Journal of Quality Engineering and Management

Approximation of spline regression curves using the genetic algorithm

Document Type : Original Article

Authors

Mehdi Bashiri
Fatemeh Vakilian
Fatemeh Soghandi

Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran.

Abstract
Curve fitting is an important tool in data analysis, geometric modeling, and other engineering applications. When the shape of the measured data function is complex, estimating the curve using a polynomial function becomes difficult. In such cases, spline functions are generally preferred due to their higher accuracy and smoother approximation compared to other approximation functions. Often, for proper spline fitting, the number and locations of knots are unknown. Therefore, this paper presents a genetic algorithm to simultaneously determine the number and positions of knots based on a minimum error objective function without any restrictive assumptions. The proposed algorithm employs both the maximum likelihood estimation and least squares error methods for curve fitting. The performance of the proposed algorithm is evaluated using numerical examples with both methods. Simulation results indicate that when observations follow a normal distribution, the least squares method performs better. However, the main advantage of the maximum likelihood-based approach is its applicability to all statistical distributions. Finally, the effectiveness of the proposed approach is demonstrated through a practical case study.

Keywords

Spline function, genetic algorithm, knot points, maximum likelihood estimation, least squares error
Journal of Quality Engineering and Management
Volume 5, Issue 1
Spring 2015
Pages 39-48

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