An Improved Population-Based Incremental Learning Algorithm

An Improved Population-Based Incremental Learning Algorithm

Komla A. Folly (Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa)
Copyright: © 2013 |Pages: 27
DOI: 10.4018/jsir.2013010102
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Abstract

Population-Based Incremental Learning (PBIL) is a relatively new class of Evolutionary Algorithms (EA) that has been recently applied to a range of optimization problems in engineering with promising results. PBIL combines aspects of Genetic Algorithm with competitive learning. The learning rate in the standard PBIL is generally fixed which makes it difficult for the algorithm to explore the search space effectively. In this paper, a PBIL with adapting learning rate is proposed. The Adaptive PBIL (APBIL) is able to thoroughly explore the search space at the start of the run and maintain the diversity consistently during the run longer than the standard PBIL. The proposed algorithm is validated by applying it to power system controller parameters optimization problem. Simulation results show that the Adaptive PBIL based controller performs better than the standard PBIL based controller, in particular under small disturbance.
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1. Introduction

Engineering optimization problems arise in varities of engineering applications. These optimizations problems were generally difficult or impossible to solve using conventional optimization methods. In the last three decades or so, there has been a growing interest in applying Evolutionary Algorithm (EA) to engineering optimization problems. The most widely used EA is Genetic Algorithms (GAs) (Goldberg, 1989). Although GAs provide a robust and powerful adaptive search mechanism, they have several drawbacks. Some of these drawbacks include the slow convergence of the algorithm when solving complex problems, the problem of “genetic drift” which prevents GAs from maintaining diversity in the population, and the difficulty to optimally select the genetic operators such as population size, crossover and mutation rates (Davis, 1996; Yao, Kharma, & Grogono, 2010).

In the last few years, Particle Swarm Optimization (PSO) which belongs to the family of Swarm Intelligence has also been proposed as an alternative to GAs (Kennedy et al., 2001; Abido, 2001; Venayagamoorthy, 2005).

Recently, a novel type of Evolutionary Algorithm called Population-Based Incremental Learning (PBIL) which belongs to the family of Estimation of Distribution Algorithms (EDA) has received increasing attention (Baluja, 1994; Baluja & Caruana, 1995; Green, 1996; Folly, 2006, Sheetekela & Folly, 2010; Mitra et al., 2009). PBIL is simpler and more effective than GAs. In addition, PBIL has less overhead than GAs (Baluja & Caruana, 1995; Green, 1996; Gosling, 2004). The main reason for this simplicity is that in PBIL, the crossover operator is abstracted away and the role of population is redefined (Baluja, 1994; Baluja & Caruana, 1995). Furthermore, PBIL works with a probability vector (PV) which controls the random bit strings generated by PBIL and is used to create other individuals through learning. Learning in PBIL consists of using the current probability vector (PV) to create N individuals. The best individual is used to update the probability vector, increasing the probability of producing solutions similar to the current best individuals (Baluja & Caruana, 1995; Green, 1996). It has been shown that PBIL outperforms standard GAs approaches on a variety of optimization problems including commonly used benchmark problems (Baluja, 1994; Baluja & Caruana, 1995).

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