Grid search evaluation

Various grid search designs to select vectors x to evaluate fix). 

The experimental conditions are now chosen by a grid search such that the dctXTX is maximized. To this purpose each new condition is individually added to the set of existing data settings and the determinant of the matrix XTX is evaluated. This is done for each grid point to determine the highest value. 

A very simple method is the grid search, where each point at the given grid is evaluated and in that way the minimum is found. If necessary, the grid is reduced to estimate the parameters locally more precisely. 

In GA-SVM, the quality of SVM for regression depends on several parameters namely, kernel type k, which determines the sample distribution in the mapping space, and its corresponding parameter o, capacity parameter C, and s-insensitive loss function. The three parameters were optimized in a systematic grid search-way and the final optimal model was determined. Six general statistical parameters were selected to evaluate the prediction ability of the constructed model. These parameters are root mean square error of prediction... 

The selection of a method for one-dimensional search is based on the tradeoff between the number of function evaluations and computer time. We can find the optimum by evaluating the objective function at many values of x, using a small grid spacing (Ax) over the allowable range of x values, but this method is generally inefficient. There are three classes of techniques that can be used efficiently for one-dimensional search indirect, region elimination, and interpolation. 

It is perhaps useful to think of the pattern search method as an attempt to combine the certainty of the multivariate grid method with the ease of the univariate search method, in the sense that it seeks to avoid the enormous numbers of function evaluations inherent in the grid method, without getting involved in the (possibly fruitless and misleading) process of optimizing the variables separately. 

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