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Optimizaiton with random error

University of British Columbia

A new evolutionary operation called the complicial method is presented. The main criterion, which is adhered to, is that changes in the independent variables are restricted to a small step-size from a previous best trial. The complicial method is essentially a modification of the simplicial method proposed by Spendley, Hext and Himsworth in which these authors employ regular type arrays in a sequential type search for the optimum. The complicial method differs from the simplicial method in that an irregular array is formed when (and only when) the last trial is proven to be the best of those previously tested. The design of this irregular array is such that a regular array can be formed when the last trial is proven not to be the best so far. The complicial method is compared to the simplicial method for a wide variety of response surfaces in both the absence and presence of random error. It is found that the complicial method is much more effective (i.e. the relative effectiveness is very large) for almost all the test response surfaces involving a small number of variables. Although an increase in the amount of random error decreases the effectiveness of both methods, the relative effectiveness generally remains unchanged. However, as the number of variables is increased the relative effectiveness is found to decrease markedly. This is explained by considerations of the basic design of the regular and irregular arrays. Because the complicial method sacrifices some of the simplicity characteristic of the simplicial method, it is recommended that the complicial method be applied only in situations where the relative effectiveness is very large. Therefore, this method is best used for all types of response surfaces involving a small number, of variables.

Text

2011-07-15

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http://hdl.handle.net/2429/36023

Chemical and Biological Engineering

University of British Columbia

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