基于最坏排序近似的协方差矩阵自适应进化策略及其在靠泊控制中的应用
Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks
摘要：
在这项研究中，我们考虑了一个连续的最小-最大优化问题$\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$，其目标函数是一个黑箱。我们提出了一种新的方法来最大限度地减少最坏情况下的目标函数$F(x) = \max_{y} f(x,y)$直接使用协方差矩阵自适应演化策略（CMA-ES），其中解决方案的候选人的排名近似我们提出的最坏情况下的排名近似（WRA）机制。我们开发了两个变种的WRA结合CMA-ES和近似梯度上升的数值求解器的内部最大化问题。数值实验表明，当目标函数为光滑强凸-凹函数且$x$和$y$之间的相互作用较强时，该方法的性能优于现有的几种方法.我们调查所提出的方法的优点，目标函数不限于光滑强凸-凹函数的问题。在具有不确定性的非凸-凹函数的鲁棒靠泊控制问题中，证明了该方法的有效性。在具有不确定性的船舶靠泊鲁棒控制问题中，证明了该方法的有效性。
英文摘要：
In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function $F(x) = \max_{y} f(x,y)$ directly using a covariance matrix adaptation evolution strategy (CMA-ES) in which the rankings of solution candidates are approximated by our proposed worst-case ranking approximation (WRA) mechanism. We develop two variants of WRA combined with CMA-ES and approximate gradient ascent as numerical solvers for the inner maximization problem. Numerical experiments show that our proposed approach outperforms several existing approaches when the objective function is a smooth strongly convex--concave function and the interaction between $x$ and $y$ is strong. We investigate the advantages of the proposed approach for problems where the objective function is not limited to smooth strongly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.ngly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.
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