Abstract
Multi-objective genetic Takagi-Sugeno (TS) fuzzy systems use multiobjective evolutionary algorithms to generate a set of fuzzy rule-based systems of the TS type with different trade-offs between, generally, complexity/interpretability and accuracy. The application of these algorithms requires a large number of TS system generations and evaluations.When we deal with high dimensional data sets, these tasks can be very time-consuming, thus making an adequate exploration of the search space very problematic. In this chapter, we propose two techniques to speed up generation and evaluation of TS systems. The first technique aims to speed up the identification of the consequent parameters of the TS rules, one of the most timeconsuming phases in TS generation. The application of this technique produces as a side-effect a decoupling of the rules in the TS system. Thus, modifications in a rule do not affect the other rules. Exploiting this property, the second technique proposes to store specific values used in the parents, so as to reuse them in the offspring and to avoid wasting time. We show the advantages of the proposed method in terms of computing time saving and improved search space exploration through two examples of multi-objective genetic learning of compact and accurate TS-type fuzzy systems for a high dimensional data set in the regression and time series forecasting domains.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angelov, P.P., Filev, D.P.: An approach to online identification of Takagi-Sugeno fuzzy models. IEEE Trans. on Systems, Man and Cybernetics: part B Cyb. 34(1), 484–498 (2004)
Babuska, R.: Fuzzy modeling for control. Kluwer Academic Publishers, Boston (1998)
Botta, A., Lazzerini, B., Marcelloni, F.: Context adaptation of Mamdani fuzzy rule-based systems. International Journal of Intelligent Systems 23(4), 397–418 (2008)
Botta, A., Lazzerini, B., Marcelloni, F., Stefanescu, D.C.: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index. Soft Computing 13(5), 437–449 (2009)
Branke, J., Schmeck, H., Deb, K.: Parallelizing multi-objective evolutionary algorithms: Cone separation. In: Proc. of the IEEE Congress on Evolutionary Computation 2004 - CEC 2004, Portland, Oregon, USA, June 19-23, pp. 1952–1957 (2004)
Bui, L.T., Abbass, H.A., Essam, D.: Fitness inheritance for noisy evolutionary multi-objective optimization. In: Proc. of the 2005 Conference on Genetic and Evolutionary Computation, Washington, D.C., USA, June 25-29, pp. 779–785 (2005)
Chen, C.-H., Hong, T.-P., Tseng, V.S., Chen, L.-C.: A multi-objective genetic-fuzzy data mining algorithm. In: Proc. of the IEEE International Conference on Granular Computing, Hangzhou, China, August 26-28, pp. 115–120 (2008)
Cococcioni, M., Corsini, G., Lazzerini, B., Marcelloni, F.: Approaching the ocean color problem using fuzzy rules. IEEE T. on Syst., Man & Cyb. - part B: Cyb. 34(3), 1360–1373 (2004)
Cococcioni, M., Corsini, G., Lazzerini, B., Marcelloni, F.: Solving the ocean color inverse problem by using evolutionary multi-objective optimization of neuro-fuzzy systems. International Journal of Knowledge-Based and Intelligent Engineering Systems 12(5-6), 339–355 (2008)
Cococcioni, M., Ducange, P., Lazzerini, B., Marcelloni, F.: A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems. Soft Computing 11(11), 1013–1031 (2007)
Cococcioni, M., Lazzerini, B., Marcelloni, F.: Fast multiobjective genetic rule learning using an efficient method for Takagi-Sugeno fuzzy systems identification. In: Proc. of the 8th Int. Conference on Hybrid Intelligent Systems (HIS 2008), Barcelona, Spain, pp. 272–277 (2008)
Cococcioni, M.: The Evolutionary Multiobjective Optimization of Fuzzy Rule-Based Systems Bibliography Page (2009), http://www2.ing.unipi.it/~g000502/emofrbss.html
Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9, 251–280 (1990)
Ducheyne, E.I., De Baets, B., De Wulf, R.R.: Fitness inheritance in multiple objective evolutionary algorithms: A test bench and real-world evaluation. Appl. Soft Comp. 8, 337–349 (2008)
Getreuer, P.: Writing fast Matlab code (2009), http://www.mathworks.com/matlabcentral/fileexchange/5685
Herrera, F.: Genetic fuzzy systems: Taxonomy, current research trends and prospects. Evolutionary Intelligence 1, 27–46 (2008)
Huang, X., Pan, V.Y.: Fast rectangular matrix multiplication and applications. Journal of Complexity 14, 257–299 (1998)
Ishibuchi, H.: Multiobjective genetic fuzzy systems: review and future research directions. In: Proc. of Fuzz-IEEE 2007, London, UK, July 23-26, pp. 1–6 (2007)
Ishibuchi, H., Murata, T., Turksen, I.B.: Selecting linguistic classification rules by two-objective genetic algorithms. In: Proc. of the 1995 IEEE International Conference on System, Man and Cybernetics, Vancouver, BC, Canada, vol. 2, pp. 1410–1415 (1995)
Ishibuchi, H., Murata, T., Turksen, I.B.: Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets and Systems 89(2), 135–150 (1997)
Ishibuchi, H., Nakashima, T., Murata, T.: Three-objective genetics-based machine learning for linguistic rule extraction. Information Sciences 136(1-4), 109–133 (2001)
Ishibuchi, H., Nojima, Y.: Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. Int. J. of Appr. Reas. 4(1), 4–31 (2007)
Ishibuchi, H., Yamamoto, T.: Interpretability issues in fuzzy genetics-based machine learning for linguistic modelling. In: Lawry, J., Shanahan, J.G., Ralescu, A.L. (eds.) Modelling with Words. LNCS, vol. 2873, pp. 209–228. Springer, Heidelberg (2003)
Jang, J.-S.R.: ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. on Systems, Man and Cybernetics 23(3), 665–685 (1993)
Jin, Y.: Fuzzy modeling of high-dimensional systems: Complexity reduction and interpretability improvement. IEEE Trans. on Fuzzy Systems 8(2), 212–223 (2000)
Jin, Y.: A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing 9, 3–12 (2005)
Knowles, J.D.: ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. on Evol. Comp. 10(1), 50–66 (2006)
Knowles, J.D., Corne, D.W.: Approximating the non dominated front using the Pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)
Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1977)
Nauck, D.D.: GNU Fuzzy. In: Proc. of FUZZ-IEEE 2007, London, UK, pp. 1–6 (2007)
Schraudolph, N.N.: A fast, compact approximation of the exponential function. Neural Computation 11, 853–862 (1999)
Soukkou, A., Khellaf, A., Leulmi, S.: Multiobjective optimisation of robust Takagi-Sugeno fuzzy neural controller with hybrid learning algorithm. Int. Journal of Modelling, Identification and Control 2(4), 332–346 (2007)
Streichert, F., Ulmer, H., Zell, A.: arallelization of Multi-objective Evolutionary Algorithms Using Clustering Algorithms. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 92–107. Springer, Heidelberg (2005)
Tan, K.C., Yang, Y.J., Goh, C.K.: A distributed Cooperative coevolutionary algorithm for multiobjective optimization. IEEE Trans. on Evolutionary Computation 10(5), 527–549 (2006)
Van Veldhuizen, D.A., Zydallis, J.B., Lamont, G.B.: Considerations in engineering parallel multiobjective evolutionary algorithms. IEEE Trans. on Evol. Comp. 7(2), 144–173 (2003)
Yen, J., Gillespie, L.W., Gillespie, C.W.: Improving the interpretability of TSK fuzzy models by combining global learning and local learning. IEEE Trans. on Fuzzy Syst. 6(4), 530–537 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cococcioni, M., Lazzerini, B., Marcelloni, F. (2010). Towards Efficient Multi-objective Genetic Takagi-Sugeno Fuzzy Systems for High Dimensional Problems. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-10701-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10700-9
Online ISBN: 978-3-642-10701-6
eBook Packages: EngineeringEngineering (R0)