Conference Paper

Effects of learning rate on the performance of the population based incremental learning algorithm

Dept. of Electr. Eng., Univ. of Cape Town, Rondebosch, South Africa
DOI: 10.1109/IJCNN.2009.5179080 Conference: International Joint Conference on Neural Networks, IJCNN 2009, Atlanta, Georgia, USA, 14-19 June 2009
Source: IEEE Xplore

ABSTRACT

The effect of learning rate (LR) on the performance of a newly introduced evolutionary algorithm called population-based incremental learning (PBIL) is investigated in this paper. PBIL is a technique that combines a simple genetic algorithm (GA) with competitive learning (CL). Although CL is often studied in the context of artificial neural networks (ANNs), it plays a vital role in PBIL in that the idea of creating a prototype vector in learning vector quantization (LVQ) is central to PBIL. In PBIL, the crossover operator of GAs is abstracted away and the role of population is redefined. PBIL maintains a real-valued probability vector (PV) or prototype vector from which solutions are generated. The probability vector controls the random bitstrings generated by PBIL and is used to create other individuals through learning. The setting of the learning rate (LR) can greatly affect the performance of PBIL. However, the effect of the learning rate in PBIL is not yet fully understood. In this paper, PBIL is used to design power system stabilizers (PSSs) for a multi-machine power system. Four cases studies with different learning rate patterns are investigated. These include fixed LR; purely adaptive LR; fixed LR followed by adaptive LR; and adaptive LR followed by fixed LR. It is shown that a smaller learning rate leads to more exploration of the algorithm which introduces more diversity in the population at the cost of slower convergence. On the other hand, a higher learning rate means more exploitation of the algorithm and hence, this could lead to a premature convergence in the case of fixed LR. Therefore, in setting the LR, a trade-off is needed between exploitation and exploration.

Download full-text

Full-text

Available from: Komla Folly
  • Source
    • "The proposed approach is applied to a power system controller design. The effectiveness of the proposed algorithm is demonstrated by comparing it to the Adaptive PBIL (AP- BIL) introduced in [19], [22] and the standard PBIL (SPBIL) with fixed learning rate [14]-[17]. Simulation results show that the parallel PBIL (PPBIL) based on two-population is as effective as the Adaptive PBIL (APBIL) and performs better than the standard PBIL (SPBIL). "
    [Show abstract] [Hide abstract]
    ABSTRACT: 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
    Preview · Article · Jan 2013
  • [Show abstract] [Hide abstract]
    ABSTRACT: A portfolio selection problem is about finding an optimal scheme to allocate a fixed amount of capital to a set of available assets. The optimal scheme is very helpful for investors in making decisions. However, finding the optimal scheme is difficult and time-consuming especially when the number of assets is large and some actual investment constraints are considered. This paper proposes a new approach based on estimation of distribution algorithms (EDAs) for solving a cardinality constrained portfolio selection (CCPS) problem. The proposed algorithm, termed PBIL-CCPS, hybridizes an EDA called population-based incremental learning (PBIL) algorithm and a continuous PBIL (PBILc) algorithm, to optimize the selection of assets and the allocation of capital respectively. The proposed algorithm adopts an adaptive parameter control strategy and an elitist strategy. The performance of the proposed algorithm is compared with a genetic algorithm and a particle swarm optimization algorithm. The results demonstrate that the proposed algorithm can achieve a satisfactory result for portfolio selection and perform well in searching nondominated portfolios with high expected returns.
    No preview · Conference Paper · Dec 2010
  • [Show abstract] [Hide abstract]
    ABSTRACT: The aim of the online nonlinear system identification is the accurate modeling of the current local input-output behavior of the plant without using any prior knowledge and offline modeling phase. It is a challenging task for many intelligent systems when used for real-time control applications. In this paper, we propose a novel computationally efficient extended fuzzy functions (EFF) model for system identification of unknown nonlinear discrete-time systems. The main contributions are to introduce an effective quasi-nonlinear model (EFF) and propose adaptive learning rates (ALR) for recursive least squares (RLS) and gradient-descent (GD) methods. The asymptotic convergence of the modeling errors and boundedness of the parameters are proved by using the input-to-state stability (ISS) approach. Numerical simulations are performed for Box–Jenkins gas furnace system and a nonlinear dynamic system. The benefits of its accuracy, stability and simple implementation in practice indicate that EFF model is a promising technique for online identification of nonlinear systems. Copyright © 2010 John Wiley & Sons, Ltd.
    No preview · Article · Feb 2011 · International Journal of Adaptive Control and Signal Processing
Show more