Global selection procedures

To arrive at a true optimal subset of variables (wavelengths) for a given data set, consideration of all possible combinations should in principle be used but it is computationally prohibitive. Since each variable can either appear, or not, in the equation and since this is true with every variable, there are 2 -possible equations (subsets) altogether. For spectral data containing 500 variables, this means 2 possibilities. For this type of problems, i.e. for search of an optimal solution out of the millions possible, the stochastic search heuristics, such as Genetic Algorithms or Simulated Annealing, are the most powerful tools [14,15]. 

Genetic Algorithm (GA) requires binary coding of possible solutions. In the case of feature selection, elements in the bitstring are set to zero for non-selected variables, while elements representing selected features are set to one. The initial population of bitstrings is selected randomly. All strings are then 

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Since an exhaustive search—eventually combined with exhaustive evaluation— is practically impossible, any variable selection procedure will mostly yield subopti-mal variable subsets, with the hope that they approximate the global optimum in the best possible way. A strategy could be to apply different algorithms for variable selection and save the best candidate solutions (typically 5-20 variable subsets). With this low number of potentially interesting models, it is possible to perform a detailed evaluation (like repeated double CV) in order to find one or several variables... 

Global fit procedure on all selected temperature ranges for continuous parameter estimation... 

The unknowns in this equation are the local coordinates of the foot (i.e. and 7]). After insertion of the global coordinates of the foot found at step 6 in the left-hand side, and the global coordinates of the nodal points in a given element in the right-hand side of this equation, it is solved using the Newton-Raphson method. If the foot is actually inside the selected element then for a quadrilateral element its local coordinates must be between -1 and +1 (a suitable criteria should be used in other types of elements). If the search is not successful then another element is selected and the procedure is repeated. 

The difficulty with this procedure is that simple refinement routines, such as simplex or least squares, lead only to the nearest minimum in the cost function which is unlikely to be the global minimum. The refinement procedure therefore has to be one that randomly samples different parts of configuration space so as to be able to reach different minima, ultimately selecting the global minimum. Two refinement methods have been proposed, simulated annealing and the genetic algorithm. 

The first action was to select and secure an alpha emitter. For that Oak Ridge National Laboratory was identified as a possible source. Two years later, after implementing agreements and safety procedures, we had secured samples of bismuth 213 with actinium 225 to serve as the alpha source for the program. To develop the radionucleotide delivery system (the cow), the Karlsruhe Atomic Energy Laboratory was contracted. This approach serves as an example of a global collaborative program. 

Because this optimization only concerned program parameters and not selectivity parameters, the response surface will have been relatively simple. Therefore, the probability that the Simplex procedure would arrive at the global optimum rather than at a local one was greater than it was in section 5.3, where we described the use of the Simplex method for selectivity optimization. 

The response surface for the optimization of the primary (program) parameters in programmed temperature GC is less convoluted than a typical response surface obtained in selectivity optimization procedures (see section 5.1). This will increase the possibility of a Simplex procedure locating the global optimum. 

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