B-spline curve fitting with invasive weed optimization. (English) Zbl 1480.65039
Summary: B-spline curves and surfaces are generally used in computer aided design (CAD), data visualization, virtual reality, surface modeling and many other fields. Especially, data fitting with B-splines is a challenging problem in reverse engineering. In addition to this, B-splines are the most preferred approximating curve because they are very flexible and have powerful mathematical properties and, can represent a large variety of shapes efficiently [A. Gálvez and A. Iglesias, “Efficient particle swarm optimization approach for data fitting with free knot \(B\)-splines”, Comput.-Aided Des. 43, No. 12, 1683–1692 (2011; doi:10.1016/j.cad.2011.07.010)]. The selection of the knots in B-spline approximation has an important and considerable effect on the behavior of the final approximation. Recently, in literature, there has been a considerable attention paid to employing algorithms inspired by natural processes or events to solve optimization problems such as genetic algorithms, simulated annealing, ant colony optimization and particle swarm optimization. Invasive weed optimization (IWO) is a novel optimization method inspired from ecological events and is a phenomenon used in agriculture. In this paper, optimal knots are selected for B-spline curve fitting through invasive weed optimization method. Test functions which are selected from the literature are used to measure performance. Results are compared with other approaches used in B-spline curve fitting such as Lasso, particle swarm optimization, the improved clustering algorithm, genetic algorithms and artificial immune system. The experimental results illustrate that results from IWO are generally better than results from other methods.
MSC:
| 65D10 | Numerical smoothing, curve fitting |
| 65D07 | Numerical computation using splines |
| 68U07 | Computer science aspects of computer-aided design |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
invasive weed optimization; weed colony; B-spline curves; knot selection; curve fitting; reverse engineeringReferences:
| [1] | Gálvez, A.; Iglesias, A., Efficient particle swarm optimization approach for data fitting with free knot-splines, Comput.-Aided Des., 43, 12, 1683-1692 (2011) |
| [2] | Gálvez, A.; Iglesias, A.; Puig-Pey, J., Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction, Inf. Sci., 182, 1, 56-76 (2012) |
| [3] | Galvez, A.; Iglesias, A., Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points, Inf. Sci., 192, 174-192 (2012) |
| [4] | Ulker, E.; Arslan, A., Automatic knot adjustment using an artificial immune system for B-spline curve approximation, Inf. Sci., 179, 10, 1483-1494 (2009) |
| [5] | Ulker, E.; Arslan, A., The calculation of parametric NURBS surface interval values using neural networks, (Proceedings of the sixth international conference on computational science (ICCS), 3992 (2006)), 247-254 · Zbl 1155.65315 |
| [6] | Pinel, L.; Tiller, W., The Nurbs Book (1997), Springer · Zbl 0868.68106 |
| [7] | Alexa, M.; Behr, J.; Cohen-Or, D.; Fleishman, S.; Levin, D.; Silva, C. T., Computing and rendering point set surfaces, IEEE Trans. Vis. Comput. Graph., 9, 1, 3-15 (2003) |
| [8] | Lancaster, P.; Salkauskas, K., Surfaces generated by moving least-squares methods, Math. Comput., 37, 155, 141-158 (1981) · Zbl 0469.41005 |
| [9] | Levin, D., The approximation power of moving least-squares, Math. Comput., 67, 224, 1517-1531 (1998) · Zbl 0911.41016 |
| [10] | Huang, Y. B.; Qian, X. P.; Chen, S. L., Multi-sensor calibration through iterative registration and fusion, Comput.-Aided Des., 41, 4, 240-255 (2009) |
| [11] | De Boor, C., A Practical Guide to Splines (2001), Springer Verlag · Zbl 0987.65015 |
| [12] | Yuan, Y.; Chen, N.; Zhou, S., Adaptive B-spline knot selection using multi-resolution basis set, IIE (Institute of Industrial Engineers) Trans., 45, 12, 1263-1277 (2013) |
| [13] | Tirandaz, H.; Nasrabadi, A.; Haddadnia, J., Curve matching and character recognition by using B-spline curves, IACSIT Int. J. Eng. Technol., 3, 2, 183-186 (2011) |
| [14] | Valenzuela, O.; Pasadas, M., Using simulated annealing for knot placement for cubic spline approximation, (Proceedings of the 2010 International Conference on Mathematical Models for Engineering Science (2010)) |
| [15] | Galvez, A.; Iglesias, A., Efficient particle swarm optimization approach for data fitting with free knot B-splines, Comput.-Aided Des., 43, 12, 1683-1692 (2011) |
| [16] | Valenzuela, O.; Pasadas, M.; Rojas, I.; Guillen, A.; Pomares, H., Automatic knot adjustment for B-spline smoothing approximation using improved clustering algorithm, (Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ - IEEE) (2013)) |
| [17] | Gálvez, A.; Iglesias, A.; Avila, A.; Otero, C.; Arias, R.; Manchado, C., Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting, Appl. Soft Comput., 26, 90-106 (2015) |
| [18] | Mehrabian, A. R.; Lucas, C., A novel numerical optimization algorithm inspired from weed colonization, Ecol. Inf., 1, 4, 355-366 (2006) |
| [19] | Roy, S.; Islam, S. M.; Das, S.; Ghosh, S.; Vasilakos, A. V., A simulated weed colony system with subregional differential evolution for multimodal optimization, Eng. Optim., 45, 4, 459-481 (2013) |
| [20] | Chen, H.; Zhou, Y. Q.; He, S. C.; Ouyang, X. X.; Guo, P. G., Invasive weed optimization algorithm for solving permutation flow-shop scheduling problem, J. Comput. Theor. Nanosci., 10, 3, 708-713 (2013) |
| [21] | Pourjafari, E.; Mojallali, H., Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering, Swarm Evol. Comput., 4, 33-43 (2012) |
| [22] | Maghsoudlou, H.; Afshar-Nadjafi, B.; Niaki, S. T.A., A multi-objective invasive weeds optimization algorithm for solving multi-skill multi-mode resource constrained project scheduling problem, Comput. Chem. Eng., 88, 157-169 (2016) |
| [23] | Nikoofard, A. H.; Hajimirsadeghi, H.; Rahimi-Kian, A.; Lucas, C., Multiobjective invasive weed optimization: application to analysis of Pareto improvement models in electricity markets, Appl. Soft Comput., 12, 1, 100-112 (2012) |
| [24] | Rezaei Pouya, A.; Solimanpur, M.; Jahangoshai Rezaee, M., Solving multi-objective portfolio optimization problem using invasive weed optimization, Swarm Evol. Comput., 28, 42-57 (2016) |
| [25] | Sudha Rani, D.; Subrahmanyam, N.; Sydulu, M., Multi-objective invasive weed optimization - an application to optimal network reconfiguration in radial distribution systems, Int. J. Electr. Power Energy Syst., 73, 932-942 (2015) |
| [26] | Zhou, Y.; Chen, H.; Zhou, G., Invasive weed optimization algorithm for optimization no-idle flow shop scheduling problem, Neurocomputing, 137, 285-292 (2014) |
| [27] | Ojha, A. K.; Naidu, Y. R., A hybrid cat swarm optimization with invasive weed optimization, (Proceedings of the 2015 International Conference on Electrical, Electronics, Signals, Communication and Optimization (EESCO) (2015)) |
| [28] | Zhao, Y. W.; Leng, L. L.; Qian, Z. Y.; Wang, W. L., A discrete hybrid invasive weed optimization algorithm for the capacitated vehicle routing problem, Proc. Comput. Sci., 91, 978-987 (2016) |
| [29] | Kasdirin, H. A.; Yahya, N. M.; Aras, M. S.M.; Tokhi, M. O., Hybridizing invasive weed optimization with firefly algorithm for unconstrained and constrained optimization problems, J. Theor. Appl. Inf. Technol., 95, 4, 912-927 (2017) |
| [30] | Chen, H.; Zhou, Y. Q.; He, S. C.; Ouyang, X. X.; Guo, P. G., Invasive weed optimization algorithm for solving permutation flow-shop scheduling problem, J. Comput. Theor. Nanosci., 10, 3, 708-713 (2013) |
| [31] | Ulker, E., Surface Modeling Using Artificial Intelligence Techniques, 142 (2007), Selçuk University - Electronic Electrical Engineering Department: Selçuk University - Electronic Electrical Engineering Department Kenya, Turkish, Ph.D. thesis |
| [32] | Siyal, A. A.; Azizli, K. A.; Man, Z.; Ullah, H., Effects of parameters on the setting time of fly ash based geopolymers using Taguchi method, Proc. Eng., 148, 302-307 (2016) |
| [33] | Bilga, P. S.; Singh, S.; Kumar, R., Optimization of energy consumption response parameters for turning operation using Taguchi method, J. Clean. Prod., 137, 1406-1417 (2016) |
| [34] | Das, A.; Majumder, A.; Das, P. K., Detection of apposite PSO parameters using Taguchi based grey relational analysis: optimization and implementation aspects on manufacturing related problem, Proc. Mater. Sci., 6, 597-604 (2014) |
| [35] | Liu, X. Y.; Zhao, S. P.; Qin, Y.; Zhao, J.; Wan-Nawang, W. A., A parametric study on the bending accuracy in micro W-bending using Taguchi method, Measurement, 100, 233-242 (2017) |
| [36] | Dhiman, N. M.; Shukla, S. P.; Kisku, G. C., Statistical optimization of process parameters for removal of dyes from wastewater on chitosan cenospheres nanocomposite using response surface methodology, J. Clean. Prod., 149, 597-606 (2017) |
| [37] | Kennedy, J.; Eberhart, R., Particle swarm optimization, (Proceedings of the 1995 IEEE International Conference on Neural Networks Proceedings, 1-6 (1995)), 1942-1948 |
| [38] | Gálvez, A.; Iglesias, A.; Avila, A.; Otero, C.; Arias, R.; Manchado, C., Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting, Appl. Soft Comput., 26, 90-106 (2015) |
| [39] | De Boor, C. and J.R. Rice, Least squares cubic spline approximation II - variable knots. Computer Science Technical Report, 1968.; De Boor, C. and J.R. Rice, Least squares cubic spline approximation II - variable knots. Computer Science Technical Report, 1968. |
| [40] | Jupp, D. L.B., Approximation to data by splines with free knots, SIAM J. Numer. Anal., 15, 2, 328-343 (1978) · Zbl 0403.65004 |
| [41] | Schwetlick, H.; Schutze, T., Least-squares approximation by splines with free knots, Bit, 35, 3, 361-384 (1995) · Zbl 0847.65004 |
| [42] | Miyata, S.; Shen, X. T., Adaptive free-knot splines, J. Comput. Graph. Stat., 12, 1, 197-213 (2003) |
| [43] | Yoshimoto, F.; Harada, T.; Yoshimoto, Y., Data fitting with a spline using a real-coded genetic algorithm, Comput.-Aided Des., 35, 8, 751-760 (2003) |
| [44] | Li, W. S.; Xu, S. H.; Zhao, G.; Goh, L. P., Adaptive knot placement in B-spline curve approximation, Comput.-Aided Des., 37, 8, 791-797 (2005) · Zbl 1206.65033 |
| [45] | Yoshimoto, F.; Moriyama, M.; Harada, T., Automatic knot placement by a genetic algorithm for data fitting with a spline, (Proceedings of the 1999 International Conference on Shape Modeling and Applications, Proceedings (1999)), 162-169 |
| [46] | Sarfraz, M.; Raza, S. A., Capturing outline of fonts using genetic algorithm and splines, (Proceedings of the 2001 International Conference on Information Visualisation (2001)), 738-743 |
| [47] | Zhao, X. Y.; Zhang, C. M.; Yang, B.; Li, P. P., Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation, Comput.-Aided Des., 43, 6, 598-604 (2011) |
| [48] | Ulker, E., B-spline curve approximation using Pareto envelope-based selection algorithm-PESA, Int. J. Comput. Eng., 2, 1, 60-63 (2013) |
| [49] | Valenzuela, O.; Delgado-Marquez, B.; Pasadas, M., Evolutionary computation for optimal knots allocation in smoothing splines, Appl. Math. Model., 37, 8, 5851-5863 (2013) |
| [50] | Galvez, A.; Iglesias, A., Firefly algorithm for explicit B-spline curve fitting to data points, Math. Probl. Eng., 2013 (2013), . Article ID 528215, 12 pages · Zbl 1296.65020 |
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