Abstract
Gravitational search algorithm (GSA) has shown an effective performance for solving real-world optimization problems. However, it suffers from premature convergence because of quick losing of diversity. To enhance its performance, this paper proposes a novel GSA algorithm, called GSA–PWL (piecewise linear)–SQP (sequential quadratic programming), which employs a diversity enhancing mechanism and an accelerated local search strategy to achieve a trade-off between exploration and exploitation abilities. A comprehensive experimental study is conducted on a set of benchmark functions. Comparison results show that GSA–PWL–SQP obtains a promising performance on the majority of the test problems. Furthermore, the GSA–PWL–SQP is applied to data fitting with B-splines to solve very difficult continuous multimodal and multivariate nonlinear optimization problem. The method of data fitting based on GSA–PWL–SQP yields very accurate results even for curves with singularities and/or cusps and is very efficient in terms of data points error, AIC and BIC criteria.
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References
Yildiz AR (2013) Comparison of evolutionary-based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26:327–333
Yildiz AR (2013) Hybrid Taguchi-differential evolution algorithm for optimization of multi-pass turning operations. Appl Soft Comput 13:1433–1439
Yildiz AR (2008) Hybrid Taguchi-harmony search algorithm for solving engineering optimization problems. Int J Ind EngTheory Appl Pract 15:286–293
Yildiz AR (2009) A new design optimization framework based on immune algorithm and Taguchi method. Comput Ind 60:613–620
Yildiz AR, Solanki KN (2012) Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach. Int J Adv Manuf Technol 59:367–376
Yildiz AR (2013) Optimization of cutting parameters in multi-pass turning using artificial bee colony-based approach. Inf Sci 220:399–407
Ahari H, Khajepour A, Bedi S, Melek WW (2011) A genetic algorithm for optimization of laminated dies manufacturing. Comput Aided Des 43:730–737
Yoshimoto F, Harada T, Yoshimoto Y (2003) Data fitting with a spline using a real-coded genetic algorithm. Comput Aided Des 35:751–760
Pal P, Tigga AM, Kumar A (2005) Feature extraction from large CAD databases using genetic algorithm. Comput Aided Des 37:545–558
Renner G, Ekárt A (2003) Genetic algorithms in computer aided design. Comput Aided Des 35:709–726
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248
Rashedi E, Nezamabadi-pour H, Saryazdi S (2011) Filter modeling using gravitational search algorithm. Eng Appl Artif Intell 24:117–122
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2010) BGSA: binary gravitational search algorithm. Nat Comput 9:727–745
Sarafrazi S, Nezamabadi-pour H, Saryazdi S (2011) Disruption: a new operator in gravitational search algorithm. Scientia Iranica 18:539–548
Li C, Zhou J (2011) Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm. Energy Convers Manag 52:374–381
Shaw B, Mukherjee V, Ghoshal SP (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int J Electr Power Energy Syst 35:21–33
Yin M, Hu Y, Yang F, Li X, Gu W (2011) A novel hybrid K-harmonic means and gravitational search algorithm approach for clustering. Expert Syst Appl 38:9319–9324
Khajehzadeh M, Raihan Taha M, El-Shafie A, Eslami M (2012) A modified gravitational search algorithm for slope stability analysis. Eng Appl Artif Intell 25:1589–1597
Han XH, Chang XM (2012) A chaotic digital secure communication based on a modified gravitational search algorithm filter. Inf Sci 208:14–27
Mirjalili SA, Mohd Hashim SZ, Sardroudi HM (2012) Training feed forward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218:11125–11137
Ghasemi A, Shayeghi H, Alkhatib H (2013) Robust design of multimachine power system stabilizers using fuzzy gravitational search algorithm. Int J Electr Power Energy Syst 51:190–200
Vijaya Kumar J, Vinod Kumar DM, Edukondalu K (2013) Strategic bidding using fuzzy adaptive gravitational search algorithm in a pool based electricity market. Appl Soft Comput 13:2445–2455
Mendel E, Krohling RA, Campos M (2011) Swarm algorithms with chaotic jumps applied to noisy optimization problems. Inf Sci 181:4494–4514
Tripathi PK, Bandyopadhyay S, Pal SK (2007) Multi-objective particle swarm optimization with time variant inertia and acceleration coefficients. Inf Sci 177:5033–5049
Wilson RB (1963) A simplicial algorithm for concave programming. PhD thesis, Harvard University, Cambridge
Fletcher R (1987) Practical methods of optimization. Wiley, New York
Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3–18
García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180:2044–2064
Haupt RL, Haupt SE (2004) Practical genetic algorithms, 2nd edn. Wiley, New York
Van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971
Barnhill RE (1992) Geometric processing for design and manufacturing. SIAM, Philadelphia
Patrikalakis NM, Maekawa T (2002) Shape interrogation for computer aided design and manufacturing. Springer, Heidelberg
Pottmann H, Leopoldseder S, Hofer M, Steiner T, Wang W (2005) Industrial geometry: recent advances and applications in CAD. Comput Aided Des 37:751–766
Varady T, Martin RR, Cox J (1997) Reverse engineering of geometric models—an introduction. Comput Aided Des 29(4):255–268
Hoschek J, Lasser D (1993) Fundamentals of computer aided geometric design. AK Peters, Wellesley
Jupp DLB (1978) Approximation to data by splines with free knots. SIAM J Numer Anal 15:328–343
Molinari N, Durand JF, Sabatier R (2004) Bounded optimal knots for regression splines. Comput Stat Data Anal 45(2):159–178
Sarfraz M, Raza SA (2001) Capturing outline of fonts using genetic algorithms and splines. In: Proceedings of fifth international conference on information visualization IV’2001. IEEE Computer Society Press, New York, pp 738–743
Ulker E, Arslan A (2009) Automatic knot adjustment using an artificial immune system for B-spline curve approximation. Inf Sci 179:1483–1494
Yoshimoto F, Moriyama M, Harada T (1999) Automatic knot placement by a genetic algorithm for data fitting with a spline. In: Proceedings of shape modeling international’99. IEEE Computer Society Press, New York, pp 162–169
Zhao X, Zhang C, Yang B, Li P (2011) Adaptive knot placement using a GMM based continuous optimization algorithm in B-spline curve approximation. Comput Aided Des 43:598–604
Gálvez A, Iglesias A (2011) Efficient particle swarm optimization approach for data fitting with free knot B-splines. Comput Aided Des 43:1683–1692
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723
Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464
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This research has been supported by National Natural Science Foundation program of China (51035007).
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Han, X., Quan, L., Xiong, X. et al. Diversity enhanced and local search accelerated gravitational search algorithm for data fitting with B-splines. Engineering with Computers 31, 215–236 (2015). https://doi.org/10.1007/s00366-013-0343-9
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DOI: https://doi.org/10.1007/s00366-013-0343-9