论文标题
CMA-ES具有边缘：混合组黑盒优化的较低边缘概率
CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization
论文作者
论文摘要
这项研究针对混合企业黑盒优化（MI-BBO）问题，其中应同时优化连续和整数变量。我们在这项研究中的重点是CMA-ES，是一种基于人群的随机搜索方法，该方法从多元高斯分布（MGD）中采样求解求解的方法，该方法在连续BBO中表现出卓越的性能。 MGD，平均值和（CO）方差的参数根据CMA-ES中候选解决方案的评估值进行更新。但是，如果将CMA-ES应用于MI-BBO并直接离散化，则与整数变量相对应的方差在达到最佳解决方案之前比离散化的粒度要小得多，这导致了优化的停滞。特别是，当问题中包含二进制变量时，由于离散化的粒度变得更宽，因此这种停滞更可能发生，并且对CMA-ES的现有修改无法解决此停滞。为了克服这些局限性，我们提出了基于与MGD中整数变量产生相关的较低边缘概率的CMA-ES的简单修改。 MI-BBO基准问题的数值实验证明了该方法的效率和鲁棒性。
This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing modification to the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple modification of the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method.
