A self-adaptive migration model genetic algorithm for data mining applications

Data mining involves nontrivial process of extracting knowledge or patterns from large databases. Genetic Algorithms are efficient and robust searching and optimization methods that are used in data mining. In this paper we propose a Self-Adaptive Migration Model GA (SAMGA), where parameters of population size, the number of points of crossover and mutation rate for each population are adaptively fixed. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions and a set of actual classification datamining problems. Michigan style of classifier was used to build the classifier and the system was tested with machine learning databases of Pima Indian Diabetes database, Wisconsin Breast Cancer database and few others. The performance of our algorithm is better than others. © 2007 Elsevier Inc. All rights reserved

Noisy fitness evaluation in genetic algorithms and the dynamics of learning

A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required

Transmission function models of infinite population genetic algorithms

The so-called transmission function framework is described, and implementations of transmission function models are given for a broad range of genetic algorithms. These models describe GA's with a population of infinite size. An actual implementation of these models for a non-trivial problem involving deception is given, these models are traced, and the results are visualized by means of population flow diagrams. These diagrams show that cross-competition between different parts of the optimal solution takes place

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined

Front Matter - Soft Computing for Data Mining Applications

Efficient tools and algorithms for knowledge discovery in large data sets have been devised during the recent years. These methods exploit the capability of computers to search huge amounts of data in a fast and effective manner. However, the data to be analyzed is imprecise and afflicted with uncertainty. In the case of heterogeneous data sources such as text, audio and video, the data might moreover be ambiguous and partly conflicting. Besides, patterns and relationships of interest are usually vague and approximate. Thus, in order to make the information mining process more robust or say, human-like methods for searching and learning it requires tolerance towards imprecision, uncertainty and exceptions. Thus, they have approximate reasoning capabilities and are capable of handling partial truth. Properties of the aforementioned kind are typical soft computing. Soft computing techniques like Genetic

Binomially distributed populations for modelling GAs

We discuss a novel model for analyzing the working of genetic algorithms, when the objective function is a function of unitation. The model is exact (not approximate), and is valid for infinite populations. We introduce the notion of a binomially distributed population (BDP) as the building block of our model, and we show that the effect of uniform crossover on BDPs is to generate two other BDPs. We demonstrate that a population with any general distribution may be decomposed into several BDPs. We also show that a general multipoint crossover may be considered as a composition of several uniform crossovers. Based on these results, the effects of mutation and crossover on the distribution of strings have been characterized, and the model has been defined. The time complexity of the algorithm derived from the model is $O(\int^3)$ (where $\int$ is the problem size), a significant improvement over previous models with exponential time complexities, GASIM-a Genetic Algorithm Simulator for functions of unitation-has been implemented, and the exactness of the results obtained from GASIM has been verified from actual genetic algorithm run