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. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

The practical implementation of optimal control systems in large industrial process applications has been limited by the high costs of the required computing facilities. With the recent advances in component fabrication and the resultant decrease in hardware costs, special purpose computers, utilizing virtually no software at all, can be constructed as economical alternatives to presently available general purpose computers for use in optimal process controllers. A design for one such special purpose machine, an automatic optimizer, is presented in this thesis. Tests conducted on a working optimizer constructed on the basis of the given design, demonstrate that it is suitably fast and powerful for use in process controllers. In addition, the optimizer is inexpensive enough to be used as part of an economical process controller. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate