Multiobjective Space Search Optimization and Information Granulation in the Design of Fuzzy Radial Basis Function Neural Networks

- Journal title : Journal of Electrical Engineering and Technology
- Volume 7, Issue 4, 2012, pp.636-645
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/JEET.2012.7.4.636

Title & Authors

Multiobjective Space Search Optimization and Information Granulation in the Design of Fuzzy Radial Basis Function Neural Networks

Huang, Wei; Oh, Sung-Kwun; Zhang, Honghao;

Huang, Wei; Oh, Sung-Kwun; Zhang, Honghao;

Abstract

This study introduces an information granular-based fuzzy radial basis function neural networks (FRBFNN) based on multiobjective optimization and weighted least square (WLS). An improved multiobjective space search algorithm (IMSSA) is proposed to optimize the FRBFNN. In the design of FRBFNN, the premise part of the rules is constructed with the aid of Fuzzy C-Means (FCM) clustering while the consequent part of the fuzzy rules is developed by using four types of polynomials, namely constant, linear, quadratic, and modified quadratic. Information granulation realized with C-Means clustering helps determine the initial values of the apex parameters of the membership function of the fuzzy neural network. To enhance the flexibility of neural network, we use the WLS learning to estimate the coefficients of the polynomials. In comparison with ordinary least square commonly used in the design of fuzzy radial basis function neural networks, WLS could come with a different type of the local model in each rule when dealing with the FRBFNN. Since the performance of the FRBFNN model is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials present in the consequent parts of the rules, we carry out both structural as well as parametric optimization of the network. The proposed IMSSA that aims at the simultaneous minimization of complexity and the maximization of accuracy is exploited here to optimize the parameters of the model. Experimental results illustrate that the proposed neural network leads to better performance in comparison with some existing neurofuzzy models encountered in the literature.

Keywords

Fuzzy Radial Basis Function Neural Networks (FRBFNN);Improved Multiobjective Space Search Algorithm (IMSSA);Information Granulation (IG);Weighted Least Squares (WLS);

Language

English

Cited by

References

1.

S. Mitra, J. Basak, "FRBF: A Fuzzy Radial Basis Function Network," Neural Comput. Applic., vol. 10, pp. 244-252, 2001.

2.

F. Behloul, B.P.F. Lelieveldt, A.Boudraa, and J.H.C. Reiber, "Optimal design of radial basis function neural networks for fuzzy-rule extraction in high dimensional data," Pattern Recognition, vol. 35, pp. 659-675, 2002.

3.

W. Huang, L. Ding, "Project-scheduling problem with random time-dependent activity duration times," IEEE Transactions on Engineering Management, vol. 58, no. 2, pp. 377-387, 2011.

4.

F.J. Lin, L.T. Teng, J.W. Lin, S.Y. Chen, "Recurrent Functional-Link-Based Fuzzy-Neural-Network-Controlled Induction-Generator System Using Improved Particle Swarm Optimization," IEEE Trans. Indust. Elect., vol. 56, no. 5, pp. 1557-1577, 2009.

5.

W. Pedrycz, K.C Kwak, "Linguistic models as a framework of user-centric system modeling," IEEE Trans. Syst., man cybern. -PART A : Systems and humans, vol. 36, no. 4, pp. 727-745, 2006.

6.

W. Pedrycz, H.S. Park, S.K. Oh, "A granular-oriented development of functional radial basis function neural networks," Neurocomputing, vol. 72, pp. 420-435, 2008.

7.

D.R. Marylyn, A.M. Alison, S.B. William, S.C. Christopher, H.M. Jason, "Genetic programming neural networks: A powerful bioinformatics tool for human genetics," Applied Soft Computing, vol. 7, Issue 4, pp. 471-479, 2007.

8.

Y. Jin, "Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement," IEEE Trans. Fuzzy Syst., vol. 8, no. 2, pp. 212-221, 2000.

9.

M. Setnes, H. Roubos, "GA-based modeling and classification: complexity and performance," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 509-522, 2000.

10.

K. Deb, A. Pratab, S. Agrawal, T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGAII," IEEE Trans. Evol. Comput., vol. 6, pp. 182-197, 2002.

11.

G. Avigad, A. Moshaiov, "Interactive Evolutionary Multiobjective Search and Optimization of Set-Based Concepts," IEEE Trans. Syst., Man cybern.-Part B, vol. 38, nol. 2, pp. 381-403, 2008.

12.

B.Zafer, "Adaptive genetic algorithms applied to dynamic multiobjective problems," Applied Soft Computing, vol. 7, Issue 3, pp. 791-799, 2007.

13.

S. Chuan, Y. Zhenyu, S. Zhongzhi, Z. Lei, "A fast multi-objective evolutionary algorithm based on a tree structure," Applied Soft Computing, vol. 10, Issue 2, 468-480, 2010.

14.

K.T. Parveen, B. Sanghamitra, K.P. Sankar, "Multi- Objective Particel Swarm Optimization with time variant inertia and acceleration coefficients," Information Sciences, vol. 177, no. 22, pp. 5033-5049, 2007.

15.

S. Masato, G. Mitsuo, "Fuzzy multiple objective optimal system design by hybrid genetic algorithm," Applied Soft Computing, vol. 2, Issue 3, pp. 189-196, 2003

16.

M. Delgado, M.P. Ceullar, M.C. Pegalajar, "Multiobjective Hybrid Optimization and Training of Recurrent Neural Networks," IEEE Trans. Syst., Man cybern. -Part B, vol. 38, nol. 2, pp. 381-403, 2008.

17.

C. Marco, L. Beatrice, M. Francesco, "On reducing computational overhead in multi-objective genetic Takagi-Sugeno fuzzy systems," Applied Soft Computing, vol. 11, Issue 1, pp. 675-688, 2011.

18.

Z.Yong, W. Xiao-bei, X. Zong-yi, H. Wei-li, "On generating interpretable and precise fuzzy systems based on Pareto multi-objective cooperative coevolutionary algorithm," Applied Soft Computing, vol. 11, Issue 1, pp. 1284-1294, 2011.

19.

W. Huang, L. Ding, S.K. Oh, "Design of fuzzy radial basis function neural networks with the aid of multiobjective optimization based on simultaneous tuning," Eighth International Symposium on Neural Networks, LNCS 6677, pp. 264-273, 2011.

20.

A. Staiano, R. Tagliaferri, W. Pedrycz, "Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering," Neurocomputing, vol. 69, pp. 1570-1581, 2006.

21.

X. Hong, S. Chen, "A New RBF Neural Network with Boundary Value Constraints," IEEE Trans. Syst., Man Cybern. -PART B, vol. 39, nol. 1, pp. 298-303, 2009.

22.

C.M. Huang, F.L. Wang, "An RBF Network with OLS and EPSO Algorithms for Real-Time Power Dispatch," IEEE Trans. Power Syst., vol. 22, no. 1, pp.96-104, 2007.

23.

F. Hoffmann, "Combining boosting and evolutionary algorithms for learning of fuzzy classification rules", Fuzzy Sets and Syst.,vol. 141, pp. 47-58, 2004.

24.

W. Pedrycz, K.C. Kwak, "Boosting of granular models," Fuzzy Sets and Syst., vol. 157, pp. 2934- 2953, 2006.

25.

W. Pedrycz, P. Rai,, "Collaborative clustering with the use of fuzzy C-Means and its quantification", Fuzzy Sets and Syst., vol. 159, pp. 2399-2427, 2008.

26.

R.R. Yager, D.P. Filev, "Unified Structure and Parameter Identification," IEEE Trans. Syst. Man Cybern., vol. 23, no. 4, pp. 1198-1205, 1993.

27.

W. Huang, L. Ding, S.K. Oh, C.W. Jeong, S.C. Joo, "Identification of Fuzzy Inference System Based on Information Granulation," KSII Transactions on Internet and Information Systems, vol. 4, no. 4, pp. 575-594, 2010.

28.

W. Huang, S.K. Oh, L. Ding, H.K. Kim, S.C. Joo, "Identification of Fuzzy Inference Systems Using a Multi-objective Space Search Algorithm and Information Granulation," Journal of Electrical Engineering & Technology, vol. 6, no. 6, pp. 853-866, 2011.

29.

Q. Zhang, Y.W. Leung, "An orthogonal genetic algorithm for multimedia multicast routing," IEEE Transactions on Evolutionary Computation, vol. 3, no. 1, pp. 53-62, 1999.

30.

W. Pedrycz, "An identification algorithm in fuzzy relational system," Fuzzy Sets Syst., vol. 13, pp. 153- 167, 1984.

31.

R. M. Tong, "The evaluation of fuzzy models derived from experimental data," Fuzzy Sets Syst., vol. 13, pp 1-12, 1980.

32.

C. W. Xu., Y. Zailu, "Fuzzy model identification selflearning for dynamic system" IEEE Trans. Syst., Man cybern., vol. 17, no 4, pp, 683-689, 1987.

33.

S. K. Oh, W. Pedrycz, "Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems," Fuzzy Sets and Syst., vol. 115, no 2, pp, 205-230, 2000.

34.

B. J. Park, W. Pedrycz, S. K. Oh, "Identification of Fuzzy Models with the Aid of Evolutionary Data Granulation," IEE Proc.-Control Theory and Applications, vol. 148, pp, 406-418, 2001.

35.

H.D. Chris, J.C. Burges, L. Kaufman, A. Smola, V. Vapnik, "Support vector regression machines," Adv. Neural Inform. Process Syst. 9 (1997) 155-161.