A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing

Fitting data points to curves (usually referred to as curve reconstruction) is a major issue in computer-aided design/manufacturing (CAD/CAM). This problem appears recurrently in reverse engineering, where a set of (possibly massive and noisy) data points obtained by 3D laser scanning have to be fitted to a free-form parametric curve (typically a B-spline). Despite the large number of methods available to tackle this issue, the problem is still challenging and elusive. In fact, no satisfactory solution to the general problem has been achieved so far. In this paper we present a novel hybrid evolutionary approach (called IMCH-GAPSO) for B-spline curve reconstruction comprised of two classical bio-inspired techniques: genetic algorithms (GA) and particle swarm optimization (PSO), accounting for data parameterization and knot placement, respectively. In our setting, GA and PSO are mutually coupled in the sense that the output of one system is used as the input of the other and vice versa. This coupling is then repeated iteratively until a termination criterion (such as a prescribed error threshold or a fixed number of iterations) is attained. To evaluate the performance of our approach, it has been applied to several illustrative examples of data points from real-world applications in manufacturing. Our experimental results show that our approach performs very well, being able to reconstruct with very high accuracy extremely complicated shapes, unfeasible for reconstruction with current methods.

[1]  Terence Soule,et al.  Breeding swarms: a GA/PSO hybrid , 2005, GECCO '05.

[2]  Byoung K. Choi,et al.  Sculptured Surface Machining: Theory and applications , 2012 .

[3]  Krishnan Suresh,et al.  Constant Scallop-height Machining of Free-form Surfaces , 1994 .

[4]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[5]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

[6]  Jean-François Fontaine,et al.  Systematic error correction of a 3D laser scanning measurement device , 2011 .

[7]  Nie Ru,et al.  A GA and Particle Swarm Optimization based hybrid algorithm , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[8]  Toshinobu Harada,et al.  Data fitting with a spline using a real-coded genetic algorithm , 2003, Comput. Aided Des..

[9]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[10]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[11]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[12]  Hyungjun Park,et al.  An error-bounded approximate method for representing planar curves in B-splines , 2004, Comput. Aided Geom. Des..

[13]  P. Pirinoli,et al.  A new hybrid genetical-swarm algorithm for electromagnetic optimization , 2004, Proceedings. ICCEA 2004. 2004 3rd International Conference on Computational Electromagnetics and Its Applications, 2004..

[14]  J. Rice.  The approximation of functions , 1964 .

[15]  Ling Jing,et al.  Fitting B-spline curves by least squares support vector machines , 2005, 2005 International Conference on Neural Networks and Brain.

[16]  Andrés Iglesias,et al.  Efficient particle swarm optimization approach for data fitting with free knot B-splines , 2011, Comput. Aided Des..

[17]  Caiming Zhang,et al.  Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation , 2011, Comput. Aided Des..

[18]  Toshinobu Harada,et al.  Automatic knot placement by a genetic algorithm for data fitting with a spline , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[19]  M. Jazaeri,et al.  A hybrid particle swarm optimization-genetic algorithm for optimal location of svc devices in power system planning , 2007, 2007 42nd International Universities Power Engineering Conference.

[20]  Y. Rahmat-Samii,et al.  Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[21]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[22]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[23]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[24]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[25]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[26]  Andrés Iglesias,et al.  Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points , 2012, Inf. Sci..

[27]  Sang C. Park,et al.  Tool path generation for a surface model with defects , 2010, Comput. Ind..

[28]  C. D. Boor,et al.  Least Squares Cubic Spline Approximation I | Fixed Knots , 1968 .

[29]  Pascal Bouvry,et al.  Particle swarm optimization: Hybridization perspectives and experimental illustrations , 2011, Appl. Math. Comput..

[30]  Nicholas M. Patrikalakis,et al.  Shape Interrogation for Computer Aided Design and Manufacturing , 2002, Springer Berlin Heidelberg.

[31]  Debasish Dutta,et al.  The geometry and generation of NC tool paths , 1997 .

[32]  Knut Mørken,et al.  Knot removal for parametric B-spline curves and surfaces , 1987, Comput. Aided Geom. Des..

[33]  Jermynindustriesmanufacturing.  Dual-in-line sockets , 1972 .

[34]  Russell C. Eberhart,et al.  Comparison between Genetic Algorithms and Particle Swarm Optimization , 1998, Evolutionary Programming.

[35]  T. Lyche,et al.  A Data-Reduction Strategy for Splines with Applications to the Approximation of Functions and Data , 1988 .

[36]  Andrés Iglesias,et al.  Helical Curves on Surfaces for Computer-Aided Geometric Design and Manufacturing , 2004, ICCSA.

[37]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[38]  Oscar Castillo,et al.  Evolutionary method combining particle swarm optimization and genetic algorithms using fuzzy logic for decision making , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[39]  Wenping Wang,et al.  Control point adjustment for B-spline curve approximation , 2004, Comput. Aided Des..

[40]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[41]  Andrés Iglesias,et al.  A New Differential Approach for Parametric-Implicit Surface Intersection , 2003, International Conference on Computational Science.

[42]  Muhammad Sarfraz,et al.  Capturing outline of fonts using genetic algorithm and splines , 2001, Proceedings Fifth International Conference on Information Visualisation.

[43]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[44]  Gang Zhao,et al.  Adaptive knot placement in B-spline curve approximation , 2005, Comput. Aided Des..

[45]  Enrique F. Castillo,et al.  Some characterizations of families of surfaces using functional equations , 1997, TOGS.

[46]  Josef Hoschek,et al.  Handbook of Computer Aided Geometric Design , 2002 .

[47]  Germano Lambert-Torres,et al.  Hybrid Evolutionary Algorithm Based on PSO and GA Mutation , 2006, 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06).

[48]  D. Jupp.  Approximation to Data by Splines with Free Knots , 1978 .

[49]  Richard B. Thompson.  Designing a Baseball Cover , 1998 .

[50]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[51]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[52]  Shoichi Hasegawa,et al.  Development and investigation of efficient GA/PSO-HYBRID algorithm applicable to real-world design optimization , 2009, IEEE Comput. Intell. Mag..

[53]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[54]  Chia-Feng Juang,et al.  A hybrid of genetic algorithm and particle swarm optimization for recurrent network design , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[55]  Ahmet Arslan,et al.  Automatic knot adjustment using an artificial immune system for B-spline curve approximation , 2009, Inf. Sci..

[56]  Andrés Iglesias,et al.  Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction , 2012, Inf. Sci..

[57]  Helmut Pottmann,et al.  Industrial geometry: recent advances and applications in CAD , 2005, Comput. Aided Des..

[58]  Erwie Zahara,et al.  A hybrid genetic algorithm and particle swarm optimization for multimodal functions , 2008, Appl. Soft Comput..

[59]  Kathryn A. Ingle,et al.  Reverse Engineering , 1996, Springer US.

[60]  Hyungjun Park,et al.  B-spline curve fitting based on adaptive curve refinement using dominant points , 2007, Comput. Aided Des..

[61]  John G. Griffiths,et al.  A new cutter-path topology for milling machines , 1994, Comput. Aided Des..

[62]  Peter J. Angeline,et al.  Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences , 1998, Evolutionary Programming.

[63]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[64]  Helmut Pottmann,et al.  Fitting B-spline curves to point clouds by curvature-based squared distance minimization , 2006, TOGS.

[65]  M. Crampin,et al.  Linear approximation of curves with bounded curvature and a data reduction algorithm , 1985 .