Stackelberg Game Approach for Robust Optimization With Fuzzy Variables

In this article, a new robust optimization method is proposed to simultaneously optimize the expectation and variability of system performance with parametric uncertainties and fuzzy variables. The expectation-entropy model is presented to characterize the fuzzy robust optimization problem as an equivalent biobjective optimization problem. An approximate mapping method is developed to calculate the response of fuzzy variables, which improves the computational efficiency of objective functions. Then, according to the decision makers' preference for objectives, the optimization framework based on Stackelberg game is established. A leader-follower state transition algorithm is designed to search for the equilibrium solutions. Two practical case studies are provided to show the effectiveness of the new optimization approach in both subjective judgment and objective assessment.

Automated summary

This article proposes a new robust optimization method that simultaneously considers parametric uncertainties and fuzzy variables to optimize the expectation and variability of system performance. It introduces the expectation-entropy model to transform the fuzzy robust optimization problem into an equivalent biobjective optimization problem. An approximate mapping method is developed to calculate the response of fuzzy variables, improving the computational efficiency of the objective functions. The optimization framework based on the Stackelberg game is established according to the decision makers' preference for objectives, and a leader-follower state transition algorithm is designed to search for equilibrium solutions. Two practical case studies demonstrate the effectiveness of this new optimization approach in both subjective judgment and objective assessment.