Hybrid Particle Swarm Optimization and Group Method of Data Handling for Inductive Modeling. Godfrey C. Onwubolu, Anurag Sharma, Ashwin Dayal, Deepak Bhartu, Amal Shankar and Kenneth Katafono

Abstract. This paper proposes a new design methodology which is based on hybrid of Particle swarm optimization (PSO) and Group method of data handling (GMDH). The PSO and GMDH are two well-known nonlinear methods of mathematical modeling. The proposed method constructs a GMDH network model of a population of promising PSO solutions. The new PSO-GMDH hybrid implementation is then applied to modeling and prediction of practical datasets and its results are compared with the results obtained by GMDH-related algorithms. Results presented show that the proposed algorithm appears to perform reasonably well and hence can be applied to real-life prediction and modeling problems.

Keywords. Inductive modeling, PSO, GMDH, complex systems.

References.
1. Ivakhnenko A. G.: The Group Method of Data Handling - A rival of the Method of Stochastic Approximation. Soviet Automatic Control, 13 c/c of Avtomatika, 1, 3, 43-55, 1968.
2. Farlow, S. J. (ed.): Self-organizing Methods in Modeling. GMDH Type Algorithms. Marcel Dekker. New York, Basel, 1984
3. Madala, H.R.; Ivakhnenko, A.G.: Inductive Learning Algorithms for Complex Systems Modeling. CRC Press Inc., Boca Raton, Ann Arbor, London, Tokyo, 1994
4. Mueller, J-A., and Lemke, F.: Self-Organizing Data Mining: An Intelligent Approach to Extract Knowledge From Data, Dresden, Berlin, 1999.
5. Iba, H., de Garis, H., Sato, T.: Genetic programming using a minimum description length principle, In Advances in Genetic Programming, Kinnear, K. E. Jr (ed), Cambridge: MIT, 1994, pp 265-284.
6. Nariman-Zadeh, N., Darvizeh, A., and Ahmad-Zadeh, G. R.: Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modeling and predicting of the explosive cutting process, Nariman-Zadeh, Proc. Instn Mech. Engrs Vol 217 Part B: Nariman-Zadeh, 779-790.
7. Onwubolu, G. C.: Design of hybrid differential evolution and group method in data handling networks for modeling and prediction, Information Sciences, 178, 3618-3634, 2008, doi:10.1016/j.ins.2008.05.013.
8. Eberhart, R. C. and Kennedy, J.: A new optimizer using particle swarm theory, in Proc. Sixth International Symposium on Micro Machine and human science, Nagoya, Japan, IEEE Service Center, Piscataway, 1995
9. Clerc, M.: Discrete particle swarm optimization illustrated by the traveling salesman problem," New Optimization techniques in Engineering. Springer-Verlag, Berlin, Germany, 2004.
10. A. Carlistle, and G. Dozier, Adapting Particle Swarm Optimization to Dynamic Environments. Available at  http://www.CartistleA.edu, 1998.
11. Kennedy, J. and Eberhart, R. C.: The particle swarm: social adaptation in information processing systems," In Corne, D., Dorigo, M., and Glover, F., Eds., New Ideas in Optimization. London: McGraw?-Hill, pp. 379-387, 1999.
12. Kennedy, J. and Eberhart, R. C.: A discrete binary version of the particle swarm algorithm," International Conference on Systems, Man, and Cybernetics, 1997.
13. Kennedy, J.: The particle swarm: social adaptation of knowledge, IEEE international conference on Evolutionary computation, indianpolis, Indiana, IEEE Service Center, Piscataway, NJ, 1997.
14. Clerc, M. and Kennedy, J.: "The particle swarm: explosion, stability, and convergence in a multidimensional complex space," IEEE transactions on Evolutionary Computation, Vol. 6, 58-73, 2002.
15. Box, G .E. P., and Jenkins, G. M., Time Series Analysis, Forecasting and Control San Francisco, Holden Day, 1970, pp. 532-533.
16. Onwubolu, G. C.: Design of hybrid differential evolution and group method in data handling for modeling, International Workshop on Inductive Modeling, IWIM 2007, Prague, Czech, September 23-26, 2007, pp.87-95.
17. Onwubolu, G. C. and Sharma A.: Particle Swarm Optimization for the assignment of facilities to locations, New Optimization Techniques in Engineering, Springer-Verlag, 2004.