Multiresponse problems are common in product or process development. A conventional approach for optimizing multiple responses is to use a response surface methodology (RSM), and this approach is called multiresponse surface optimization (MRSO). In RSM, the method of steepest ascent is widely used for searching for an optimum region where a response is improved. In MRSO, it is difficult to directly apply the method of steepest ascent because MRSO includes several responses to be considered. This paper suggests a new method of steepest ascent for MRSO, which accounts for tradeoffs between multiple responses. It provides several candidate paths of steepest ascent and allows a decision maker to select the most preferred path. This generation and selection procedure is helpful to better understand the tradeoffs between the multiple responses, and ultimately, it moves the experimental region to a good region where a satisfactory compromise solution exists. A hypothetical example is employed for illustrating the proposed procedure. The results of this case study show that the proposed method searches the region containing an optimum where a satisfactory compromise solution exists.

中文翻译：

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一种使用期望函数法进行多响应面优化的最陡上升方法

多响应问题在产品或过程开发中很常见。用于优化多个响应的常规方法是使用响应表面方法（RSM），这种方法称为多响应表面优化（MRSO）。在RSM中，最陡峭上升方法广泛用于搜索响应改善的最佳区域。在MRSO中，很难直接应用最陡峭上升的方法，因为MRSO包括要考虑的几个响应。本文提出了一种新的MRSO最陡峭上升方法，该方法考虑了多个响应之间的折衷。它提供了几种最陡峭上升的候选路径，并允许决策者选择最优选的路径。此生成和选择过程有助于更好地了解多个响应之间的权衡，最终，它将实验区域移至存在令人满意的折衷解决方案的良好区域。假设的例子用来说明所提出的过程。该案例研究的结果表明，所提出的方法在包含令人满意的折衷解的最优位置进行搜索。