改进的满意度函数法在多响应优化中的应用

满意度函数法是最常用的多响应优化方法，但该方法没有考虑响应的变异性、相关性和参数估计的不确定性，针对这些问题提出了改进的满意度函数法对其进行改进，该方法将响应方差-协方差结构和预测方差结合到满意度函数中．实例分析表明，与传统满意度函数相比，用该方法进行优化得到的响应的方差和预测方差分别降低了5．6％和6．2％，满意度函数的方差降低了7％，说明优化结果比较可靠．因此，用该方法进行优化能得到比传统满意度函数法较好的结果，且对模型的预测能力和响应的波动都具有稳健性．

Application of Improved Desirability Function Method to the Multi-Response Optimization

Desirability function method is the most popular approach for multi-response optimization, however, the variation, correlation and the uncertainty of parameter estimation of the responses are ignored in this approach. Thus improved desirability function method is presented. The proposed method applies variance-covariance structure of the responses and predicted variance to desirability function. The implementation and effectiveness of the proposed method are illustrated by an example from the literature. The result shows that, compared with traditional desirability function approach, the variance and predicted variance of responses obtained by improved desirability function method reduce 5.6% and 6.2% respectively, and the variance of desirability function decreases 7%. As a result, the proposed method, which is robust to predicted quality and variation of responses, yields better results than traditional desirability function method.