed. A tractable semidefinite programming problem is obtained by using CVaR, moment method and dual theory. The distributionally model overcomes the optimism of the minimum cost consensus model and the conservatism of the robust consensus model.
1 Introduction Group decision-making refers to the decision-making opinions expressed by multiple decision makers and the final selection of the optimal decision [1–7]. It is usually used to solve problems such as solution negotiation, conflict resolution and negotiation [8–10]. The main goal of group decision-making is that all decision makers in the decision-making system can reach group consensus. Different DMs have different educational backgrounds and represent different interest groups. Therefore, in the consensus reaching process (CRP) [11–13], DMs expressed and gradually adjusted their own opinions, and finally reached a consensus. This is often inseparable from the guidance and adjustment of the moderator who represents the interests of the group. So in the process of negotiating with DMs would inevitably produce cost, such as money, time and resources. There’s no doubt that the moderate always hopes that the cost he or she has paid is
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