Abstract
This paper extends a PSO-based nonlinear regression technique to dynamic environments whereby the induced model dynamically adjusts when an environmental change is detected. As such, this work hybridizes a PSO designed for dynamic environments with a least-squares approximation technique to induce structurally optimal nonlinear regression models. The proposed model was evaluated experimentally and compared with the dynamic PSOs, namely multi-swarm, reinitialized, and charged PSOs, to optimize the model structure and the regression parameters in the dynamic environment. The obtained results show that the proposed model was adaptive to the changing environment to yield structurally optimal models which consequently, outperformed the dynamic PSOs for the given datasets.
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References
Gray, R.A., Docherty, P.D., Fisk, L.M., Murray, R.: A modified approach to objective surface generation within the Gauss-Newton parameter identification to ignore outlier data points. Biomed. Signal Process. Control 30, 162–169 (2016)
Basics on Continuous Optimization, November 2019. http://www.brnt.eu/phd/node10.html
Erdoğmuş, P., Ekiz, S.: Nonlinear regression using particle swarm optimization and genetic algorithm. Int. J. Comput. Appl. 153(6), 28–36 (2016)
Potgieter, G., Engelbrecht, A.P.: Genetic algorithm for structurally optimisation of learned polynomial expressions. Appl. Math. Comput. 186, 1441–1466 (2007)
Özel, T., Karpat, Y.: Identification of constitutive material model parameters for high-strain rate metal cutting conditions using evolutionary computational algorithms. Mater. Manuf. Processes 22(5), 659–667 (2007)
Hornik, K.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989)
Atici, U.: Prediction of the strength of mineral admixture concrete using multivariable regression analysis and an artificial neural network. Expert Syst. Appl. 38(8), 9609–9618 (2011)
Lu, Z., Yang, C., Qin, D., Luo, Y., Momayez, M.: Estimating ultrasonic time-of-flight through echo signal envelope and modified Gauss-Newton method. Measurement 94, 355–363 (2016)
Cheng, S., Zhao, C., Wu, J., Shi, Y.: Particle swarm optimization in regression analysis: a case study. In: Tan, Y., Shi, Y., Mo, H. (eds.) ICSI 2013. LNCS, vol. 7928, pp. 55–63. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38703-6_6
Abdullah, S.M., Yassin, A.I.M., Tahir, N.M.: Particle swarm optimization and least squares estimation of NARMAX. ARPN J. Eng. Appl. Sci. 10(22), 10722–10726 (2015)
Blackwell, T.M.: Particle swarm optimization in dynamic environments. Evol. Comput. Dyn. Uncertain Environ. 51, 29–49 (2007)
Draper, N.R., Smith, H.: Applied Regression Analysis, vol. 326. Wiley, Hoboken (1998)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. SSS. Springer, New York (2009). https://doi.org/10.1007/978-0-387-84858-7
Fraleigh, J.B., Beauregard, R.A.: Linear Algebra, 3rd edn. Addison-Wesley Publishing Company, Upper Saddle River (1995)
Stigler, S.M.: Gauss and the invention of least squares. Ann. Stat. 9(3), 465–474 (1981)
Yang, S., Yao, X.: A comparative study on particle swarm optimization in dynamic environments. In: Yang, S., Yao, X. (eds.) Evolutionary Computation for DOPs, pp. 109–136. Springer, Heidelberg (2013)
Blackwell, T., Branke, J.: Multi-swarm optimisation in dynamic environments. Appl. Evol. Comput. 3005, 489–500 (2004)
Blackwell, T.M., Bentley, P.J.: Don’t push me! Collision-avoidance swarms. In: Proceedings of the IEE Congress on Evolutionary Computation, vol. 2, pp. 1691–1696 (2002)
Blackwell, T.M., Bentley, P.J.: Dynamic search with charged swarms. In: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 19–26 (2002)
Blackwell, T.M., Branke, J.: Multiswarms, exclusion, and anti-convergence in dynamic environments. IEEE Trans. Evol. Comput. 10(4), 459–472 (2006)
Richter, H.: Detecting change in dynamic fitness landscapes. In: Proceedings of Congress on Evolutionary Computation, pp. 1613–1620 (2009)
Branke, J.: Evolutionary Optimization in Dynamic Environments. Kluwer, Norwell (2002)
Parrott, D., Li, X.: Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Trans. Evol. Comput. 10(4), 440–458 (2006)
Mathworks: MATLAB. www.mathworks.com
McKnight, P.E., Najab, J.: Issues with performance measures for dynamic multi-objective optimization. In: Proceedings of IEEE Symposium on Computational Intelligence in Dynamic and Uncertain Environments, pp. 17–24 (2013)
Bennett, L., Swartzendruber, L., Brown, H.: Superconductivity magnetization modeling. In: NIST (1994)
Harries, M.: Splice-2 comparative evaluation: electricity pricing. Technical Report UNSW-CSE-TR-9905. Artificial Intelligence Group, School of Computer Science and Engineering, The University of New South Wales, Sydney 2052, Australia (1999)
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Kuranga, C., Pillay, N. (2020). Nonlinear Regression in Dynamic Environments Using Particle Swarm Optimization. In: Martín-Vide, C., Vega-Rodríguez, M.A., Yang, MS. (eds) Theory and Practice of Natural Computing. TPNC 2020. Lecture Notes in Computer Science(), vol 12494. Springer, Cham. https://doi.org/10.1007/978-3-030-63000-3_11
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