Separation Simplex optimization search

Table 8. Chromatographic separation quality functions used for a Simplex search. From J. Berridge, Techniques for the automated optimization of HPLC separations , p. 26-27 (1984), Wiley Sons, England. Copyright 1984, John Wiiey Sons, Inc. Reprinted by permission of J. Wiley Sons Ltd. England...

The optimization can be carried out by several methods of linear and nonlinear regression. The mathematical methods must be chosen with criteria to fit the calculation of the applied objective functions. The most widely applied methods of nonlinear regression can be separated into two categories methods with or without using partial derivatives of the objective function to the model parameters. The most widely employed nonderivative methods are zero order, such as the methods of direct search and the Simplex (Himmelblau, 1972). The most widely used derivative methods are first order, such as the method of indirect search, Gauss-Seidel or Newton, gradient method, and the Marquardt method. 

The main disadvantage of the simplex method consists in the laige number of experiments required to find optimal working conditions. Further, the optimisation criterion characterises the separation of the sample mixture by a single number, so that the detailed information on the separation of the individual sample components is lost and because of the high probability that the search method will slide into a region with a local maximum of the optimisation criterion, the simplex optimisation method can be expected to be fully successful only with the separations of relatively simple samples. 

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