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Finite Markov chain analysis of genetic algorithms
… Genetic Algorithms on Genetic algorithms …
Finite, discrete-time Markov chain models of genetic algorithms have been used successfully in the past to understand the complex dynamics of a simple GA. Markov chains can exactly model the GA by accounting for all of the stochasticity introduced by various GA operators, such as initialization, selection, crossover, and mutation. Although such models quickly become unwieldy with increasing population size or genome length, they provide initial insights that guide our development of approximate, scalable models. In this study, we use Markov chains to analyze the stochastic e ects of the \niching operator" of a niched GA. Speci cally, we model the e ect of tness sharing on a single-locus genome. Without niching, our model is an absorbing Markov chain. With niching, we are dealing with a \quasi-ergodic" Markov chain. Rather than calculating expected times to absorption, we are interested in steady-state probabilities for positive recurrent states. Established techniques for analyzing ergodic Markov chains give us new insights into the dynamic nature of a niched GA. We explore the stability of the expected steady state distribution achieved by the niched GA. We demonstrate the \niching pressure" as a force separate from the forces of selection, drift, and mutation. Through visualization, we gain intuitions of the relationships among these separate forces. These results generalize beyond the tness sharing algorithm to all types of GA optimization of context dependent functions. In any such function, the GA must nd and maintain a diverse population of cooperative individuals rather than converging to the truly steady state of a uniform population.
Genetic Algorithms Principles Towards Hidden Markov Model
In this paper we propose a general approach based on Genetic Algorithms (GAs) to evolve Hidden Markov Models (HMM). The problem appears when experts assign probability values for HMM, they use only some limited inputs. The assigned probability values might not be accurate to serve in other cases related to the same domain. We introduce an approach based on GAs to find out the suitable probability values for the HMM to be mostly correct in more cases than what have been used to assign the probability values.
Finite Markov Chain Results in Evolutionary Computation: A Tour d'Horizon
1998
The theory of evolutionary computation has been enhanced rapidly during the last decade. This survey is the attempt to summarize the results regarding the limit and nite time behav i o r o f e v olutionary algorithms with nite search spaces and discrete time scale. Results on evolutionary algorithms beyond nite space and discrete time are also presented but with reduced elaboration.
Modelling Hierarchical Genetic Strategy as a Family of Markov Chains
Lecture Notes in Computer Science, 2002
We present Hierarchical Genetic Strategy (HGS) as a family of Markov chains applying Vose's mathematical model for Simple Genetic Algorithm. Studying its asymptotic properties and performing simply experiments we try to compare efficiency of HGS and sequential genetic algorithms.
IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 1998
This paper shows a theoretical property on the Markov chain of genetic algorithms: the stationary distribution focuses on the uniform population with the optimal solution as mutation and crossover probabilities go to zero and some selective pressure dened in this paper goes to innity. Moreover, as a result, a sucient condition for ergodicity is derived when a simulated annealing-like strategy is considered. Additionally, the uniform crossover counterpart of the Vose-Liepins formula is derived using the Markov chain model. Keywords| genetic algorithms, simulated annealing, Markov chain.
An Evolutionary survey on Markov Models
Web mining concern with the extraction of knowledge or information from the world wide web. One of the problem in web mining is to predict user's next web page request. Several techniques for this prediction purpose are employed and some of these are rough set clustering , support vector machine, fuzzy logic, neural network etc [1][2][3][4]. Besides these techniques Markov models are used in web page request prediction. In this paper we discuss about some Markov models and their technique of prediction. Keywords : World wide web , Markov model. 1 Background 1.1 Markov model Model is basically a representation of real world or the view of reality.Markov process is a process to be in more than one state and making transactions among these states.Markov models depicts the maokov process.Markov models are widely used for the purpose of predicting user's web page access request on the basis of previous web history different order markov models are used for this purpose firstly, f...
Some results about the Markov chains associated to GPs and general EAs
Geiringer's theorem is a statement which tells us something about the limiting frequency of occurrence of a certain individual when a classical genetic algorithm is executed in the absence of selection and mutation. Recently Poli, Stephens, Wright and Rowe extended the original theorem of Geiringer to include the case of variable-length genetic algorithms and linear genetic programming. In the current paper a rather powerful finite population version of Geiringer's theorem which has been established recently by Mitavskiy is used to derive a schema-based version of the theorem for nonlinear genetic programming with homologous crossover. The theorem also applies in the presence of " node mutation ". The corresponding formula in case when " node mutation " is present has been established. The limitation of the finite population Geiringer result is that it applies only in the absence of selection. In the current paper we also observe some general inequalities concerning the stationary distribution of the Markov chain associated to an evolutionary algorithm in which selection is the last (output) stage of a cycle. Moreover we prove an " anti-communism " theorem which applies to a wide class of EAs and says that for small enough mutation rate, the stationary distribution of the Markov chain modelling the EA cannot be uniform.
On the Role of Genetic Algorithms in the Pattern Recognition Task of Classification
2017
In this dissertation we ask, formulate an apparatus for answering, and answer the following three questions: Where do Genetic Algorithms fit in the greater scheme of pattern recognition? Given primitive mechanics, can Genetic Algorithms match or exceed the performance of theoretically-based methods? Can we build a generic universal Genetic Algorithm for classification? To answer these questions, we develop a genetic algorithm which optimizes MATLAB classifiers and a variable length genetic algorithm which does classification based entirely on boolean logic. We test these algorithms on disparate datasets rooted in cellular biology, music theory, and medicine. We then get results from these and compare their confusion matrices. For those unfamiliar with Genetic Algorithms, we include a primer on the subject in chapter 1, and include a literature review and our motivations. In Chapter 2, we discuss the development of the algorithms necessary as well as explore other features necessitat...