Natural Computing

, Volume 16, Issue 1, pp 75–84 | Cite as

Diversity increasing methods in PBIL-application to power system controller design: a comparison



Population-based incremental learning (PBIL) has recently received increasing attention due to its effectiveness, easy implementation and robustness. Despite this, recent literature suggests that PBIL may suffer from issues of loss of diversity in the population, resulting in premature convergence. In this paper, three diversity maintaining PBIL methods are proposed to address the issue of loss of diversity in PBIL. The first method uses an adaptive learning rate as opposed to the fixed learning rate that is normally used in the standard PBIL. In this method, the learning rate is adapted according to the degree of evolution of the search space. That is, the learning rate is increased linearly with the number of generation. The second method uses two sub-populations and conduct independent search in parallel with the same initial probability vectors, but with fixed learning rates similar to the one used in the standard PBIL. In the third method, the concept of duality or opposition is combined with parallel PBIL as a means of controlling the diversity in the population. To evaluate the performances of these methods, they are applied to the problem of controller design in power systems to improve the small-signal stability. Simulations results show that the proposed diversity maintaining methods are able to maintain the diversity in the population longer than the standard PBIL. However, PBIL with adaptive learning rate takes a little bit time to converge (more function evaluations) compared to the other methods.


Adaptive learning rate Low frequency oscillations Population-based incremental learning Parallel PBIL 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of Cape TownCape TownSouth Africa

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