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Yıl 2016, Cilt: 29 Sayı: 1, 187 - 199, 21.03.2016

Öz

Kaynakça

  • D.A. Ratkowsy, Nonlinear regression modeling: a unified practical approach, M. Dekker, Newyork, 1983.
  • J.C. Nash, M. Walker-Smith, Nonlinear Parameter Estimation, Marcel Dekker, Inc., New York, Basel (1987).
  • G.A.F. Seber, C.J. Wild, Nonlinear regression, Wiley, 2005.
  • L. Li, L. Wang, L. Liu, An effective hybrid PSOSA strategy for optimization and its application to parameter estimation, Applied Mathematics and Computation, 179 (2006) 135-146.
  • J. Kennedy, R. Eberhart (1995). Particle swarm optimization, Proceedings of IEEE International Conference on Neural Networks, Vol. 4, pp. 1942–1948.
  • R. Eberhart, J. Kennedy (1995). A New Optimizer Using Particle Swarm Theory, Proceedings of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan. IEEE Service Center Piscataway NJ,1995:39-43
  • I. Krivy, J. Tvrdik, R. Krpec, Stochastic algorithms in nonlinear regression, Computational Statistics and Data Analysis, 33 (2000) 277-290.
  • M. Kaptanoğlu, I.O. Koc, S. Erdogmus, Genetic algorithms in parameter estimation for nonlinear regression models: a experimental approach, Journal of Statistical Computation, 77(10) 2007, 851-867.
  • J. Tvrdik, I. Krivy, L. Misık, Adaptive population-based search: application to estimation of nonlinear regression parameters, Computational Statistics and Data Analysis, 52 (2007) 713-724.
  • B. Aşıkgil, A. Erar, Polynomial tapered two-stage least square method in nonlinear regression, Applied Mathematics and Computation, 219 (2013) 9743-9754.
  • S. Das, A. Abraham, A. Konar, Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives, Studies in Computational Intelligence, 116 (2008) 1–38.
  • Y. Fukuyama, Modern Heuristic Optimization Techniques, Edited by K.Y.Lee and M.A. El-Sharkawi, Institute of Electrical and Electronics Engineers, 71-83, 2008.
  • R. Eberhart, Y. Shi (2001). Particle swarm optimization: developments, applications and resources, Proceedings of IEEE International Congress on Evolutionary Computation, 1, 81–86.
  • Y. Shi and R. Eberhart, A modified particle swarm optimizer, Proceedings of IEEE International Conference on Evolutionary Computation, Anchorage, May 1998, 69–73.
  • K.Y. Lee, M.A. El-Sharkawi, Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems, IEEE press series on power engineering. Hoboken: Wiley Interscience; New Jersey, 2008.
  • W.N. Lee, J.B. Park (2011) Educational Simulator for Particle Swarm Optimization and Economic Dispatch Applications, MATLAB - A Ubiquitous Tool for the Practical Engineer, Prof. Clara Ionescu (Ed.), ISBN: 978-953-307-907-3, InTech, DOI: 10.5772/19873.
  • R.C. Eberhart, Y. Shi (2000), Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization, Proceedings of IEEE International Congress on Evolutionary Computation, 1, 84–88.
  • C. Lanczos (1956), Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
  • R.I. Jennrich, P.F. Sampson (1968), Application of stepwise regression to non-linear estimation, Technometrics, 10(1) 63-72.
  • R.R. Meyer, P.M. Roth (1972), Modified damped least squares: an algorithm for non-linear estimation. J. Inst. Math. Appl, 9, 218-233.
  • G.P. Box, W. G. Hunter, J. S. Hunter (1978), Statistics for Experimenters. New York, NY: Wiley, 483-487.
  • J.S. Kowalik, M. R. Osborne (1978), Methods for Unconstrained Optimization Problems. New York, NY: Elsevier North-Holland.
  • C. Daniel, F. S. Wood (1980), Fitting Equations to Data, Second Edition. New York, NY: John Wiley and Sons, pp. 428-431.
  • W. Nelson (1981), Analysis of Performance-Degradation Data. IEEE Transactions on Reliability, 2 (2), 149-155.
  • Kahaner, D., C. Moler, and S. Nash, (1989). Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, 441-445.
  • J. Kennedy , "The Particle Swarm: Social Adaptation of Knowledge, Proc" , IEEE International Conference on Evolutionary Computation , pp.303 -308 , 1997
  • Y. Shi and R. C. Eberhart, , "Empirical study of particle swarm optimization" , Proc. Congr. Evolutionary Computation , pp.1945 -1949 , 1999
  • Y. Shi and R. Eberhart , "Fuzzy adaptive particle swarm optimization" , Proc. IEEE Congr. Evol. Comput. , vol. 1 , pp.101 -106 , 2001
  • X. Hu , Y. Shi and R. Eberhart , "Recent advances in particle swarm" , Proc. IEEE Congr. Evol. Comput. , vol. 1 , pp.90 -97 , 2004
  • Y. del Valle, G. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez and R. Harley , "Particle swarm optimization: Basic concepts, variants and applications in power systems" , IEEE Trans. Evol. Comput. , vol. 12 , no. 2 , pp.171 -195 , 2008
  • C. A. C. Coello, G. T. Pulido, and M. S. Lechuga MS, , "Handling multiple objectives with particle swarm optimization" , IEEE Trans. Evol. Comput. , vol. 8 , no. 3 , pp.256 -279 , 2004
  • Wang X, Yang J et al (2007) Feature selection based on rough sets and particle swarm optimization. Pattern Recogn Lett 28:459–471
  • Jun Sun, Xiaojun Wu, Vasile Palade, Wei Fang, Yuhui Shi, Random drift particle swarm optimization algorithm: convergence analysis and parameter selection, Machine Learning, 101, 1-3, 345-376 (2015)

ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION

Yıl 2016, Cilt: 29 Sayı: 1, 187 - 199, 21.03.2016

Öz

Nonlinear regression models are widely used for modeling of stochastic phenomena and the estimating parameters problem plays a central role in the inference in nonlinear regression models. In this paper, this problem has been briefly discussed and an effective approach based on the Particle Swarm Optimization (PSO) algorithm is proposed in order to enhance the estimation accuracy. The PSO algorithm is tested on the well-known 28 nonlinear regression tasks of various level of difficulty. The results show that PSO approach which exhibits a rapid convergence to the minimum value of the sum of squared error function in less iterations, provides accurate estimates and is satisfactory for the parameter estimation of the nonlinear regression models.

Kaynakça

  • D.A. Ratkowsy, Nonlinear regression modeling: a unified practical approach, M. Dekker, Newyork, 1983.
  • J.C. Nash, M. Walker-Smith, Nonlinear Parameter Estimation, Marcel Dekker, Inc., New York, Basel (1987).
  • G.A.F. Seber, C.J. Wild, Nonlinear regression, Wiley, 2005.
  • L. Li, L. Wang, L. Liu, An effective hybrid PSOSA strategy for optimization and its application to parameter estimation, Applied Mathematics and Computation, 179 (2006) 135-146.
  • J. Kennedy, R. Eberhart (1995). Particle swarm optimization, Proceedings of IEEE International Conference on Neural Networks, Vol. 4, pp. 1942–1948.
  • R. Eberhart, J. Kennedy (1995). A New Optimizer Using Particle Swarm Theory, Proceedings of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan. IEEE Service Center Piscataway NJ,1995:39-43
  • I. Krivy, J. Tvrdik, R. Krpec, Stochastic algorithms in nonlinear regression, Computational Statistics and Data Analysis, 33 (2000) 277-290.
  • M. Kaptanoğlu, I.O. Koc, S. Erdogmus, Genetic algorithms in parameter estimation for nonlinear regression models: a experimental approach, Journal of Statistical Computation, 77(10) 2007, 851-867.
  • J. Tvrdik, I. Krivy, L. Misık, Adaptive population-based search: application to estimation of nonlinear regression parameters, Computational Statistics and Data Analysis, 52 (2007) 713-724.
  • B. Aşıkgil, A. Erar, Polynomial tapered two-stage least square method in nonlinear regression, Applied Mathematics and Computation, 219 (2013) 9743-9754.
  • S. Das, A. Abraham, A. Konar, Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives, Studies in Computational Intelligence, 116 (2008) 1–38.
  • Y. Fukuyama, Modern Heuristic Optimization Techniques, Edited by K.Y.Lee and M.A. El-Sharkawi, Institute of Electrical and Electronics Engineers, 71-83, 2008.
  • R. Eberhart, Y. Shi (2001). Particle swarm optimization: developments, applications and resources, Proceedings of IEEE International Congress on Evolutionary Computation, 1, 81–86.
  • Y. Shi and R. Eberhart, A modified particle swarm optimizer, Proceedings of IEEE International Conference on Evolutionary Computation, Anchorage, May 1998, 69–73.
  • K.Y. Lee, M.A. El-Sharkawi, Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems, IEEE press series on power engineering. Hoboken: Wiley Interscience; New Jersey, 2008.
  • W.N. Lee, J.B. Park (2011) Educational Simulator for Particle Swarm Optimization and Economic Dispatch Applications, MATLAB - A Ubiquitous Tool for the Practical Engineer, Prof. Clara Ionescu (Ed.), ISBN: 978-953-307-907-3, InTech, DOI: 10.5772/19873.
  • R.C. Eberhart, Y. Shi (2000), Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization, Proceedings of IEEE International Congress on Evolutionary Computation, 1, 84–88.
  • C. Lanczos (1956), Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
  • R.I. Jennrich, P.F. Sampson (1968), Application of stepwise regression to non-linear estimation, Technometrics, 10(1) 63-72.
  • R.R. Meyer, P.M. Roth (1972), Modified damped least squares: an algorithm for non-linear estimation. J. Inst. Math. Appl, 9, 218-233.
  • G.P. Box, W. G. Hunter, J. S. Hunter (1978), Statistics for Experimenters. New York, NY: Wiley, 483-487.
  • J.S. Kowalik, M. R. Osborne (1978), Methods for Unconstrained Optimization Problems. New York, NY: Elsevier North-Holland.
  • C. Daniel, F. S. Wood (1980), Fitting Equations to Data, Second Edition. New York, NY: John Wiley and Sons, pp. 428-431.
  • W. Nelson (1981), Analysis of Performance-Degradation Data. IEEE Transactions on Reliability, 2 (2), 149-155.
  • Kahaner, D., C. Moler, and S. Nash, (1989). Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, 441-445.
  • J. Kennedy , "The Particle Swarm: Social Adaptation of Knowledge, Proc" , IEEE International Conference on Evolutionary Computation , pp.303 -308 , 1997
  • Y. Shi and R. C. Eberhart, , "Empirical study of particle swarm optimization" , Proc. Congr. Evolutionary Computation , pp.1945 -1949 , 1999
  • Y. Shi and R. Eberhart , "Fuzzy adaptive particle swarm optimization" , Proc. IEEE Congr. Evol. Comput. , vol. 1 , pp.101 -106 , 2001
  • X. Hu , Y. Shi and R. Eberhart , "Recent advances in particle swarm" , Proc. IEEE Congr. Evol. Comput. , vol. 1 , pp.90 -97 , 2004
  • Y. del Valle, G. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez and R. Harley , "Particle swarm optimization: Basic concepts, variants and applications in power systems" , IEEE Trans. Evol. Comput. , vol. 12 , no. 2 , pp.171 -195 , 2008
  • C. A. C. Coello, G. T. Pulido, and M. S. Lechuga MS, , "Handling multiple objectives with particle swarm optimization" , IEEE Trans. Evol. Comput. , vol. 8 , no. 3 , pp.256 -279 , 2004
  • Wang X, Yang J et al (2007) Feature selection based on rough sets and particle swarm optimization. Pattern Recogn Lett 28:459–471
  • Jun Sun, Xiaojun Wu, Vasile Palade, Wei Fang, Yuhui Shi, Random drift particle swarm optimization algorithm: convergence analysis and parameter selection, Machine Learning, 101, 1-3, 345-376 (2015)
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Statistics
Yazarlar

Volkan Soner Özsoy

H.Hasan Örkçü

Yayımlanma Tarihi 21 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 1

Kaynak Göster

APA Özsoy, V. S., & Örkçü, H. (2016). ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION. Gazi University Journal of Science, 29(1), 187-199.
AMA Özsoy VS, Örkçü H. ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION. Gazi University Journal of Science. Mart 2016;29(1):187-199.
Chicago Özsoy, Volkan Soner, ve H.Hasan Örkçü. “ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION”. Gazi University Journal of Science 29, sy. 1 (Mart 2016): 187-99.
EndNote Özsoy VS, Örkçü H (01 Mart 2016) ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION. Gazi University Journal of Science 29 1 187–199.
IEEE V. S. Özsoy ve H. Örkçü, “ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION”, Gazi University Journal of Science, c. 29, sy. 1, ss. 187–199, 2016.
ISNAD Özsoy, Volkan Soner - Örkçü, H.Hasan. “ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION”. Gazi University Journal of Science 29/1 (Mart 2016), 187-199.
JAMA Özsoy VS, Örkçü H. ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION. Gazi University Journal of Science. 2016;29:187–199.
MLA Özsoy, Volkan Soner ve H.Hasan Örkçü. “ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION”. Gazi University Journal of Science, c. 29, sy. 1, 2016, ss. 187-99.
Vancouver Özsoy VS, Örkçü H. ESTIMATING THE PARAMETERS OF NONLINEAR REGRESSION MODELS THROUGH PARTICLE SWARM OPTIMIZATION. Gazi University Journal of Science. 2016;29(1):187-99.