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.

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 N-D $C^k$ B-Spline Scattered Data Approximation

2005 ◽  
Author(s):  
Nicholas J. Tustison ◽  
James Gee
Keyword(s):  
Function Class ◽  
Data Fitting ◽  
Scattered Data ◽  
Scattered Data Approximation ◽  
Data Approximation ◽  
B Spline ◽  
B Splines ◽  
Scattered Data Fitting ◽  
Spline Surface ◽  
Ill Conditioning

Since the 1970’s B-splines have evolved to become the {} standard for curve and surface representation due to many of their salient properties. Conventional least-squares scattered data fitting techniques for B-splines require the inversion of potentially large matrices. This is time-consuming as well as susceptible to ill-conditioning which leads to undesired results. Lee {} proposed a novel B-spline algorithm for fitting a 2-D cubic B-spline surface to scattered data in . The proposed algorithm utilizes an optional multilevel approach for better fitting results. We generalize this technique to support N-dimensional data fitting as well as arbitrary degree of B-spline. In addition, we generalize the B-spline kernel function class to accommodate this new image filter.

scholarly journals Automated calibration of a two-dimensional overland flow model by estimating Manning's roughness coefficient using genetic algorithm

2017 ◽  
Vol 20 (2) ◽  
pp. 440-456
Author(s):  
J. Drisya ◽  
D. Sathish Kumar
Keyword(s):  
Genetic Algorithm ◽  
Flow Model ◽  
Overland Flow ◽  
Fitness Function ◽  
Roughness Coefficient ◽  
Model Parameters ◽  
Automatic Data ◽  
Automated Calibration ◽  
Manning’S Roughness Coefficient ◽  
Overland Flow Model

Abstract Calibration is an important phase in the hydrological modelling process. In this study, an automated calibration framework is developed for estimating Manning's roughness coefficient. The calibration process is formulated as an optimization problem and solved using a genetic algorithm (GA). A heuristic search procedure using GA is developed by including runoff simulation process and evaluating the fitness function by comparing the experimental results. The model is calibrated and validated using datasets of Watershed Experimentation System. A loosely coupled architecture is followed with an interface program to enable automatic data transfer between overland flow model and GA. Single objective GA optimization with minimizing percentage bias, root mean square error and maximizing Nash–Sutcliffe efficiency is integrated with the model scheme. Trade-offs are observed between the different objectives and no single set of the parameter is able to optimize all objectives simultaneously. Hence, multi-objective GA using pooled and balanced aggregated function statistic are used along with the model. The results indicate that the solutions on the Pareto-front are equally good with respect to one objective, but may not be suitable regarding other objectives. The present technique can be applied to calibrate the hydrological model parameters.

scholarly journals Bayesian B-spline mapping for dynamic quantitative traits

2012 ◽  
Vol 94 (2) ◽  
pp. 85-95 ◽  
Author(s):  
JUN XING ◽  
JIAHAN LI ◽  
RUNQING YANG ◽  
XIAOJING ZHOU ◽  
SHIZHONG XU
Keyword(s):  
Legendre Polynomial ◽  
Legendre Polynomials ◽  
Simulated Dataset ◽  
Model Parameters ◽  
B Spline ◽  
B Splines ◽  
Bayesian Mapping ◽  
Bayesian Shrinkage ◽  
Dynamic Traits ◽  
Over Time

SummaryOwing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

scholarly journals Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Genetic Algorithm ◽  
Distance Measure ◽  
Dimensional Space ◽  
Fitness Function ◽  
Operating Conditions ◽  
Model Parameters ◽  
Fractional Dynamics ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Percolation Phenomena

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

scholarly journals Calibration of Dupire local volatility model using genetic algorithm of optimization

2019 ◽  
Vol 7 (1) ◽  
pp. 1-20
Author(s):  
Maksym Bondarenko ◽  
Victor Bondarenko
Keyword(s):  
Genetic Algorithm ◽  
Two Dimensions ◽  
Model Parameters ◽  
Option Prices ◽  
Local Volatility ◽  
B Splines ◽  
Market Values ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Gradient Descent Algorithm

The problem of calibration of local volatility model of Dupire has been formalized. It uses genetic algorithm as alternative to regularization approach with further application of gradient descent algorithm. Components that solve Dupire’s partial differential equation that represents dynamics of underlying asset’s price within Dupire model have been built. This price depends in particular on values of volatility parameters. Local volatility is parametrized in two dimensions (by Dupire model): time to maturity of the option and strike price (execution price). On maturity axis linear interpolation is used while on strike axis we use B-Splines. Genetic operators of mutation and selection are then applied to parameters of B-Splines. Resulting parameters allow us to obtain the values of local volatility both in knot points and intermediate points using interpolation techniques. Then we solve Dupire equation and calculate model values of option prices. To calculate cost function we simulate market values of option prices using classic Black-Scholes model. An experimental research to compare simulated market volatility and volatility obtained by means of calibration of Dupire model has been conducted. The goal is to estimate the precision of the approach and its usability in practice. To estimate the precision of obtained results we use a measure based on average deviation of modeled local volatility from values used to simulate market prices of the options. The research has shown that the approach to calibration using genetic algorithm of optimization requires some additional manipulations to achieve convergence. In particular it requires non-uniform discretization of the space of model parameters as well as usage of de Boor interpolation. Value 0.07 turns out to be the most efficient mutation parameter. Using this parameter leads to quicker convergence. It has been proved that the algorithm allows precise calibration of local volatility surface from option prices.

Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set

1987 ◽  
Vol 16 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Marilyn Lord
Keyword(s):  
Computer Aided Design ◽  
Control Point ◽  
The Body ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Data Points ◽  
Point Set ◽  
Support Surfaces ◽  
Aided Design

The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control point can be adjusted to remodel the surface locally. The resultant curves are well behaved. However, in these biomedical applications the original surface prior to modification is usually defined by a limited set of point measurements from the body segment in question. Thus there is a need initially to define a B-spline surface which interpolates this set of data points. In this paper, a computer-iterative method of fitting a B-spline surface to a given set of data points is outlined, and the technique is demonstrated for a curve. Extension to a surface is conceptually straightforward.

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