Parameter Estimation of the Kinetic \(\alpha \)-Pinene Isomerization Model Using the MCSFilter Algorithm
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Abstract
This paper aims to illustrate the application of a derivative-free multistart algorithm with coordinate search filter, designated as the MCSFilter algorithm. The problem used in this study is the parameter estimation problem of the kinetic \(\alpha \)-pinene isomerization model. This is a well known nonlinear optimization problem (NLP) that has been investigated as a case study for performance testing of most derivative based methods proposed in the literature. Since the MCSFilter algorithm features a stochastic component, it was run ten times to solve the NLP problem. The optimization problem was successfully solved in all the runs and the optimal solution demonstrates that the MCSFilter provides a good quality solution.
Keywords
MCSFilter \(\alpha \)-pinene isomerization model Multistart Derivative-free optimizationReferences
- 1.Box, G.E.P., Draper, N.R.: The Bayesian estimation of common parameters from several responses. Biometrika 52(3–4), 355–365 (1965)MathSciNetCrossRefGoogle Scholar
- 2.Box, G.E.P., Hunter, W.G., MacGregor, J.F., Erjavec, J.: Some problems associated with the analysis of multiresponse data. Technometrics 15(1), 33–51 (1973)CrossRefGoogle Scholar
- 3.Ames, W.F.: Canonical forms for non-linear kinetic differential equations. Ind. Eng. Chem. Fundam. 1(3), 214–218 (1962)CrossRefGoogle Scholar
- 4.Tjoa, I.-B., Biegler, L.T.: Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic equation systems. Ind. Eng. Chem. 30, 376–385 (1991)CrossRefGoogle Scholar
- 5.Averick, B.M., Carter, R.G., Moré, J.J., Xue, G.: The minpack-2 test problem collection. Technical report, Mathematics and Computer Science Division, Argonne National Laboratory (1992)Google Scholar
- 6.Dolan, E.D., Moré, J.J., Munson, T.S.: Benchmarking optimization software with cops 3.0. Technical report, Argonne National Laboratory (2004)Google Scholar
- 7.Egea, J.A., Rodriguez-Fernandez, M., Banga, J.R., Martí, R.: Scatter search for chemical and bio-process optimization. J. Global Optim. 37(3), 481–503 (2007)MathSciNetCrossRefGoogle Scholar
- 8.Larrosa, J.A.E.: New Heuristics for Global Optimization of Complex Bioprocesses. Ph.D. thesis, University of Vigo (2008)Google Scholar
- 9.Csendes, T.: Non-linear parameter estimation by global optimization - efficiency and reliability. Acta Cybern. 8(4), 361–370 (1988)zbMATHGoogle Scholar
- 10.Rocha, A.M.A.C., Martins, M.C., Costa, M.F.P., Fernandes, E.M.G.P.: Direct sequential based firefly algorithm for the \(\alpha \)-pinene isomerization problem. In: Gervasi, O., Murgante, B., Misra, S., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O., Stankova, E., Wang, S. (eds.) ICCSA 2016. LNCS, vol. 9786, pp. 386–401. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42085-1_30CrossRefGoogle Scholar
- 11.Fernandes, F.P., Costa, M.F.P., Fernandes, E.M.G.P.: Multilocal programming: a derivative-free filter multistart algorithm. In: Murgante, B., Misra, S., Carlini, M., Torre, C.M., Nguyen, H.-Q., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2013. LNCS, vol. 7971, pp. 333–346. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39637-3_27CrossRefGoogle Scholar
- 12.Amador, A., Fernandes, F.P., Santos, L.O., Romanenko, A.: Application of MCSFilter to estimate stiction control valve parameters. In: International Conference of Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, vol. 1863, p. 270005 (2017)Google Scholar
- 13.Storn, R., Price, K.: Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)MathSciNetCrossRefGoogle Scholar
- 14.Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. Inst. Electr. Electron. Eng. Trans. Evol. Comput. 4(3), 284–294 (2000)Google Scholar
- 15.Jones, D.R.: Direct global optimization algorithm. In: Floudas, C.A., Pardalos, P.M. (eds.) Encyclopedia of Optimization, pp. 431–440. Springer, Boston (2001). https://doi.org/10.1007/0-306-48332-7CrossRefGoogle Scholar
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