Erick Cantú-Paz

The gambler's ruin problem, genetic algorithms, and the sizing of populations

The paper presents a model for predicting the convergence quality of genetic algorithms. The model incorporates previous knowledge about decision making in genetic algorithms and the initial supply of building blocks in a novel way. The result is an equation that accurately predicts the quality of the solution found by a GA using a given population size. Adjustments for different selection intensities are considered and computational experiments demonstrate the effectiveness of the model.

Linkage Problem, Distribution Estimation, and Bayesian Networks

This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. The BOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

Migration Policies, Selection Pressure, and Parallel Evolutionary Algorithms

This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.

Efficient parallel genetic algorithms : theory and practice

Parallel genetic algorithms (GAs) are complex programs that are controlled by many parameters, which affect their search quality and their efficiency. The goal of this paper is to provide guidelines to choose those parameters rationally. The investigation centers on the sizing of populations, because previous studies show that there is a crucial relation between solution quality and population size. As a first step, the paper shows how to size a simple GA to reach a solution of a desired quality. The simple GA is then parallelized, and its execution time is optimized. The rest of the paper deals with parallel GAs with multiple populations. Two bounding cases of the migration rate and topology are analyzed, and the case that yields good speedups is optimized. Later, the models are specialized to consider sparse topologies and migration rates that are more likely to be used by practitioners. The paper also presents the additional advantages of combining multi- and single-population parallel GAs. The results of this work are simple models that practitioners may use to design efficient and competent parallel GAs.

Inducing oblique decision trees with evolutionary algorithms

This paper illustrates the application of evolutionary algorithms (EAs) to the problem of oblique decision-tree (DT) induction. The objectives are to demonstrate that EAs can find classifiers whose accuracy is competitive with other oblique tree construction methods, and that, at least in some cases, this can be accomplished in a shorter time. We performed experiments with a (1+1) evolution strategy and a simple genetic algorithm on public domain and artificial data sets, and compared the results with three other oblique and one axis-parallel DT algorithms. The empirical results suggest that the EAs quickly find competitive classifiers, and that EAs scale up better than traditional methods to the dimensionality of the domain and the number of instances used in training. In addition, we show that the classification accuracy improves when the trees obtained with the EAs are combined in ensembles, and that sometimes it is possible to build the ensemble of evolutionary trees in less time than a single traditional oblique tree.

An empirical comparison of combinations of evolutionary algorithms and neural networks for classification problems

There are numerous combinations of neural networks (NNs) and evolutionary algorithms (EAs) used in classification problems. EAs have been used to train the networks, design their architecture, and select feature subsets. However, most of these combinations have been tested on only a few data sets and many comparisons are done inappropriately measuring the performance on training data or without using proper statistical tests to support the conclusions. This paper presents an empirical evaluation of eight combinations of EAs and NNs on 15 public-domain and artificial data sets. Our objective is to identify the methods that consistently produce accurate classifiers that generalize well. In most cases, the combinations of EAs and NNs perform equally well on the data sets we tried and were not more accurate than hand-designed neural networks trained with simple backpropagation.

Scalable Optimization via Probabilistic Modeling

Scalable optimization via probabilistic modelin , Scalable optimization via probabilistic modelin , کتابخانه دیجیتال جندی شاپور اهواز

Feature selection in scientific applications

Numerous applications of data mining to scientific data involve the induction of a classification model. In many cases, the collection of data is not performed with this task in mind, and therefore, the data might contain irrelevant or redundant features that affect negatively the accuracy of the induction algorithms. The size and dimensionality of typical scientific data make it difficult to use any available domain information to identify features that discriminate between the classes of interest. Similarly, exploratory data analysis techniques have limitations on the amount and dimensionality of the data they can process effectively. In this paper, we describe applications of efficient feature selection methods to data sets from astronomy, plasma physics, and remote sensing. We use variations of recently proposed filter methods as well as traditional wrapper approaches, where practical. We discuss the general challenges of feature selection in scientific datasets, the strategies for success that were common among our diverse applications, and the lessons learned in solving these problems.

Markov chain models of parallel genetic algorithms

Implementations of parallel genetic algorithms (GA) with multiple populations are common, but they introduce several parameters whose effect on the quality of the search is not well understood. Parameters such as the number of populations, their size, the topology of communications, and the migration rate have to be set carefully to reach adequate solutions. This paper presents models that predict the effects of the parallel GA parameters on its search quality. The paper reviews some recent results on the case where each population is connected to all the others and the migration rate is set to the maximum value possible. This bounding case is the simplest to analyze, and it introduces the methodology that is used in the remainder of the paper to analyze parallel GA with arbitrary migration rates and communication topologies. This investigation considers that migration occurs only after each population converges; then, incoming individuals are incorporated into the populations and the algorithm restarts. The models find the probability that each population converges to the correct solution after each restart, and also calculate the long-run chance of success. The accuracy of the models is verified with experiments using one additively decomposable function.

Feature Subset Selection, Class Separability, and Genetic Algorithms

The performance of classification algorithms in machine learning is affected by the features used to describe the labeled examples presented to the inducers. Therefore, the problem of feature subset selection has received considerable attention. Genetic approaches to this problem usually follow the wrapper approach: treat the inducer as a black box that is used to evaluate candidate feature subsets. The evaluations might take a considerable time and the traditional approach might be impractical for large data sets. This paper describes a hybrid of a simple genetic algorithm and a method based on class separability applied to the selection of feature subsets for classification problems. The proposed hybrid was compared against each of its components and two other feature selection wrappers that are used widely. The objective of this paper is to determine if the proposed hybrid presents advantages over the other methods in terms of accuracy or speed in this problem. The experiments used a Naive Bayes classifier and public-domain and artificial data sets. The experiments suggest that the hybrid usually finds compact feature subsets that give the most accurate results, while beating the execution time of the other wrappers.