A hierarchical genetic algorithm approach for curve fitting with B-splines
A hierarchical genetic algorithm approach for curve fitting with B-splines
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DOI：
10.1007/s10710-014-9231-3
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发表时间：
2015-06
影响因子：
2.6
通讯作者：
C. H. García-Capulín;F. Cuevas;G. Trejo-Caballero;H. Rostro-González
中科院分区：
文献类型：
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作者：
C. H. García-Capulín;F. Cuevas;G. Trejo-Caballero;H. Rostro-González
使用样条曲线的自动曲线拟合已广泛应用于数据分析和工程应用中。与样条数据拟合相关的一个重要问题是节点数量和位置的适当选择以及样条系数的计算。通常，为了解决这个非线性问题，这些参数是单独估计的。在本文中，我们使用分层遗传算法来解决 B 样条曲线拟合问题。所提出的方法基于一种用于染色体表示的新型分层基因结构，它使我们能够自动同时确定结的数量和位置以及 B 样条系数。我们的方法能够在 B 样条基函数内找到具有最少参数的最佳解决方案。该方法完全基于遗传算法，不需要平滑因子或结点位置等主观参数来执行求解。为了验证所提出方法的有效性，包括了对平滑函数的多次测试的模拟结果以及与文献中的成功方法的比较。
Automatic curve fitting using splines has been widely used in data analysis and engineering applications. An important issue associated with data fitting by splines is the adequate selection of the number and location of the knots, as well as the calculation of the spline coefficients. Typically, these parameters are estimated separately with the aim of solving this non-linear problem. In this paper, we use a hierarchical genetic algorithm to tackle the B-spline curve fitting problem. 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, and the B-spline coefficients automatically and simultaneously. Our approach is able to find optimal solutions with the fewest parameters within the B-spline basis functions. 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 functions and comparison with a successful method from the literature have been included.