Sequential search strategy

Spectra and chemical structure searches are based on distance and similarity measures as introduced in Section 5.2. Different strategies are known sequential search, search based on inverted lists, and hierarchical search trees. The strategies are explained for search of spectra. 

Feature-selection techniques can be generally considered as a combination of both a search algorithm and a criterion function. The solution to feature-selection problem is offered by the search algorithm, which generates a subset of features and compares them on the basis of the criterion function. From a computational viewpoint, an exhaustive search for the optimal solution becomes intractable even for moderate values of features (Siedlecki and Sklansky 1988). Despite these apparent difficulties, many feature-selection approaches have been developed (Serpico and Bruzzone 1994). The sequential forward selection (SFS) and the sequential backward selection (SBS) techniques are the simplest suboptimal search strategies they can identify the best feature subset achievable by adding (to an empty set in SFS) or removing (from the complete set from SBS) one feature at a time, until the desired number of features is achieved. 

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]. 

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.)... 

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 . 

Minimization methods that incorporate only function values generally involve some systematic method to search the conformational space. In coordinate descent methods, the search directions are the standard basis vectors. A sweep through these n search vectors produces a sequential modification of one function variable at a time. Through repeated sweeping of the n-dimensional space, a local minimum might ultimately be found. Unfortunately, this strategy is inefficient and not reliable.3 4... 

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. 

Sequential strategies of optimization are based on an initial design of an experiment followed by a sequence of further measurements in the direction of the steepest ascent or descent. That is, no quantitative relationship between factors and responses is evaluated, but the response surface is searched along an optimal (invisible) path. The two strategies are exemplified in Figure 4.1. 

If the search is performed for an object from the lower levels, it is useful to limit the number of its iterations. For instance, suppose we want to solve a problem of maximum level that is a generic objective function bounds, linear, nonlinear equality and inequality constraints. The search for a new point that is better than the previous one can be performed with different strategies that can be used sequentially or in parallel, as required. The most important are the following ... 

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