昂贵的多响应黑箱函数的统计优化
Statistical optimization of expensive multi-response black-box functions
摘要：
假定一组$P$过程参数$p_i$、$i=1,\dots,P$通过未知函数关系$ϕ: \mathbf{p} \mapsto \mathbf{d}, \, \mathbb{R}^{P} \to \mathbb{R}^{D}$确定一组$D$描述符变量$d_j$、$j=1,\dots,D$的结果，其中$\mathbf{p}=(p_1,\dots,p_{P})$、$\mathbf{d}=(d_1,\dots,d_{D})$。期望找到过程参数的适当值$\mathbf{\hat p} = ({\hat p}_1,\dots, {\hat p}_P)$，使得描述符变量$ϕ(\mathbf {\hat p})$的对应值接近给定目标$\mathbf d^*=(d^*_1,\dots,d^*_D)$，假设存在至少一个精确解。已经开发了一种使用降维技术的顺序方法来实现这一点。在仿真研究中，所提出的方法和算法NSGA-II，SMS-EMOA和MOEA/D的结果进行了比较。
英文摘要：
Assume that a set of $P$ process parameters $p_i$, $i=1,\dots,P$, determines the outcome of a set of $D$ descriptor variables $d_j$, $j=1,\dots,D$, via an unknown functional relationship $ϕ: \mathbf{p} \mapsto \mathbf{d}, \, \mathbb{R}^{P} \to \mathbb{R}^{D}$, where $\mathbf{p}=(p_1,\dots,p_{P})$, $\mathbf{d}=(d_1,\dots,d_{D})$. It is desired to find appropriate values $\mathbf{\hat p} = ({\hat p}_1,\dots, {\hat p}_P)$ for the process parameters such that the corresponding values of the descriptor variables $ϕ(\mathbf {\hat p})$ are close to a given target $\mathbf d^*=(d^*_1,\dots,d^*_D)$, assuming that at least one exact solution exists. A sequential approach using dimension reduction techniques has been developed to achieve this. In a simulation study, results of the suggested approach and the algorithms NSGA-II, SMS-EMOA and MOEA/D are compared.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
