Simulated annealing , subset

As might be expected, established optimisation techniques such as simulated annealing and genetic algorithms have been used to tackle the subset selection problem. These methods... 

Linear Models. Variable selection approaches can be applied in combination with both linear and nonlinear optimization algorithms. Exhaustive analysis of all possible combinations of descriptor subsets to find a specific subset of variables that affords the best correlation with the target property is practically impossible because of the combinatorial nature of this problem. Thus, stochastic sampling approaches such as genetic or evolutionary algorithms (GA or EA) or simulated annealing (SA) are employed. To illustrate one such application we shall consider the GA-PLS method, which was implemented as follows (136). 

Models can be generated using stepwise addition multiple linear regression as the descriptor selection criterion. Leaps-and-bounds regression [10] and simulated annealing (ANNUN) can be used to find a subset of descriptors that yield a statistically sound model. The best descriptor subset found with multiple linear regression can also be used to build a computational neural network model. The root mean square (rms) errors and the predictive power of the neural network model are usually improved due to the higher number of adjustable parameters and nonlinear behavior of the computational neural network model. 

Figure 5. Calculated vs. observed -log( 5o) values using a computational neural network model with the descriptor subset selected by generalized simulated annealing (anndes).

Partitioning is most appropriate when one is only interested in the subsets or clusters, while hierarchical decomposition is most applicable when one seeks to show similarity relationships between clusters. Section 2.1 formalizes the combinatorics of the partitional strategy and Section 2.2 does the same for hierarchical methods. The formulations we derive here provide the basis for the application of the simulated annealing algorithm to the underl5dng optimization problem as we show in Section 3. 

Montelione [18, 19] programs alignment random subset is used as input to CONGEN simulated annealing/ restrained molecular dynamics simulations... 

Agrafiotis [60] has also developed a simulated annealing method for maximising diversity. The method employs a user-defined objective function and can therefore be tailored to encode different selection criteria. The results of subset selection can be visualized using Sammon s nonlinear mapping algorithm [61]. 

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]. 

---