Continuous D-optimality design

Kono s designs [46] are attempts to reduce the number of design points in continuous D-optimality designs (constructed on a hypercube), by replacing all points in centers of two-dimensional planes with one point in the hypercube center. The number of design points by Kono s designs is defined by this expression ... 

With a view to establishing suitable experimental conditions for preparative runs, the important experimental factors must be identified. To this end, a D-optimal design was used. The experimental variables considered are summarized in Table 4. It is seen that the variables describe both continuous and discrete variations. It is possible to use polynomial response function in such cases too, provided that the discrete variation is made to distinguish between only two alternatives. The model coefficients of the discrete variation is made to distinguish between only two alternatives. The model coefficients of the discrete variables describe the systematic variation of the response due to the alternatives. 

The approach of using a mathematical model to map responses predictively and then to use these models to optimize is limited to cases in which the relatively simple, normally quadratic model describes the phenomenon in the optimum region with sufficient accuracy. When this is not the case, one possibility is to reduce the size of the domain. Another is to use a more complex model or a non-polynomial model better suited to the phenomenon in question. The D-optimal designs and exchange algorithms are useful here as in all cases of change of experimental zone or mathematical model. In any case, response surface methodology in optimization is only applicable to continuous functions. 

G. Liu, B.J. van Wie, D. Leatzow, B. Weyrauch, T. Tiffany, Experimental design modeling of carryover to optimize air-segmented continuous flow analysis, Anal. Chim. Acta 408 (2000) 21. 

Figure 6.26. Graphic representation of the connex between biokinetics and corresponding optimal continuous bioreactor design in four cases (a-d) (Moser, 1983b).

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