Alternating variable search

Optimization using the alternating variable search method... 

Whenever the procedure construct-variable-influence-pathways has to generate a number of alternative variable-influence paths, it employs a breadth-first search strategy. The procedure, expand-node, is used to establish the expansion list through the following algorithm ... 

The method of steepest descent uses only first-order derivatives to determine the search direction. Alternatively, Newton s method for single-variable optimization can be adapted to carry out multivariable optimization, taking advantage of both first- and second-order derivatives to obtain better search directions1. However, second-order derivatives must be evaluated, either analytically or numerically, and multimodal functions can make the method unstable. Therefore, while this method is potentially very powerful, it also has some practical difficulties. 

A general alternative to stepwise-type searching methods for variable selection would be methods that attempt to explore as much of the possible solution space as possible. An exhaustive search of all possible combinations of variables is possible only for problems that involve relatively few x variables. However, it... 

There are two schools of thought in model building. One method is to search for correlations amongst a vast array of physicochemical and structural variables, with no preconceived notion of mechanism. This approach avoids bias and may detect an unexpected relationship, but there is a danger of finding chance relationships that can be misleading (Topliss and Edwards, 1979). The alternative method is to suggest a physical model and make a choice of appropriate descriptors to test that model. 

A data set with 2°<20 140° CuKa was collected for a barrelshaped crystal on an Enraf Nonius CAD4 diffractometer with a 3.5° variable-speed 6-20 scan to accommodate the broad diffractions. From 196 unique diffractions above background (2o) out of 2170 measured diffractions, the structure was solved independently by the Multan direct method and a search of hypothetical structures. The resulting framework (Figure 2) is 81 predicted by J.V. Smith(4). Refinement to R 16% yielded the framework geometry, but the T-0 distances did not correspond satisfactorily to Al, P alternation, and the TPAOH was not located. Nevertheless the framework topology appeared correct, and the calculated powder pattern (Figure lb) was satisfactory. 

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