Grid Searches

Non-derivative Methods.—Multivariate Grid Search. The oldest of the direct search methods is the multivariate grid search. This has a long history in quantum chemistry as it has been the preferred method in optimizing the energy with respect to nuclear positions and with respect to orbital exponents. The algorithm for the method is very simple. In this and subsequent algorithms we use x to indicate the variables and a to indicate a chosen point. 

The method needs no explicit justification. It is apparent that if a minimum exists it is, in the long run, possible to find it by this strategy. 

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The grid. search technique can easily be applied to acyclic systems. Ring sy.slems can be treated as pseudo-acyclic by cutting one ring bond. The major drawback of this technique is that, because of the restricted number of degrees of freedom in... 

The systematic, or grid, search is only possible for small molecules. For larger systems tlrere are methods which can be used for perturbing a geometry from a local minimum to another minimum. Some commonly used methods for conformational sampling are ... 

Fig. 3. Projections on the (<1>, maps of the CICADA conformational search of the pentasaccharide. The dots indicate the values of all the optimized conformations determined by CICADA at each glycosidic linkange in 8 kcal/mol energy window For comparison, the isocontours, drawn in 1 Kcal/mol steps with an outer limit of 8 kcal/mol, represent the energy level of each disaccharide and calculated with the relaxed grid search approach. Dashed regions represent the locations of the low energy conformation of the pentasaccharide plotted on the potential energy surfaces of the constituting disaccharide segments...

Figure 4.32 Experimental design shoving the grid search solvent optimization system employed by PESOS (A) and an exa ple of a simplex search for a global optimum (B).

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... 

The next step, the grid search, is essentially a brute-force method in which the experimental range is divided into a grid of specific size and methodically searched. The method is called an exhaustive grid search. From an input of the desired criteria, the program prints out all points (formulations) that satisfy the constraints. 

A reported application of canonical analysis involved a novel combination of the canonical form of the regression equation with a computer-aided grid search technique to optimize controlled drug release from a pellet system prepared by extrusion and spheronization [28,29]. Formulation factors were used as independent variables, and in vitro dissolution was the main response, or dependent variable. Both a minimum and a maximum drug release rate was predicted and verified by preparation and testing of the predicted formulations. Excellent agreement between the predicted values and the actual values was evident for the four-component pellet system in this study. 

The description given by Zimmer seems to indicate a grid search based on local optimization rather than dynamic programming. 

Response surfaces are mostly described mathematically by polynomial approximations of 1st and 2nd degree. Grid search corresponds to a com-... 

Perczel, A., O. Farkas, and I. G. Csizmadia. 1996. Peptide Models XVI. The Identification of Selected HCO-l-SER-NH2 Conformers via a Systematic Grid Search Using Ab Initio Potential Energy Surfaces. J. Comput. Chem. 17, 821-834. 

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

Random Search / 6.1.2 Grid Search / 6.1.3 Univariate Search / 6.1.4 Simplex Search Method / 6.1.5 Conjugate Search Directions / 6.1.6 Summary... 

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