A Hierarchical Genetic Algorithm for System Identification and Curve Fitting with a Supercomputer Implementation

1999 ◽  
pp. 111-137 ◽  
Author(s):  
Mehmet Gulsen ◽  
Alice E. Smith
Keyword(s):  
Genetic Algorithm ◽  
System Identification ◽  
Curve Fitting ◽  
Hierarchical Genetic Algorithm

scholarly journals Automatic Curve Fitting Based on Radial Basis Functions and a Hierarchical Genetic Algorithm

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez ◽  
C. H. Garcia-Capulin ◽  
O. G. Ibarra-Manzano ◽  
J. G. Avina-Cervantes ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Radial Basis Functions ◽  
Curve Fitting ◽  
Least Squares Method ◽  
Selection Criterion ◽  
Search Space ◽  
Basis Functions ◽  
Compact Representation ◽  
Radial Basis ◽  
Hierarchical Genetic Algorithm

Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included.

A hierarchical genetic algorithm approach for curve fitting with B-splines

2014 ◽  
Vol 16 (2) ◽  
pp. 151-166 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez
Keyword(s):  
Genetic Algorithm ◽  
Curve Fitting ◽  
B Splines ◽  
Genetic Algorithm Approach ◽  
Hierarchical Genetic Algorithm

scholarly journals Parallel Hierarchical Genetic Algorithm for Scattered Data Fitting through B-Splines

2019 ◽  
Vol 9 (11) ◽  
pp. 2336 ◽  
Author(s):  
Jose Edgar Lara-Ramirez ◽  
Carlos Hugo Garcia-Capulin ◽  
Maria de Jesus Estudillo-Ayala ◽  
Juan Gabriel Avina-Cervantes ◽  
Raul Enrique Sanchez-Yanez ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Curve Fitting ◽  
Fitness Function ◽  
Scattered Data ◽  
Model Parameters ◽  
B Spline ◽  
B Splines ◽  
Scattered Data Fitting ◽  
Data Points ◽  
Hierarchical Genetic Algorithm

Curve fitting to unorganized data points is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of scattered and noisy data points, the goal is to construct a curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Although many papers have addressed the problem, this remains very challenging. In this paper we propose to solve the curve fitting problem to noisy scattered data using a parallel hierarchical genetic algorithm and B-splines. We use a novel hierarchical structure to represent both the model structure and the model parameters. The best B-spline model is searched using bi-objective fitness function. As a result, our method determines the number and locations of the knots, and the B-spline coefficients simultaneously and automatically. In addition, to accelerate the estimation of B-spline parameters the algorithm is implemented with two levels of parallelism, taking advantages of the new hardware platforms. Finally, to validate our approach, we fitted curves from scattered noisy points and results were compared through numerical simulations with several methods, which are widely used in fitting tasks. Results show a better performance on the reference methods.

scholarly journals Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez
Keyword(s):  
Genetic Algorithm ◽  
Geometric Modeling ◽  
Data Set ◽  
Surface Approximation ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Surface Dimension ◽  
Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

HIERARCHICAL GENETIC ALGORITHM FOR NEAR-OPTIMAL FEEDFORWARD NEURAL NETWORK DESIGN

2002 ◽  
Vol 12 (01) ◽  
pp. 31-43 ◽  
Author(s):  
GARY YEN ◽  
HAIMING LU
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Neural Networks ◽  
Cost Function ◽  
Design Procedure ◽  
Optimal Solution ◽  
Traditional Learning ◽  
Feed Forward Neural Network ◽  
Optimal Solution Set ◽  
Hierarchical Genetic Algorithm

In this paper, we propose a genetic algorithm based design procedure for a multi-layer feed-forward neural network. A hierarchical genetic algorithm is used to evolve both the neural network's topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi-objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey–Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi-layer Perceptron networks and radial-basis function networks. Based upon the chosen cost function, a linear weight combination decision-making approach has been applied to derive an approximated Pareto-optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two-objective optimization problem.

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