Deryck Forsyth Brown

Using a Markov network model in a univariate EDA: an empirical cost-benefit analysis

This paper presents an empirical cost-benefit analysis of an algorithm called Distribution Estimation Using MRF with direct sampling (DEUMd). DEUMd belongs to the family of Estimation of Distribution Algorithm (EDA). Particularly it is a univariate EDA. DEUMd uses a computationally more expensive model to estimate the probability distribution than other univariate EDAs. We investigate the performance of DEUMd in a range of optimization problem. Our experiments shows a better performance (in terms of the number of fitness evaluation needed by the algorithm to find a solution and the quality of the solution) of DEUMd on most of the problems analysed in this paper in comparison to that of other univariate EDAs. We conclude that use of a Markov Network in a univariate EDA can be of net benefit in defined set of circumstances.

Approaches to selection and their effect on fitness modelling in an Estimation of Distribution Algorithm

Selection is one of the defining characteristics of an evolutionary algorithm, yet inherent in the selection process is the loss of some information from a population. Poor solutions may provide information about how to bias the search toward good solutions. Many estimation of distribution algorithms (EDAs) use truncation selection which discards all solutions below a certain fitness, thus losing this information. Our previous work on distribution estimation using Markov networks (DEUM) has described an EDA which constructs a model of the fitness function; a unique feature of this approach is that because selective pressure is built into the model itself selection becomes optional. This paper outlines a series of experiments which make use of this property to examine the effects of selection on the population. We look at the impact of selecting only highly fit solutions, only poor solutions, selecting a mixture of highly fit and poor solutions, and abandoning selection altogether. We show that in some circumstances, particularly where some information about the problem is already known, selection of the fittest only is suboptimal.

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

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 DEUMd. DEUM and DEUMd 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.

Markov Random Field Modelling of Royal Road Genetic Algorithms

Markov Random Fields (MRFs) [5] are a class of probabalistic models that have been applied for many years to the analysis of visual patterns or textures. In this paper, our objective is to establish MRFs as an interesting approach to modelling genetic algorithms. Our approach bears strong similarities to recent work on the Bayesian Optimisation Algorithm [9], but there are also some significant differences. We establish a theoretical result that every genetic algorithm problem can be characterised in terms of a MRF model. This allows us to construct an explicit probabilistic model of the GA fitness function. The model can be used to generate chromosomes, and derive a MRF fitness measure for the population. We then use a specific MRF model to analyse two Royal Road problems, relating our analysis to that of Mitchell et al. [7].

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

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.

Estimating the distribution in an EDA

This paper presents an extension to our work on estimating the probability distribution by using a Markov Random Field (MRF) model in an Estimation of Distribution Algorithm (EDA) [1]. We propose a method that directly samples a MRF model to generate new population. We also present a new EDA, called the Distribution Estimation Using MRF with direct sampling (DEUMd), that uses this method, and iteratively refines the probability distribution to generate better solutions. Our experiments show that the direct sampling of a MRF model as estimation of distribution provides a significant advantage over other techniques on problems where a univariate EDA is typically used.

Incorporating a Metropolis method in a distribution estimation using Markov random field algorithm

Markov random field (MRF) modelling techniques have been recently proposed as a novel approach to probabilistic modelling for estimation of distribution algorithms (EDAs) (S. K. Shakya et al., 2004). An EDA using this technique was called distribution estimation using Markov random fields (DEUM). DEUM was later extended to DEUM/sub d/ (S. Shakya et al., 2005). DEUM and DEUM/sub 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/sub d/ to incorporate a simple Metropolis method and empirically shows that for linear univariate problems the proposed univariate MRF models are very effective. In particular, the proposed DEUM/sub d/ algorithm can find the solution in O(n) fitness evaluations. Furthermore, we suggest that the Metropolis method can also be used to extend the DEUM approach to multivariate problems.