Sequential optimization

Perkin-Elmer Plasma II Optimized sequential system 70... 

An unknown mixture can be screened on a set of orthogonal systems as a first step in the method development procedure. The chromatographic and/or electrophoretic system, on which the best separation was achieved, can then be retained for further method optimization. Sequentially, the pH and the organic modifier composition of the mobile phase can be adjusted to improve the separation on the CS. If necessary, also the temperature can be modified, while for gradient methods the gradient slope can be considered. For CE methods, the optimization steps will be different from RP chromatography methods. Other factors will be optimized depending on the type of CE method, e.g., CZE and MEKC. However, for the development of CE methods, we would like to refer to Chapter 4 of this book. 

Grate, J. W., Fadeff, S. K., and Egorov, O., Separation-optimized sequential injection method for rapid automated separation and determination of 90Sr in nuclear waste, Analyst, 124, 203-210, 1999. 

Independent parameters with a simple effect on the resolution may be optimized sequentially, i.e. one after the other (section 5.1.1). Hence, after the selectivity has been optimized, the shortest possible column length or the highest possible flowrate may be established that will provide sufficient resolution. Adapting the length of the column is the preferred strategy, because it will lead to both faster analysis and lower pressure drops. 

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 . 

FIGURE 8.24 Schematic representation of an optimal sequential composite design. 

To avoid these kinds of problems, some new experimental designs have been proposed [26,27], Called optimal composite sequential designs (OCSD), these designs are an extension of optimal sequential designs (OSD) in that they are optimal for more than one type of model. The structure of a typical OCSD is shown in Figure 8.24. 

Optimal Sequential Composite Design for Two Process Variables and Two Polynomial Models Mu Full Second-Order Model and M2, Incomplete Third-Order Model... 

This design is used in the same manner as the previously described optimal sequential designs, except that now it is possible to use either of the models described in Equation 8.71 and Equation 8.72. We start the investigation by performing experiments 1 to 6. After that, we continue with experiments 7 to 9. Once we have completed more than kx experiments, it becomes possible to build a model with structure Mv For example, if the model built over points 1 to 8 appeared to be inadequate, we could continue the experimental work by adding additional measurements according to the list in Table 8.11. Once we have completed more than k2 experiments, we can build a... 

The objective of a spread design is to identify a subset of molecules in which the molecules are as dissimilar as possible under a given similarity metric. For a given metric to measure the similarity of a subset, all subsets of size k (plus any molecules previously selected) could be evaluated and the subset that produces the lowest similarity measure chosen. In practice, simple non-optimal sequential algorithms are often used to approximate the maximally dissimilar subset two such algorithms are described below. 

Timing The time point(s) selected may not be optimal Sequential effects on different subsets after exposure to cyclosporine Huby et al. (1995)... 

Carlin BP, Kadane JB, Gelfand AE (1998) Approaches for optimal sequential decision analysis in clinical trials. Biometrics 54 964-975. 

To summarize, the approach followed in Section 2.3.d on optimal sequential design is illustrated in Fig. 2.3.d.2-2 by means of a kind of flow diagram (from Froment [45,46]). 

Kiefer, J. (1957), Optimal Sequential Search and Approximation Methods under Minimum Regularity Conditions, SIAM Journal of Applied Mathematics, Vol. 5, pp. 105—136. 

Simultaneous dynamic optimization. In order to validate this approach, the sjm-thesis of MTBE is used as case study. Three spatial variables and sixteen control-related parameters were optimized during a time horizon of 14400 s. A tradeoff between control and economic performances exists in the design of RD processes, as shown in table 6.5. The design optimized sequentially with respect to dynamic behavior led to a RD process... 

Formulating design as a dynamic optimization problem, we found that for the synthesis of MTBE, a tradeoff between control and economic performances exists. We solved this multiobjective optimization problem by incorporating appropriate time-invariant parameters e.g. column diameter, heat transfer areas and controllers parameters) in the frame of a dynamic optimization problem in the presence of deterministic disturbances. The design optimized sequentially with respect to dynamic behavior leads to a RD process with a total annualized cost higher than that obtained using simultaneous optimization of spatial and control structures. 

Other methods based on the cavity pressure are also not suitable for optimizing sequential molding processes, since a pressure threshold, which could be used to open a nozzle, can only be set when a pressure rise has occurred. However, the location of the melt at this moment is unknown because the position depends on the viscosity of the melt. An optimization of weld lines or a targeted manipulation of the melt flow is a function of pressure and is therefore not possible either. 

MSBSV90] S. Malik, E. Sentovich, R. K. Brayton, and A. Sangiovanni-Vincentelli. Retiming and resynthesis Optimizing sequential networks with combinational techniques. In Proceedings of the Hawaii International Conference on System Sciences, pages 397-406, Hawaii, 1990. 

In the early years of process development, chemistry, variables were optimized sequentially and through multiple loops. The variables are rarely independent, and this is a slow and inefficient process. More modern work optimizes variables simultaneously, using multiple parallel experiments with computer analysis of the outcomes. 

To make this note self-contained we shall reproduce the details of the optimal sequential coloring algorithm in [6]. The idea of the algorithm is simple the intervals are colored sequentially from left to right. As soon as an interval has ended, its color is released (pushed on a stack) and can be reused for the first interval that starts after the current one ended in other words, we can reuse the same channel for both pairs of components. The details follow. 

---