Systematic sequential optimization

A systematic sequential optimization procedure may be used to establish an optimum multisegment temperature program. 

Stan and Steinbach [613] have described a sequential optimization procedure for programmed temperature GC that searches for an optimum multisegment program in a systematic way. This procedure can be divided into three different stages ... 

Simplex optimization of the primary (program) parameters in programmed temperature GC analysis has been demonstrated [612]. A systematic sequential search [613] may be used as an alternative. The Simplex method may be used to optimize a limited number of program parameters, whereas the latter approach was developed for the optimization of multisegment gradients. The use of interpretive methods has so far only been suggested [614,615]. 

As was the case in its application to the optimization of chromatographic selectivity under constant conditions, the Simplex algorithm appears to require a rather large number of experiments. This is also true for a systematic sequential procedure. 

After a few refinement cycles (a typical number is 5) the protocol above converges in some examples [18]. The path segments calculated with Ssdel or with the initial value formulation (equation (12) with a step size, A// (j) are essentially the same (Figs. 4 and 5). Sometimes, however, the process is difficult to converge and the step size in sequential optimizations does not decrease in a substantial and systematic way [18]. 

Figure 4.9. Optimization of product yieid through sequential and systematic screening and selection of genetic construct and recombinant host cells that produce the highest yield and genetic stability. The schematically presented steps are required to develop a master cell-bank, and working stock for the production of biologically active recombinant proteins in pharmaceutical scale.

Given the mere handful of reports in the published literature (6,38,39,52), there are many avenues open in the development of systematic approaches to optimization in SFC. In addition to the opportunities mentioned in the sections on the simplex method and window diagram approach, others include the exploration of other sequential or simultaneous optimization strategies such as optiplex, simulated annealing, method of steepest ascent, etc. that are potentially useful in SFC. 

There have been several other proposed procedures for syaemetic generation of optimal process flowsheets without ua initial process structure. Of note is one developed by Mahalec and Motard36 and incorporated into a computer program they called BALTAZAR. Like AIDES, it can be used for die synthesis of an entire chemical plant but takes a more sophisticated approach to processing objectives and constraints. It is based on a systematic resolution of conflicts between a set of processing rales and die processing objectives. The procedure is based on a sequential depth-first approach which employs several structural... 

The statistical analysis of data requires a proper design of experiments to prove or disprove a certain hypothesis which has been formulated in advance. From the viewpoint of a puritanical statistician most QSAR analyses are forbidden , because they are retrospective studies and, in addition, many different hypotheses (i.e. combinations of independent variables) are tested sequentially. Indeed, many problems arise from the application of regression analysis in ill-conditioned data sets. Only in later stages of lead structure optimization are certain hypotheses, e.g. on the influence of more lipophilic, electronegative, polar, or bulky substituents in a certain position, systematically tested, now fulfilling the requirements for the proper application of statistical methods. 

Efficient experimentation is based on the methods of experimental design and its quantitative evaluation. The latter can be performed by means of mathematical models or graphical representations. Alternatively, sequential methods are apphed, such as the simplex method, instead of these simultaneous methods of experimental optimization. There, the optimum conditions are found by systematic search for the objective criterion, for example, the maximum yield of a chemical reaction, in the space of all experimental variables. 

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