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Theoretical analysis of steady state genetic algorithms

Alexandru Agapie, Alden H. Wright (2014)

Applications of Mathematics

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are...

Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2003)

RAIRO - Operations Research - Recherche Opérationnelle

We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)

RAIRO - Operations Research

We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Transient random walk in ℤ 2 with stationary orientations

Françoise Pène (2009)

ESAIM: Probability and Statistics

In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412]. We study a random walk in ℤ 2 with random orientations. We suppose that the orientation of the kth floor is given by ξ k , where ( ξ k ) k ∈ ℤ is a stationary sequence of random variables. Once the environment fixed, the random walk can go either up or down or can stay in the present floor (but moving with respect to its orientation). This model was introduced by Campanino and Pétritis in [Markov Process....

Two algorithms based on Markov chains and their application to recognition of protein coding genes in prokaryotic genomes

Małgorzata Grabińska, Paweł Błażej, Paweł Mackiewicz (2013)

Applicationes Mathematicae

Methods based on the theory of Markov chains are most commonly used in the recognition of protein coding sequences. However, they require big learning sets to fill up all elements in transition probability matrices describing dependence between nucleotides in the analyzed sequences. Moreover, gene prediction is strongly influenced by the nucleotide bias measured by e.g. G+C content. In this paper we compare two methods: (i) the classical GeneMark algorithm, which uses a three-periodic non-homogeneous...

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