Comparison of Convergence Behavior in the Simple Genetic Algorithm and the Infinite Population Model PDF Download
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Author: Michael D. O'Conner
Publisher:
ISBN:
Category : Demographics
Languages : en
Pages : 246
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Book Description
Author: Michael D. O'Conner
Publisher:
ISBN:
Category : Demographics
Languages : en
Pages : 246
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Author: Allen Eugene Nix
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 136
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Author:
Publisher:
ISBN:
Category : Genetic algorithms
Languages : en
Pages : 30
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Abstract: "Infinite population models show a deterministic behaviour. Genetic algorithms with finite populations behave non-deterministicly [sic]. For small population sizes, the results obtained with these models differ strongly from the results predicted by the infinite population model. When the population size is increased towards infinity, a convergence to the results predicted by the infinite population models is observed. In real GA's random decisions are used during the run of the GA. These random decisions can lead to a behaviour that results in a deviation of the GA from the expected path of evolution. In this report four sources of non-determinism are identified. Finite population models are generated by explicitly modelling two of these sources. When comparing the results to runs of actual genetic algorithms, similar results are obtained. Hence, this model shows what are the most important sources of non-determinism in the GA for the problem at hand."
Author: Bo Song
Publisher:
ISBN: 9781361383155
Category :
Languages : en
Pages :
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This dissertation, "Theoretical Analysis and Approximation of Infinite Population Models for Evolutionary Algorithms" by Bo, Song, 宋博, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Evolutionary algorithms are general purpose optimization algorithms. Despite their successes in many real-world applications, the theoretical analyses of the underlying evolutionary processes and of the behaviors of these algorithms remain incomplete. This thesis focuses on one major approach of studying evolutionary algorithms theoretically - the dynamical system approach. More specifically, we are concerned with the theoretical foundations and practical approximations of infinite population models of evolutionary algorithms on continuous optimization problems. Infinite population models are generally derived from general state space Markov chains by exploiting symmetry between individuals in the population and analyzing the limiting case when the population size goes to infinity. They are usually described by difference equations (or transition equations) between marginal probability density functions of consecutive generations. Previously, there are very few studies on the theoretical foundations of infinite population models of evolutionary algorithms. In the first part of this thesis, we show that the convergence proofs in a widely cited study in this area were in fact wrong and incomplete. We further show that the modeling assumption of exchangeability of individuals in that study cannot yield the transition equation in general. This essentially creates a vacuum in the theoretical foundations of infinite population models. In order to fill the gap, we build a novel analytical framework based on convergence in distribution for random elements taking values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Then, we use the framework to analyze various operators of the simple evolutionary algorithm. The mutation operator and the k-ary recombination operator are readily analyzed. Our analyses show that for these operators, they have the property of producing identically and independently distributed populations, in the sense that if the initial population is identically and independently distributed, as the population size goes to infinity, in the limit all subsequent generations are also identically and independently distributed. This means that for these operators, the transition equations derived for independently and identically distributed populations can actually predict the real population dynamics as the population size goes to infinity. This provides a theoretical justification for infinite population models. For the infinite population model of proportionate selection, although we have not proved its convergence, we carry out various analyses and report our results. Finally, to bridge the gap between theory and practice, we propose a general approximation scheme for the transition equations of infinite population models. This scheme is based on Gaussian mixture approximation of functions, and in general it can solve the transition equations in closed form. We prove that given any generation number k, by choosing appropriate values of parameters, the approximation error between our scheme and the infinite population model can be arbitrarily small for all populations before the kth generation. Experimental results show that the p
Author: Grzegorz Rozenberg
Publisher: Springer
ISBN: 9783540929093
Category : Computers
Languages : en
Pages : 2052
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Book Description
Natural Computing is the field of research that investigates both human-designed computing inspired by nature and computing taking place in nature, i.e., it investigates models and computational techniques inspired by nature and also it investigates phenomena taking place in nature in terms of information processing. Examples of the first strand of research covered by the handbook include neural computation inspired by the functioning of the brain; evolutionary computation inspired by Darwinian evolution of species; cellular automata inspired by intercellular communication; swarm intelligence inspired by the behavior of groups of organisms; artificial immune systems inspired by the natural immune system; artificial life systems inspired by the properties of natural life in general; membrane computing inspired by the compartmentalized ways in which cells process information; and amorphous computing inspired by morphogenesis. Other examples of natural-computing paradigms are molecular computing and quantum computing, where the goal is to replace traditional electronic hardware, e.g., by bioware in molecular computing. In molecular computing, data are encoded as biomolecules and then molecular biology tools are used to transform the data, thus performing computations. In quantum computing, one exploits quantum-mechanical phenomena to perform computations and secure communications more efficiently than classical physics and, hence, traditional hardware allows. The second strand of research covered by the handbook, computation taking place in nature, is represented by investigations into, among others, the computational nature of self-assembly, which lies at the core of nanoscience, the computational nature of developmental processes, the computational nature of biochemical reactions, the computational nature of bacterial communication, the computational nature of brain processes, and the systems biology approach to bionetworks where cellular processes are treated in terms of communication and interaction, and, hence, in terms of computation. We are now witnessing exciting interaction between computer science and the natural sciences. While the natural sciences are rapidly absorbing notions, techniques and methodologies intrinsic to information processing, computer science is adapting and extending its traditional notion of computation, and computational techniques, to account for computation taking place in nature around us. Natural Computing is an important catalyst for this two-way interaction, and this handbook is a major record of this important development.
Author: Richard K. Belew
Publisher: Morgan Kaufmann
ISBN: 9781558604605
Category : Computers
Languages : en
Pages : 480
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Book Description
Author: Mrinal K. Sen
Publisher: Cambridge University Press
ISBN: 1107011906
Category : Mathematics
Languages : en
Pages : 303
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Book Description
An up-to-date overview of global optimization methods used to formulate and interpret geophysical observations, for researchers, graduate students and professionals.
Author: Cees H. M. van Kemenade
Publisher:
ISBN:
Category : Genetic algorithms
Languages : en
Pages : 25
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Book Description
Abstract: "Cross-competition between non-overlapping building blocks can strongly influence the performance of evolutionary algorithms. The choice of the selection scheme can have a strong influence on the performance of a genetic algorithm. This paper describes a number of different genetic algorithms, all involving elitism. Infinite population models are presented for each of these algorithms. A problem involving cross-competition is introduced and we show how we can make use of equivalence-classes to make an efficient tracing of the transmission-function models possible on this type of problems [sic]. By adding a small extension to the models it is possible to predict the qualitative behavior of finite population genetic algorithms on this type of problems [sic] also. Using this model the reliability of the different genetic algorithms and the influence of population sizing on the reliability is investigated."
Author: Hung T. Nguyen
Publisher: Springer Science & Business Media
ISBN: 1461555051
Category : Mathematics
Languages : en
Pages : 532
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Book Description
The analysis and control of complex systems have been the main motivation for the emergence of fuzzy set theory since its inception. It is also a major research field where many applications, especially industrial ones, have made fuzzy logic famous. This unique handbook is devoted to an extensive, organized, and up-to-date presentation of fuzzy systems engineering methods. The book includes detailed material and extensive bibliographies, written by leading experts in the field, on topics such as: Use of fuzzy logic in various control systems. Fuzzy rule-based modeling and its universal approximation properties. Learning and tuning techniques for fuzzy models, using neural networks and genetic algorithms. Fuzzy control methods, including issues such as stability analysis and design techniques, as well as the relationship with traditional linear control. Fuzzy sets relation to the study of chaotic systems, and the fuzzy extension of set-valued approaches to systems modeling through the use of differential inclusions. Fuzzy Systems: Modeling and Control is part of The Handbooks of Fuzzy Sets Series. The series provides a complete picture of contemporary fuzzy set theory and its applications. This volume is a key reference for systems engineers and scientists seeking a guide to the vast amount of literature in fuzzy logic modeling and control.
Author: M.K. Sen
Publisher: Elsevier
ISBN: 008053256X
Category : Science
Languages : en
Pages : 294
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Book Description
One of the major goals of geophysical inversion is to find earth models that explain the geophysical observations. Thus the branch of mathematics known as optimization has found significant use in many geophysical applications.Both local and global optimization methods are used in the estimation of material properties from geophysical data. As the title of the book suggests, the aim of this book is to describe the application of several recently developed global optimization methods to geophysical problems. • The well known linear and gradient based optimization methods have been summarized in order to explain their advantages and limitations• The theory of simulated annealing and genetic algorithms have been described in sufficient detail for the readers to understand the underlying fundamental principles upon which these algorithms are based• The algorithms have been described using simple flow charts (the algorithms are general and can be applied to a wide variety of problemsStudents, researchers and practitioners will be able to design practical algorithms to solve their specific geophysical inversion problems. The book is virtually self-contained so that there are no prerequisites, except for a fundamental mathematical background that includes a basic understanding of linear algebra and calculus.
