Sequential simplex strategy

With new synthetic methods, mechanistic details are still obscured. It is not likely that such details will be revealed until the preparative utility of the procedure has been demonstrated. This means that an optimization of the experimental conditions must generally precede a mechanistic understanding. Hence, the optimum conditions must be inferred from experimental observations. The common method of adjusting one-variable-at-a-time, is a poor strategy, especially in optimization studies (see below). It is necessary to use multivariate strategies also for determining the optimum experimental conditions. There are many useful, and very simple strategies for this sequential simplex search, the method of steepest ascent, response surface methods. These will be discussed in Chapters 9 - 12. 

Since we wished to optimize this series with a minimal expenditure of our synthetic resources, the sequential simplex technique (SSO) was selected (11,12). This strategy is very resource efficient, requiring only n + 1 compounds to start the optimization, where n is the number of physiochemical parameters used to describe the characteristics of a substituent. We selected pi to account for lipophilicity and field (F) and resonance (R) were used to describe the electronic effects of each substituent (14). Verloop s Sterimol parameters (H), minimum van der Waals radius (B] ) and length (L) were selected to describe the size of the substituent. Using cluster analysis, we selected a set of six substituents that cover physiochemical parameter space well (15). These are-listed in Figure 6. 

For the optimization of, for instance, a tablet formulation, two strategies are available a sequential or a simultaneous approach. The sequential approach consists of a series of measurements where each new measurement is performed after the response of the previous one is knovm. The new experiment is planned according to a direction in the search space that looks promising with respect to the quality criterion which has to be optimized. Such a strategy is also called a hill-climbing method. The Simplex method is a well known example of such a strategy. Textbooks are available that describe the Simplex methods [20]. 

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. 

In a sequential strategy only a few experiments at a time are carried out and, on the basis of the results, the experiment to be carried out next is defined. These designs are used when the optimum of a single response is the only information desired. The best known sequential method is called the simplex method. However, it does not provide much information about a model relating the response with the factors studied. Despite the fact that it would be possible to map part of the response surface (the route followed to reach the optimum), the model obtained would not necessarily be a good one to describe the whole response surface and that is the reason why, when a model of the response surface is needed, one should prefer simultaneous methods. There are several situations where sequential designs are not suitable. One of them is when more than one response needs to be optimized. It also happens that these methods are trapped on a local optimum, and do not find the global optimum. 

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