Stackelberg-Nash Game Approach for Constrained Robust Optimization With Fuzzy Variables

In this article, the problem of robust optimization is considered for dynamical systems with both constraints and uncertainties. Conditions are established to ensure the existence of solutions to the problem with both robust optimality and feasibility. The objective performance with respect to fuzzy uncertainties is evaluated based on the expectation-entropy model. A feasibility robustness analysis method is proposed to handle the uncertainties in the constraints. Using the hierarchy structure in robust design, the optimization framework based on Stackelberg-Nash game is developed. A leader-followers state transition algorithm is designed to search for the equilibrium solution. Two application examples are given to demonstrate that the proposed robust optimization method can accurately evaluate the robustness performance and successfully search for a compromise solution.

Automated summary

This article explores the robust optimization problem for dynamical systems with constraints and uncertainties, establishing conditions for the existence of solutions and evaluating objective performance under fuzzy uncertainties. By leveraging hierarchy structure and game theory, an optimization framework and algorithm are developed to search for equilibrium solutions.