Population-Based Incremental Learning (PBIL) algorithm is a combination of evolutionary optimization and competitive learning derived from artificial neural networks. PBIL has recently received increasing attention in various engineering fields due to its effectiveness, easy implementation and robustness. Despite these strengths, it was reported in the last few years that PBIL suffers from issues of loss of diversity in the population. To deal with this shortcoming, this paper uses parallel PBIL based on multi-population. In parallel PBIL, two populations are used where both probability vectors (PVs) are initialized to 0.5. It is believed that by introducing two populations, the diversity in the population can be increased and better results can be obtained. The approach is applied to power system controller design. Simulations results show that the parallel PBIL approach performs better than the standard PBIL and is as effective as another diversity increasing PBIL called adaptive PBIL
If the inline PDF is not rendering correctly, you can download the PDF file here.
 S. Baluja, Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning, CMU-CS-94-163, Carnegie Mellon University, 1994.
 F. G. Lobo, and D.E. Golberg, The parameter-less genetic algorithm in practice, International Journal of Information Sciences 2004; 167, pp.217-32.
 S. Baluja, and R. Caruana, Removing the Genetics from the Standard Genetic Algorithm, Tech. Rep. CMU-CS-95-141), Carnegie Mellon University, 1995.
 J. H. Holland, Adaptation in nature and artificial systems. The University of Michigan Press, 1975.
 L. Davis, Handbook of genetic algorithms, International Thomson Computer Press, 1996.
 D. E. Goldberg, Genetic algorithms in search, optimization & machine learning. Addison-Wesley, 1989.
 K. Price, R.M. Storn, and J.A. Lampinen, Differential evolution: A practical approach to global optimization, Springer, ISBN 978-3-540-20950-8, 2005.
 T. Mulumba, and K. A. Folly, Power system stabilizer design: comparative analysis between differential evolution and population- based incremental learning”, In: 20th Southern African Universities’ Power Engineering Conference (SAUPEC ), 2011.
 M. Dorigo, and G Di Caro, The Ant Colony Optimization: a new teta-Heuristic, In: Evolutionary Computation (CEC), 1999.
 J. F. Kennedy, R. C. Eberhart R.C., & Y. Shi, Swarm Intelligence. Morgan Kaufmann, 2001.
 T. K. Das, and G.K. Venayagamoorthy ”Design of Power System Stabilizers using Small Population Based PSO,” IEEE PES General Meeting 2006.
 J. R. Greene, Population-Based Incremental Learning as a Simple,Versatile Tool for Engineering Optimization, In: Proceedings of the First International Conf. on EC and Applications, 1996, pp.258-269
 F. Southey, F. Karray, Approching Evolutionary Robotics through Population-Based Incremental Learning, In: IEEE International Conference on Systems, Man and Cybernetics, Vol. 2, 1999, pp. 710-715.
 KA Folly, Performance Evaluation of power system stabilizers based on Population-Based Incremental Learning (PBIL) Algorithm, International Journal of Power and Energy Systems, Vol. 33, Issue 7, 2011, pp. 1279-1287.
 K.A. Folly, Design of Power System Stabilizer: A Comparison Between Genetic Algorithms (GAs) and Population-Based Incremental Learning (PBIL), In: Proc. of the IEEE PES ,General Meeting, 2006
 K.A. Folly, Robust Controller Design Based on a Combination of Genetic Algorithms (GAs) and Competitive Learning, In: International Joint Conference on Neural Networks, 2007, pp. 3045-3050.
 P. Mitra, C. Yan, L. Grant, G.K. Venayagamoorthy, and K. Folly, Comparative Study of Population-Based Techniques for Power System Stabilizer Design, in Proc. of Intelligent System Applications to Power Systems, 2009.
 P. Kundur, Power System Stability and Control. McGraw - Hill, Inc. 1994.
 KA Folly, An Improved Population-Based Incremental Learning Algorithm, International Journal of Swarm Intelligence Research (IJSIR), Vol.4, No.1, 2013, pp. 35-61.
 C. Conzalez, J.A. Lozano and P. Larranaga, The convergence behavior of the PBIL Algorithm: A preliminary approach, In: Proc. of Artificial Neural Nets and Genetic Algorithms, 2001.
 R. Rastegar, A. Hariri, M. Mazoochi, The Population-Based Incremental Learning Algorithm Converges to Local Optima, Neurocomputing, 69, 2006, pp. 1772-1775.
 KA Folly, G.K. Venayagamoorthy, Effect of Learning Rate on the Performance of the Population-Based Incremental Learning Algorithm, In: Proc. of the International Joint Conf. on Neural Network (IJCNN), 2009.
 S. Yang and H. Richter, Hyper-Learning for Population-Based Incremental Learning in Dynamic Environment, In: IEEE Congress on Evolutionary Computation, 2009.
 M. Ventresca, H. R. Tizhoosh, A diversity Maintaining Population Based Incremental Learning Algorithm, Information Sciences, 178, 2008, pp. 4038-4056
 S. Y. Yang, S.L. Ho, G.Z. Ni, J.M. Machado and K.F.Wong, A new Implementation of Population- Based Incremental Learning Method for Optimizations in Electromagnetics, IEEE Trans. On Magnetics 43 (4), 2007, pp. 1601-1604.
 S. Yang and X. Yao, Experimental Study on Population-Based Incremental Learning Algorithms for Dynamic Optimization Problems, Soft Computing, 9(11), 2005, pp. 815-834
 G. Rogers, Power system oscillations, Kluwer academic Publishers, 2000