Abstract
Cooperative multi-objective optimization tool is proposed for solving the order reduction problem for linear time invariant systems. Normally, the adequacy of an order reduction problem solution is estimated using two different criteria, but only one of them identifies the model. In this study, it was suggested to identify the parameters using both of the criteria, and since the criteria are complex and multi-extremum there is a need for a powerful optimization algorithm to be used. The proposed approach is based on the cooperation of heterogeneous algorithms implemented in the islands scheme and it has proved its efficiency in solving various multi-objective optimization problems. It allows us to receive a set of lower order models, which are non-dominated solutions for the given criteria and an estimation of the Pareto set. The results of this study are compared to the results of solving the same problems using various approaches and heuristic optimization tools and it is demonstrated that the set of solutions not only outperforms these approaches by the main criterion, but also provides good solutions with another criterion and a combination of them using the same computational resources.
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References
Ramesh, K., Nirmalkumar, A., Gurusamy, G.: Order reduction of LTIV continuous MIMO system using stability preserving approximation method. Int. J. Comput. Appl. 36, 1–8 (2011)
Desai, S., Prasad, R.: A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh approximation. Appl. Math. Model. 37, 8016–8028 (2013)
Narwal, A., Prasad, B.R.: A novel order reduction approach for LTI Systems using Cuckoo Search optimization and stability equation. IETE J. Res. 62(2), 154–163 (2016)
Chen, T.C., Chang, C.Y., Han, K.W.: Reduction of transfer functions by the stability equation method. J. Franklin Inst. 308(4), 389–404 (1979)
Parmar, G., Prasad, R., Mukherjee, S.: Order reduction of linear dynamic systems using stability equation method and GA. Int. J. comput. Inf. Eng. 1(1), 26–32 (2007)
Ryzhikov, I., Semenkin, E., Akhmedova, Sh.: LTI system order reduction approach based on asymptotical equivalence and the co-operation of biology-related algorithms. In: IOP Conference Series: Materials Science and Engineering, vol. 173, Conference 1
Brester, C., Semenkin, E.: Cooperative multi-objective genetic algorithm with parallel implementation. In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds.) ICSI 2015. LNCS, vol. 9140, pp. 471–478. Springer, Cham (2015). doi:10.1007/978-3-319-20466-6_49
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Wang, R.: Preference-Inspired Co-evolutionary Algorithms. A thesis submitted in partial fulfillment for the degree of the Doctor of Philosophy. p. 231, University of Sheffield (2013)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary Methods for Design Optimisation and Control with Application to Industrial Problems EUROGEN 2001 vol.3242, No. 103, pp. 95–100 (2002)
Whitley, D., Rana, S., Heckendorn, R.B.: Island model genetic algorithms and linearly separable problems. In: Corne, D., Shapiro, J.L. (eds.) AISB EC 1997. LNCS, vol. 1305, pp. 109–125. Springer, Heidelberg (1997). doi:10.1007/BFb0027170
Zhang, Q., Zhou, A., Zhao, S., Suganthan, P. N., Liu, W., Tiwari, S.: Multi-objective optimization test instances for the CEC 2009 special session and competition. University of Essex and Nanyang Technological University, Technical. report. CES-487 (2008)
Brester, C., Kauhanen, J., Tuomainen, T.P., Semenkin, E., Kolehmainen, M.: Comparison of two-criterion evolutionary filtering techniques in cardiovascular predictive modelling. In: Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016), Lisbon, Portugal. vol. 1, pp. 140–145. (2016)
Brester, C., Semenkin, E., Sidorov, M., Kovalev, I., Zelenkov, P. Evolutionary feature selection for emotion recognition in multilingual speech analysis. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2015), Sendai, Japan, pp. 2406–2411. (2015)
Brester, C., Semenkin, E., Sidorov, M., Semenkina, O. Multicriteria neural network design in the speech-based emotion recognition problem. In: Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2015), Colmar, France, vol. 1, pp. 621–628. (2015)
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This research is supported by the Russian Foundation for Basic Research within project No 16-01-00767.
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Ryzhikov, I., Brester, C., Semenkin, E. (2017). A Novel Linear Time Invariant Systems Order Reduction Approach Based on a Cooperative Multi-objective Genetic Algorithm. In: Tan, Y., Takagi, H., Shi, Y., Niu, B. (eds) Advances in Swarm Intelligence. ICSI 2017. Lecture Notes in Computer Science(), vol 10386. Springer, Cham. https://doi.org/10.1007/978-3-319-61833-3_6
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