Sequential or simultaneous optimization

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]. 

In the simultaneous approach the experiments are planned beforehand (preferably using experimental design techniques) and performed randomly. With RSM techniques the obtained experimental data can be used to model the quality criterion as a function of the design variables. Then an optimal setting of the design variables can be calculated. All the optimization experiments described in this book are using the simultaneous approach. The simultaneous approach uses in almost all 

One of the drawbacks of sequential optimization methods is that optimizing two or more criteria at the same time is hard, if not impossible. If the two or more criteria are combined in one overall criterion, which is advocated sometimes, then ambiguous results are obtained. This is shown in Chapter 4. There are ways to overcome this ambiguity to some extent [21]. Another drawback of a sequential procedure is that it gives not much information on the dependence of the criterion on the design variables. In the context of robustness this is a very serious drawback. This is one of the reasons why the use of sequential optimization methods is not present in this book. 

In practice often more than one quality criterion is relevant. In the case of the need to build in robustness, at least two criteria are already needed the quality criterion itself and its associated robustness criterion. Hence, optimization has to be done on more than one criterion simultaneously. If a simultaneous optimization technique is used then there are procedures to deal with multiple optimization criteria. Several methods for multi-criteria optimization have been proposed and recently a tutorial/review has appeared [22]. 

An introduction to one particular multi-criteria optimization method -the so called Pareto-Optimality method - is discussed in Chapter 4, where also an application of this method is given. 

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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. 

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