Optimization strategy sequential

There are two main multivariate optimization strategies sequential and simultaneous. In a simultaneous strategy a certain number of experiments defined according to an experimental design, such as a factorial or mixture design, are carried out. The experimental results are then used to obtain models (see equations 2-4 in Section 1.3) from which the optima Can be derived. 

Optimization methods can be classified in several ways, and the choice is largely subjective. For our purposes, it is convenient to categorize them as sequential or simultaneous. A sequential method is one in which the experimental and evaluation stages alternate throughout the procedure, with the results of previous experiments being used to predict further experiments in search of the optimum. In contrast, with a simultaneous optimization strategy, most if not all experiments are completed prior to evaluation. (Note that simultaneous has a different meaning here than in the previous section.)... 

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. 

The complexity of the response surface is what makes the optimization of chromatographic selectivity stand out as a particular optimization problem rather than as an example to which known optimization strategies from other fields can be readily applied. This is illustrated by the application of univariate optimization. In univariate optimization (or univariate search) methods the parameters of interest are optimized sequentially. An optimum is located by varying a given parameter and keeping all other parameters constant. In this way, an optimum value is obtained for that particular parameter. From this moment on the optimum value is assigned to the parameter and another parameter is varied in order to establish its optimum value . 

There are two main multivariate optimization strategies those based on sequential designs and those based on simultaneous designs. 

For these reasons, multivariate approaches seem better. The multivariate approaches, the topic of this chapter, can be further divided into sequential and simultaneous strategies (7-9). In sequential optimization strategies, initially only a few experiments are performed and their results are used to define the next experiment(s) (7, 8,10). In simultaneous approaches, a predefined number of experiments are performed according to a well-defined experimen-... 

Whenever a new CE method is being developed, optimization strategies are usually applied to improve analysis speed, sensitivity, and resolution, using these three parameters or a combination of them as the monitored output (also called response or performance criteria). Very frequently, a step-by-step approach in which each factor is varied sequentially is followed. In this case, all parameters are kept constant, while the parameter of interest is varied and the response is measured. Depending on the problem (especially when the number of factors to optimize is very low) and on the performance criteria, univariate optimization can be useful, that is, the analysis of a single compound with only one component of the BGE. However, in most cases, a step-by-step optimization is laborious and tedious because it typically requires a high number of experiments. Furthermore, and more important, it does not consider possible interactions between factors. 

The report commented above for the determination of sulfonamides in pharmaceuticals [11] is a useful example of the development of an analytical procedure, where a sequential optimization is made. Next, the development of a procedure for the analysis of mixtures of p-blockers and diuretics [14] will show the usefulness of the interpretive optimization strategy shown in Chapter 8, which was assisted by the software (see Appendix I). 

The issue of parallel versus sequential synthesis using multimode or monomode cavities, respectively, deserves special comment. While the parallel set-up allows for a considerably higher throughput achievable in the relatively short timeframe of a microwave-enhanced chemical reaction, the individual control over each reaction vessel in terms of reaction temperature/pressure is limited. In the parallel mode, all reaction vessels are exposed to the same irradiation conditions. In order to ensure similar temperatures in each vessel, the same volume of the identical solvent should be used in each reaction vessel because of the dielectric properties involved [86]. As an alternative to parallel processing, the automated sequential synthesis of libraries can be a viable strategy if small focused libraries (20-200 compounds) need to be prepared. Irradiating each individual reaction vessel separately gives better control over the reaction parameters and allows for the rapid optimization of reaction conditions. For the preparation of relatively small libraries, where delicate chemistries are to be performed, the sequential format may be preferable. This is discussed in more detail in Chapter 5. 

Kisala, T. P. R. A. Trevino-Lozano J. F. Boston H. I. Britt et al. Sequential Modular and Simultaneous Modular Strategies for Process Flowsheet Optimization. Comput Chem Eng 11 567-579 (1987). 

The classic methods use an ODE solver in combination with an optimization algorithm and solve the problem sequentially. This solution strategy is referred to as a sequential solution and optimization approach, since for each iteration the optimization variables are set and then the differential equation constraints are integrated. Though straightforward, this approach is generally inefficient because it requires the accurate solution of the model equations at each iteration within the optimization, even when iterates are far from the final optimal solution. 

The simultaneous solution strategy offers several advantages over the sequential approach. A wide range of constraints may be easily incorporated and the solution of the optimization problem provides useful sensitivity information at little additional cost. On the other hand, the sequential approach is straightforward to implement and also has the advantage of well-developed error control. Error control for numerical integrators (used in the sequential approach) is relatively mature when compared, for example, to that of orthogonal collocation on finite elements (a possible technique for a simultaneous approach). 

A strategy for the enantioseparation of basic compounds was described by SokolieP and Koller [35] and is displayed in Figure 3.7. All steps from method development till validation are included in the flow chart. Perhaps a disadvantage in this approach is that sequential screening and optimization steps are used (i.e., every factor is optimized individually). The use of the developed scheme was demonstrated for one compound, for which the method was developed, optimized, and validated. The generic applicability of this approach was not considered and is unknown. 

Fig. 14.2 Different drug discovery strategies (A) Sequential optimization (historic approach) - first optimization of affinity, while ADME properties are treated at a later stage. (B) Multidimensional scenario - combined optimization of affinity and ADME properties, simultaneous monitor changes in relevant properties [20],...

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