Abstract
Problem statement: A direct method, such as least squares technique is usually used to solve problems involving matching a curve or a surface to a set of data points. The solution obtained by this direct method is precise or very good in approximation, but computationally not very efficient. Thus, in this study, we propose an indirect approach using Particle Swarm Optimization (PSO) technique as an alternative. Approach: As a case study, we use conic curve which satisfy C0 continuity to be fitted to a given set of data points. PSO, a soft computing method is employed to optimize the control points and weights which are then used in conic equations. Results: Best fitted conic curve that represents all the given data points is then obtained. Conclusion: We use an indirect technique of soft computing methods, i.e., PSO to fit a curve to a given data set. We believe that other types of soft computing based heuristic procedures may also be used to solve related problems or to find its effectiveness.
Highlights
Curve fitting is the process of constructing a curve, or mathematical function that has the best fit to a series of data points, possibly subject to certain constraints
Particle Swarm Optimization (PSO) is a population based optimization tool which could be implemented and applied to solve various function optimization problems, or problems that can be transformed into function optimization forms
Particle Swarm Optimization: PSO starts by having a population of particles initialized with random positions marked by vector xi and random velocities vi (Das et al, 2008)
Summary
Curve fitting is the process of constructing a curve, or mathematical function that has the best fit to a series of data points, possibly subject to certain constraints. A related topic in statistics is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fitted to observed data with certain random errors. Particle Swarm Optimization: PSO starts by having a population of particles initialized with random positions marked by vector xi and random velocities vi (Das et al, 2008).
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