Robust Multiobjective Optimization With Robust Consensus

Consider a multiobjective robust optimization problem, where a set of weighted decision makers provides their preferences a priori. The preferences are provided either in the objective space or in the decision variable space using fuzzy numbers. To solve this problem, an indicator to measure consensus, an indicator to measure the robustness of the solutions to their degree of consensus, and a reformulation of the multiobjective robust optimization problem, are required. It is necessary for the reformulated problem to generate robust solutions that also enjoy high degree of consensus. In this paper, we have addressed these three issues. For this purpose, we have proposed two approaches to define consensus. Then, we have extended these approaches to define robust consensus, an indicator to measure the robustness of a given solution to its degree of consensus. Though these approaches can be used to define a countless number of measures, we have proposed 12 definitions of consensus, and hence, robust consensus. Furthermore, we have proposed two ways for the reformulation. Experimental results illustrate that the behavior of the proposed definitions and of the reformulations are consistent with our expectations.