Selectivity optimization grid search

For the optimization itself, two major steps were used the feasibility search and the grid search. The feasibility program is used to locate a set of response constraints that are just at the limit of possibility. One selects the several values for the responses of interest (i.e., the responses one wishes to constrain), and a search of the response surface is made to determine whether a solution is feasible. For example, the constraints in Table 6 were fed into the computer and were relaxed one... 

For the important case of the optimization of the mobile phase composition in reversed phase LC (RPLC), a typical two-dimensional response surface tends to be much less rugged, especially if the number of sample components is relatively small (n<10). A typical example is shown in figure 5.5. The selection of the normalized resolution product (r, eqn.4.19) as the criterion has also contributed to the smoother appearance of figure 5.5 relative to figure 5.1. Note that the criterion r has been recommended in chapter 4 for optimization processes in which the dimensions of the column are to be optimized after completion of the procedure (table 4.11). Therefore, the grid search approach is more appropriate for this kind of optimization than for optimization processes on the final analytical column. 

The SVM model was developed by using the LIBSVM software version 2.86 [50] with the RBF kernel function. The grid-search approach was adopted to select the optimal parameters C and y using the standard 5-fold cross validation within the training set. The optimal C and y values for the resulting SVM model were 128.0 and 0.03125, respectively, with the 5-fold cross validation training ER of 6.98 %. 

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... 

With only a single variable it is computationally inexpensive to perform a grid search to find the value of a that minimizes G. The bond valences are calculated from the A-X and B-X distances and tabulated values of bond valence parameters [11]. Figure 2 shows the G and B VSs of the A, B, and X ions in SrTiOs as a function of lattice parameter. The observed lattice parameter is a = 3.901(1) A [12] and the predicted lattice parameter is 3.930 A. For larger lattice parameters the BVS of the ions decreases as the interatomic distances increase, and for smaller lattice parameters the BVS of the ions increase as a result of shorter interatomic distances. The optimized structure and lattice parameter is selected where the minimum of G is obtained. Note this is where the BVSs of the ions are near the ideal formal oxidation states, which are shown as horizontal dashed lines. 

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