A Study of the Nelder and Mead Modified Simplex Method with the Second-Order Designs on Uni-and Dual- Response Systems
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Abstract
Modified simplex method (MSM) is a method for finding the optimal conditions of industrial processes. In general, this approach will research for the proper conditions under a consideration of a uni-response system, an average of process yields. However, the uni-response system may not be valid when the variance of yields is not constant. This research concerns a dual-response system, with both average and variance of responses. The objective of this work is to compare the efficiency of the MSM with the completion of the central composite and hexagon designs on various systems for determining the optimal values of a process in the presence of noise. On both uni- and dual-response systems, the average of actual responses and the average of distance between true optimum point and estimated optimum point are not significantly different when compared. However, the average of standard deviation of actual responses from the MSM with the central composite design seems to be worse. In summary, the optimization strategy of the MSM based on hexagon design leads to the better condition with fewer experimental trials whilst searching for the maximum.
Keywords: uni response, dual response, optimization strategy, modified simplex method, hexagon
Corresponding author: E-mail: Ipongch@engr.tu.ac.th
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