Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

ABSTRACT

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

KEYWORDS

Radial Basis Function Network, Orthogonal Least Squares Algorithm, Particle Swarm Optimization, Mackey-Glass Chaotic Time-Series

Radial Basis Function Network, Orthogonal Least Squares Algorithm, Particle Swarm Optimization, Mackey-Glass Chaotic Time-Series

Cite this paper

nullM. Zirkohi, M. Fateh and A. Akbarzade, "Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares,"*Journal of Software Engineering and Applications*, Vol. 3 No. 7, 2010, pp. 704-708. doi: 10.4236/jsea.2010.37080.

nullM. Zirkohi, M. Fateh and A. Akbarzade, "Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares,"

References

[1] S. Chen, S. A. Billings, C. F. N. Cowan and P. M. Grant, “Non-Linear Systems Identification Using Radial Basis Functions,” International Journal of Systems Science, Vol. 21, No. 12, 1990, pp. 2513-2539.

[2] M. M. Gupta and L. Jin, “Static and Dynamic Neural Networks,” John Wiley, 2003.

[3] R. Segal and M. L. Kothari, “Radial Basis Function (RBF) Network Adaptive Power System Stabilizer,” IEEE Tran- sactions on Power Systems, Vol. 15, No. 2, 2000, pp. 722-727.

[4] S. A. Billings and X. Hong. “Dual Orthogonal Radial Basis Function Networks for Nonlinear Time Series Prediction,” Neural Networks, Vol. 11, No. 3, 1998, pp. 479-493.

[5] D. Shi, D. S. Yeung and J. Gao. “Sensitivity Analysis Applied to the Construction of Radial Basis Function Networks,” Neural Networks, Vol. 18, No. 7, 2005, pp. 951-957.

[6] S. Chen, C. F. N. Cowan and P. M. Grant, “Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks,” IEEE Transactions on Neural Networks, Vol. 2, No. 2, March 1991, pp. 302-309.

[7] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, Vol. 4, 1995, pp. 1942-1948.

[8] S. Naka, T. Genji, T. Yura and Y. Fukuyama, “A Hybrid Particle Swarm Optimization for Distribution State Estimation,” IEEE Transactions on Power Systems, Vol. 18, No. 1, 2003, pp. 60-68.

[9] M. Clerc, “The Swarm and the Queen: Towards the Deterministic and Adaptive Particle Swarm Optimization,” Proceedings of the Congress on Evolutionary Computation, Washington, DC, 1999, pp. 1951-1957.

[10] A. Alfi and M. M. Fateh, “Parameter Identification Based on a Modified PSO Applied to Suspension System,” Journal of Software Engineering & Applications, Vol. 3, 2010, pp. 221-229.

[11] A. Chatterjee, “Velocity Relaxed and Craziness-Based Swarm Optimized Intelligent PID and PSS Controlled AVR System,” Electrical Power and Energy Systems, Vol. 31, No. 7-8, 2009, pp. 323-333.

[12] A. Ratnaweera and S. K. Halgamuge, “Self Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficient,” IEEE Transactions on Evolutionary Computation, Vol. 8, No. 3, 2004, pp. 240-255.

[13] L. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall International, 1997.

[1] S. Chen, S. A. Billings, C. F. N. Cowan and P. M. Grant, “Non-Linear Systems Identification Using Radial Basis Functions,” International Journal of Systems Science, Vol. 21, No. 12, 1990, pp. 2513-2539.

[2] M. M. Gupta and L. Jin, “Static and Dynamic Neural Networks,” John Wiley, 2003.

[3] R. Segal and M. L. Kothari, “Radial Basis Function (RBF) Network Adaptive Power System Stabilizer,” IEEE Tran- sactions on Power Systems, Vol. 15, No. 2, 2000, pp. 722-727.

[4] S. A. Billings and X. Hong. “Dual Orthogonal Radial Basis Function Networks for Nonlinear Time Series Prediction,” Neural Networks, Vol. 11, No. 3, 1998, pp. 479-493.

[5] D. Shi, D. S. Yeung and J. Gao. “Sensitivity Analysis Applied to the Construction of Radial Basis Function Networks,” Neural Networks, Vol. 18, No. 7, 2005, pp. 951-957.

[6] S. Chen, C. F. N. Cowan and P. M. Grant, “Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks,” IEEE Transactions on Neural Networks, Vol. 2, No. 2, March 1991, pp. 302-309.

[7] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, Vol. 4, 1995, pp. 1942-1948.

[8] S. Naka, T. Genji, T. Yura and Y. Fukuyama, “A Hybrid Particle Swarm Optimization for Distribution State Estimation,” IEEE Transactions on Power Systems, Vol. 18, No. 1, 2003, pp. 60-68.

[9] M. Clerc, “The Swarm and the Queen: Towards the Deterministic and Adaptive Particle Swarm Optimization,” Proceedings of the Congress on Evolutionary Computation, Washington, DC, 1999, pp. 1951-1957.

[10] A. Alfi and M. M. Fateh, “Parameter Identification Based on a Modified PSO Applied to Suspension System,” Journal of Software Engineering & Applications, Vol. 3, 2010, pp. 221-229.

[11] A. Chatterjee, “Velocity Relaxed and Craziness-Based Swarm Optimized Intelligent PID and PSS Controlled AVR System,” Electrical Power and Energy Systems, Vol. 31, No. 7-8, 2009, pp. 323-333.

[12] A. Ratnaweera and S. K. Halgamuge, “Self Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficient,” IEEE Transactions on Evolutionary Computation, Vol. 8, No. 3, 2004, pp. 240-255.

[13] L. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall International, 1997.