Stackelberg–Nash Game Approach for Constrained Robust Optimization With Fuzzy Variables
Stackelberg–Nash Game Approach for Constrained Robust Optimization With Fuzzy Variables
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DOI：
10.1109/tfuzz.2020.3025697
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发表时间：
2021-11
影响因子：
11.9
通讯作者：
Jie Han;Chunhua Yang;C. Lim;Xiaojun Zhou;Peng Shi
中科院分区：
文献类型：
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作者：
Jie Han;Chunhua Yang;C. Lim;Xiaojun Zhou;Peng Shi
研究了具有约束和不确定性的动态系统的鲁棒优化问题。建立了问题解的鲁棒最优性和可行性的条件。基于期望-熵模型对模糊不确定性的客观性能进行了评价。针对约束条件中的不确定性，提出了一种可行性鲁棒性分析方法。利用稳健设计中的层次结构，建立了基于Stackelberg-Nash博弈的优化框架。设计了一种leader - follower状态转移算法来寻找平衡解。两个应用实例表明，所提出的鲁棒优化方法能够准确地评价鲁棒性能，并能成功地寻找到一个折衷解。
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.