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Sensitivity Analysis during the Optimization Process Using Genetic Algorithms

Authors: M. A. Rubio, A. Urquia

Abstract:

Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.

Keywords: Optimization, sensitivity, genetic algorithms, model calibration.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129563

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References:


[1] C. D. Chio, A. Brabazon, M. Ebner, M. Farooq, A. Fink, J. Grahl, G. Greenfield, P. Machado, M. O’Neill, E. Tarantino, and N. Urquhart, Applications of Evolutionary Computation. Springer, 2010.
[2] R. L. Johnston, Applications of Evolutionary Computation in Chemistry. Springer, 2004.
[3] C. Karr and L. M. Freeman, Industrial Applications of Genetic Algorithms. CRC Press, 1998.
[4] T. Back, U. Hammel, and H.-P. Schwefel, “Evolutionary computation: Comments on the history and current state,” IEEE Trans. Evol. Comput., vol. 1, no. 1, pp. 3–17, 1997.
[5] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 1989.
[6] L. Davis, Handbook of Genetic Algorithms. Van Nostrand Reinhold Company, 1991.
[7] A. E. Eiben and J. Smith, Introduction to Evolutionary Computing. Springer, 2010.
[8] M. A. Rubio, A. Urquia, and S. Dormido, “An approach to the calibration of Modelica models,” in Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools, 2007.
[9] K. Edwards, T. F. Edgar, and V. Manousiouthakis, “Kinetic model reduction using genetic algorithms,” Computers chem. Engng., vol. 22, pp. 239–246, 1998.
[10] M. L. Raymer, W. F. Punch, E. D. Goodman, L. A. Kuhn, and A. K. Jain, “Dimensionality reduction using genetic algorithms,” IEEE Transactions on Evolutionary Computation, vol. 4, no. 2, pp. 164 – 171, 2000.
[11] K. Chan, A. Saltelli, and S. Tarantola, “Sensitivity analysis of model output: variance-based methods make the difference,” in Proceedings of the Winter Simulation Conference, 1997.
[12] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, Global Sensitivity Analysis: The Primer. Wiley, 2008.
[13] A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis. Wiley, 2008.
[14] W. Chen, X. Lu, C. Yao, G. Zhu, and Z. Xu, “An efficient approach based on bi-sensitivity analysis and genetic algorithm for calibration of activated sludge models,” Chemical Engineering Journal, vol. 259, pp. 845–853, 2015.
[15] M. Vazquez-Cruz, R. Guzman-Cruz, O. C.-P. I.L. Lopez-Cruz, I. Torres-Pacheco, and R. Guevara-Gonzalez, “Global sensitivity analysis by means of efast and sobol methods and calibration of reduced state-variable tomgro model using genetic algorithms,” Computers and Electronics in Agriculture, vol. 100, pp. 1–12, 2014.
[16] C. Andres, C. F. Valerio, and P. Franz, “Validation of an advanced lithium-ion battery model for electric and hybrid drive trains,” in EET-2008 European Ele-Drive Conference. International Advanced Mobility Forum, 2008.
[17] N. Nishida, Y. Takahashi, and S. Wakao, “Robust design optimization approach by combination of sensitivity analysis and sigma level estimation,” IEEE Transactions on Magnetics, vol. 44, no. 6, pp. 998–1001, 2008.
[18] D. G. Vieira, D. A. G. Vieira, W. M. Caminhas, and J. A. Vasconcelos, “A hybrid approach combining genetic algorithm and sensitivity information extracted from a parallel layer perceptron,” IEEE Transactions on Magnetics, vol. 41, no. 5, pp. 1740 – 1743, 2005.
[19] W. T. Eadie, Statistical Methods in Experimental Physics. Elsevier, 1983.
[20] R. L. Plackett, “Karl Pearson and the chi-squared test,” International Statistical Review, vol. 51, no. 1, pp. 59–72, 1983.
[21] H. Shimazaki and S. Shinomoto, “A method for selecting the bin size of a time histogram,” Neural Computation, vol. 19, no. 6, pp. 1503–1527, 2007.
[22] K. A. D. Jong, “An analysis of the behavior of a class of genetic adaptive systems,” Ph.D. dissertation, University of Michigan Ann Arbor, MI, USA, 1975.
[23] H. Muhlenbein, M. Schomisch, and J. Born, “The parallel genetic algorithm as function optimizer,” Parallel Computing, vol. 17, no. 6-7, pp. 619 – 632, 1991.
[24] T. Back, D. Fogel, and Z. Michalewicz, Handbook of Evolutionary Computation. Bristol and Oxford University Press, 1997.