Standard Population-Based Incremental Learning Research Articles

A Modification of the PBIL Algorithm Inspired by the CMA-ES Algorithm in Discrete Knapsack Problem

The subject of this paper is the comparison of two algorithms belonging to the class of evolutionary algorithms. The first one is the well-known Population-Based Incremental Learning (PBIL) algorithm, while the second one, proposed by us, is a modification of it and based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. In the proposed Covariance Matrix Adaptation Population-Based Incremental Learning (CMA-PBIL) algorithm, the probability distribution of population is described by two parameters: the covariance matrix and the probability vector. The comparison of algorithms was performed in the discrete domain of the solution space, where we used the well-known knapsack problem in a variety of data correlations. The results obtained show that the proposed CMA-PBIL algorithm can perform better than standard PBIL in some cases. Therefore, the proposed algorithm can be a reasonable alternative to the PBIL algorithm in the discrete space domain.

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.

An Improved Population-Based Incremental Learning Algorithm

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.

Tuning the PBIL algorithm to solve a real-world FAP problem

Frequency planning, also known as frequency assignment problem (FAP), is a very important task for current GSM operators. FAP basically tries to minimise the number of interferences (or conflicts in the communications) caused when a limited number of frequencies has to be assigned to a quite high number of transceivers (and there are much more transceivers than frequencies). In this work, we focus on solving this problem for a realistic-sized, real-world GSM network using the population-based incremental learning (PBIL) algorithm. The work described here is divided in two parts. In the first one, we analyse and fix the standard PBIL algorithm to solve the FAP; whereas in the second, we take as initial point the results obtained with the standard version of PBIL and we perform a complete study with the most relevant variations of the algorithm to discover which approach can compute the best frequency plans for real-world instances.

Evolution-Based Methods for Selecting Point Data for Object Localization: Applications to Computer-Assisted Surgery

Object localization has applications in many areas of engineering and science. The goal is to spatially locate an arbitrarily shaped object. In many applications, it is desirable to minimize the number of measurements collected while ensuring sufficient localization accuracy. In surgery, for example, collecting a large number of localization measurements may either extend the time required to perform a surgical procedure or increase the radiation dosage to which a patient is exposed. Localization accuracy is a function of the spatial distribution of discrete measurements over an object when measurement noise is present. In previous work (J. of Image Guided Surgery, Simon et al., 1995), metrics were presented to evaluate the information available from a set of discrete object measurements. In this study, new approaches to the discrete point data selection problem are described. These include hillclimbing, genetic algorithms (GAs), and Population-Based Incremental Learning (PBIL). Extensions of the standard GA and PBIL methods that employ multiple parallel populations are explored. The results of extensive empirical testing are provided. The results suggest that a combination of PBIL and hillclimbing result in the best overall performance. A computer-assisted surgical system that incorporates some of the methods presented in this paper is currently being evaluated in cadaver trials.