From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CADCAM
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-24
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Fitting spline curves to data points is a very important issue in many applied fields.
It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way.
In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail.
This paper presents a new bioinspired method to tackle this issue.
In this method, optimization is performed through a combination of two techniques.
Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme.
Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector.
This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition.
Our method is applied to some illustrative real-world examples from the CAD/CAM field.
Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.
American Psychological Association (APA)
Gálvez, Akemi& Iglesias, Andrés. 2013. From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CADCAM. The Scientific World Journal،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1032745
Modern Language Association (MLA)
Gálvez, Akemi& Iglesias, Andrés. From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CADCAM. The Scientific World Journal No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-1032745
American Medical Association (AMA)
Gálvez, Akemi& Iglesias, Andrés. From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CADCAM. The Scientific World Journal. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1032745
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1032745