A new search procedure of steepest ascent in response surface exploration

The method of steepest ascent direction has been widely accepted for process optimization in the applications of response surface methodology (RSM). The procedure of steepest ascent direction is performed on experiments run along the gradient of a fitted linear model. Therefore, the RSM practitioner needs to decide a suitable stopping rule such that the optimum point estimate in the search direction can be determined. However, the details of how to deflect and then halt a search in the steepest ascent direction are not thoroughly described in the literature. In common practice, it is convenient to use the simple stopping rules after one to three response deteriorations in a row after a series of fitted linear models used for exploration. In the literature, there are two formal stopping rules proposed, that is, Myers and Khuri's [A new procedure for steepest ascent, Comm. Statist. Theory Methods A 8(14) (1979), pp. 1359-1376] stopping rule and del Castillo's [Stopping rules for steepest ascent in experimental optimization, Comm. Statist. Simul. Comput. 26(4) (1997), pp. 1599-1615] stopping rule. This paper develops a new procedure for determining how to adjust and then when to stop a steepest ascent search in response surface exploration. This proposal wishes to provide the RSM practitioner with a clear-cut and easy-to-implement procedure that can attain the optimum mean response more accurately than the existing procedures. Through the study of simulation optimization, it shows that the average optimum point and response returned by using the new search procedure are considerably improved when compared with two existing stopping rules. The number of experimental trials required for convergence is greatly reduced as well.