Convergence Analysis of Surrogate Assisted (1+1) Evolutionary Algorithm

2012 ◽  
Vol 263-266 ◽  
pp. 2339-2343
Author(s):  
Ying Ming Jin
Keyword(s):  
Markov Chain ◽  
Evolutionary Algorithm ◽  
Convergence Analysis ◽  
Perturbation Analysis ◽  
Surrogate Model ◽  
Transition Matrix ◽  
Matrix Perturbation ◽  
Finite Markov Chain ◽  
Matrix Perturbation Analysis

This paper analyzes the convergence deviation of surrogate assisted (1+1)EA. A model of surrogate assisted (1+1)EA can be built by the finite markov chain, then we got the transition matrix of this algorithm. The deviation of surrogate model can be expressed by the perturbation of transition matrix. So we can estimate the convergence deviation with the method of matrix perturbation analysis. Analyzing of the convergence changes brought by surrogate model’s deviations can help us to have a better select of the surrogate model.

Optimal decision procedures for finite Markov chains. Part III: General convex systems

1973 ◽  
Vol 5 (3) ◽  
pp. 541-553 ◽  
Author(s):  
John Bather
Keyword(s):  
Markov Chain ◽  
Transition Matrix ◽  
Classification Scheme ◽  
Optimal Decision ◽  
Finite Markov Chain ◽  
Long Run ◽  
General Convex ◽  
Finite Markov Chains ◽  
Different Levels ◽  
Family Of Distributions

This paper is concerned with the general problem of finding an optimal transition matrix for a finite Markov chain, where the probabilities for each transition must be chosen from a given convex family of distributions. The immediate cost is determined by this choice, but it is required to minimise the average expected cost in the long run. The problem is investigated by classifying the states according to the accessibility relations between them. If an optimal policy exists, it can be found by considering the convex subsystems associated with the states at different levels in the classification scheme.

Geometric bounds on iterative approximations for nearly completely decomposable Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 521-529 ◽  
Author(s):  
Guy Louchard ◽  
Guy Latouche
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Perturbation Analysis ◽  
Stochastic Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Finite Markov Chain ◽  
Stationary Probability Vector

We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

Addenda to processes defined on a finite Markov chain

1967 ◽  
Vol 63 (1) ◽  
pp. 187-193 ◽  
Author(s):  
Julian Keilson ◽  
David M. G. Wishart
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Transition Matrix ◽  
Finite Markov Chain ◽  
Marginal Process ◽  
Stochastic Transition ◽  
Matrix Distribution ◽  
Finite Markov Chains ◽  
Image Position ◽  
Irreducible Markov Chain

Introduction. Two previous papers (1,2) have dealt with additive processes defined on finite Markov chains. Such a process in discrete time may be treated as a bivariate Markov process {R(k), X(k)}. The process R(k) is an irreducible Markov chain on states r = 1, 2, …, R governed by a stochastic transition matrix B0 with components brs. The marginal process X(k) ‘defined’ on the chain R(k) is a sum of random increments ξ(i) dependent on the chain, i.e. if the ith transition takes the chain from state r to state s, ξ,(i) is chosen from a distribution function Drs(x) indexed by r and s. The distribution of the bivariate process may be represented by a vector F(x, k) with componentsThese are generated recursively by the relationwhere the increment matrix distribution B(x) has components brsDrs(x). We denote the nth moment of B(x) by Bn = ∫xndB(x), so that B0 = B(∞).

Image registration based on matrix perturbation analysis using spectral graph

2009 ◽  
Vol 7 (11) ◽  
pp. 996-1000 ◽  
Author(s):  
冷成财 Chengcai Leng ◽  
田铮 Zheng Tian ◽  
李婧 Jing Li ◽  
丁明涛 Mingtao Ding
Keyword(s):  
Image Registration ◽  
Perturbation Analysis ◽  
Matrix Perturbation ◽  
Spectral Graph ◽  
Matrix Perturbation Analysis

Geometric bounds on iterative approximations for nearly completely decomposable Markov chains

1990 ◽  
Vol 27 (3) ◽  
pp. 521-529 ◽  
Author(s):  
Guy Louchard ◽  
Guy Latouche
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Perturbation Analysis ◽  
Stochastic Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Finite Markov Chain ◽  
Stationary Probability Vector

We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

A Matrix Factorization Problem in the Theory of Random Variables Defined on a Finite Markov Chain

1962 ◽  
Vol 58 (2) ◽  
pp. 268-285 ◽  
Author(s):  
H. D. Miller
Keyword(s):  
Markov Chain ◽  
Matrix Factorization ◽  
Transition Matrix ◽  
Random Variables ◽  
Finite Markov Chain ◽  
Stieltjes Transform ◽  
Factorization Problem ◽  
Regular Elements ◽  
The Matrix ◽  
Image Position

SummaryLet {kr} (r = 0, 1, 2, …; 1 ≤ kr ≤ h) be a positively regular, finite Markov chain with transition matrix P = (pjk). For each possible transition j → k let gjk(x)(− ∞ ≤ x ≤ ∞) be a given distribution function. The sequence of random variables {ξr} is defined where ξr has the distribution gjk(x) if the rth transition takes the chain from state j to state k. It is supposed that each distribution gjk(x) admits a two-sided Laplace-Stieltjes transform in a real t-interval surrounding t = 0. Let P(t) denote the matrix {Pjkmjk(t)}. It is shown, using probability arguments, that I − sP(t) admits a Wiener-Hopf type of factorization in two ways for suitable values of s where the plus-factors are non-singular, bounded and have regular elements in a right half of the complex t-plane and the minus-factors have similar properties in an overlapping left half-plane (Theorem 1).

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