Markov Random Field Modelling of Royal Road Genetic Algorithms

2006 IEEE International Conference on Evolutionary Computation

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Markov Random Field (MRF) modelling techniques have been recently proposed as a novel approach to probabilistic modelling for Estimation of Distribution Algorithms (EDAs). An EDA using this technique was called Distribution Estimation using Markov Random Fields (DEUM). DEUM was later extended to DEUM d . DEUM and DEUM d use a univariate model of probability distribution, and have been shown to perform better than other univariate EDAs for a range of optimization problems. This paper extends DEUM to use a bivariate model and applies it to the Ising spin glass problems. We propose two variants of DEUM that use different sampling techniques. Our experimental result show a noticeable gain in performance.

“…In [1], MRF theory was used to provide a formulation of the jpd, p(x), that relates solution fitness, f (X = x) (or simply f (x)), to the energy U (x). To be precise:…”

Section: Ieee Congress On Evolutionary Computationmentioning

confidence: 99%

Solving the Ising Spin Glass Problem using a Bivariate EDA based on Markov Random Fields

Shakya

2006 IEEE International Conference on Evolutionary Computation

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“…In [1] it was shown that an equation for each individual in a population may be derived from the joint probability distribution shown in (1). This relates solution fitness to an energy function calculated from the values taken by variables in a set of individuals:…”

Section: Background 31 Distribution Estimation Using Markov Networkmentioning

confidence: 99%

“…The initial theory was published in [1] and DEUM was first presented in [11]. Background on DEUM can be found in [12].…”

Section: Introductionmentioning

confidence: 99%

Solving the MAXSAT problem using a multivariate EDA based on Markov networks

Brownlee

Proceedings of the 9th Annual Conference Companion on Genetic and Evolutionary Computation

2007

Markov Networks (also known as Markov Random Fields) have been proposed as a new approach to probabilistic modelling in Estimation of Distribution Algorithms (EDAs). An EDA employing this approach called Distribution Estimation Using Markov Networks (DEUM) has been proposed and shown to work well on a variety of problems, using a unique fitness modelling approach. Previously DEUM has only been demonstrated on univariate and bivariate complexity problems. Here we show that it can be extended to a difficult multivariate problem and is capable of accurately modelling a fitness function and locating an optimum with a very small number of function evaluations.

“…In [4], MRF theory was used to provide a formulation of the joint probability distribution that relates solution fitness, f (x), to an energy function, U (x), calculated from the values of the solution variables. To be precise:…”

Section: Mrf Approach To Probabilistic Modellingmentioning

confidence: 99%

“…Here, f (x) is the fitness of an individual x, U (x) is an energy function derived from the allele values, and T is a temperature coefficient, which in [4] has a constant value of 1. The summations are over all possible solutions y. U (x) gives the full specification of the joint probability distribution, so it can be regarded as a probabilistic model of the fitness function.…”

Section: Mrf Approach To Probabilistic Modellingmentioning

confidence: 99%

Incorporating a Metropolis method in a Distribution Estimation using Markov Random Field Algorithm

Shakya

2005 IEEE Congress on Evolutionary Computation

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