Fundamentals of neural networks: architectures, algorithms, and applications
Fundamentals of neural networks: architectures, algorithms, and applications
Neural network design
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Pattern Search Algorithms for Mixed Variable Programming
SIAM Journal on Optimization
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Designing Neural Networks using Genetic Algorithms
Proceedings of the 3rd International Conference on Genetic Algorithms
A framework for managing models in nonlinear optimization of computationally expensive functions
A framework for managing models in nonlinear optimization of computationally expensive functions
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
Generalized pattern searches with derivative information
Mathematical Programming: Series A and B
Structure optimization of neural networks for evolutionary design optimization
Soft Computing - A Fusion of Foundations, Methodologies and Applications
An Algorithm Model for Mixed Variable Programming
SIAM Journal on Optimization
Expert Systems with Applications: An International Journal
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A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization. When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function, and the connectivity among neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrates equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully connected feedforward network having four nonlinear hidden layers and 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 × 500 grid point discretization of the parameter space.