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 $\phi: \mathbf{p} \mapsto \mathbf{d}, \, \mathbb{R}^{P} \to \mathbb{R}^{D}$, 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 $\phi (\mathbf {\hat p})$ 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.

翻译：假设存在一组 $P$ 个过程参数 $p_i$，$i=1,\dots,P$，通过未知的函数关系 $\phi: \mathbf{p} \mapsto \mathbf{d}, \, \mathbb{R}^{P} \to \mathbb{R}^{D}$ 决定了一组 $D$ 个描述变量 $d_j$，$j=1,\dots,D$ 的结果，其中 $\mathbf{p}=(p_1,\dots,p_{P})$，$\mathbf{d}=(d_1,\dots,d_{D})$。我们的目标是找到过程参数的适当值 $\mathbf{\hat p} = ({\hat p}_1,\dots,{\hat p}_P)$，使得对应的描述变量值 $\phi (\mathbf {\hat p})$ 尽可能接近给定的目标 $\mathbf d^*=(d^*_1,\dots,d^*_D)$，并假设至少存在一个精确解。为此，本文开发了一种采用降维技术的序贯方法。通过仿真研究，将所提方法的结果与 NSGA-II、SMS-EMOA 和 MOEA/D 算法进行了比较。