Optimization by estimation of distribution with DEUM framework based on Markov random fields

Shakya, Siddhartha; McCall, John

doi:10.1007/s11633-007-0262-6

Cited by 66 publications

(25 citation statements)

References 19 publications

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“…The deceptive3 function [13] (9) and the trap function [41] (15) are used in our experiments. Both of these functions are widely used in the EDA literature to test the performance of different EDAs [34,44,55].…”

Section: Function Benchmarkmentioning

confidence: 99%

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A Markovianity based optimisation algorithm

Shakya

Santana

Lozano

2011

Genet Program Evolvable Mach

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Several Estimation of Distribution Algorithms (EDAs) based on Markov networks have been recently proposed. The key idea behind these EDAs was to factorise the joint probability distribution of solution variables in terms of cliques in the undirected graph. As such, they made use of the global Markov property of the Markov network in one form or another. This paper presents a Markov Network based EDA that is based on the use of the local Markov property, the Markovianity, and does not directly model the joint distribution. We call it Markovianity based Optimisation Algorithm. The algorithm combines a novel method for extracting the neighbourhood structure from the mutual information between the variables, with a Gibbs sampler method to generate new points. We present an extensive empirical validation of the algorithm on problems with complex interactions, comparing its performance with other EDAs that use higher order interactions. We extend the analysis to other functions with discrete representation, where EDA results are scarce, comparing the algorithm with state of the art EDAs that use marginal product factorisations.

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Section: Function Benchmarkmentioning

confidence: 99%

“…Some research on the use of undirected graphical models (Markov networks) [3,27,37] in EDAs has also been done [47,48,50,[54][55][56][57]. Nevertheless, in comparison with their counterparts, EDAs that use undirected models have been less studied and fewer applications to practical problems have been introduced.…”

Section: Introductionmentioning

confidence: 99%

A Markovianity based optimisation algorithm

Shakya

Santana

Lozano

2011

Genet Program Evolvable Mach

Self Cite

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“…Other EDAs, such as those based on Bayesian networks and Markov networks (Santana 2005;Shakya and McCall 2007), learn the structure and parameters of the model in each generation.…”

Section: Factorized Distributionsmentioning

confidence: 99%

“…In Mateda-2.0, Cliques are also used to represent the neighborhood structure in models based on Markov networks (Santana 2005;Shakya and McCall 2007). In this particular case, the first column of Cliques(i,:) represents the number of neighbors for variable X i .…”

Section: General Description Of the Mateda-20 Implementationmentioning

confidence: 99%

Mateda-2.0: AMATLABPackage for the Implementation and Analysis of Estimation of Distribution Algorithms

Santana¹,

Bielza²,

Larrañaga³

et al. 2010

J. Stat. Soft.

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This paper describes Mateda-2.0, a MATLAB package for estimation of distribution algorithms (EDAs). This package can be used to solve single and multi-objective discrete and continuous optimization problems using EDAs based on undirected and directed probabilistic graphical models. The implementation contains several methods commonly employed by EDAs. It is also conceived as an open package to allow users to incorporate different combinations of selection, learning, sampling, and local search procedures. Additionally, it includes methods to extract, process and visualize the structures learned by the probabilistic models. This way, it can unveil previously unknown information about the optimization problem domain. Mateda-2.0 also incorporates a module for creating and validating function models based on the probabilistic models learned by EDAs.

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“…The performance of an EDA highly depends on how well it estimates and samples the probability distribution. A wide variety of EDAs using probabilistic graphical modeling techniques [12][13][14] to estimate and sample the probability distribution have been proposed and are the subject of active research. However, EDA using probabilistic graphical modeling techniques generally spend too much time on the learning about the probability distribution of the promising individuals.…”

Section: Introductionmentioning

confidence: 99%

EDA-Based Multi-objective Optimization Using Preference Order Ranking and Multivariate Gaussian Copula

Gao

Peng

et al. 2013

Advances in Neural Networks – ISNN 2013

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Abstract. Estimation of distribution algorithms (EDAs) are a class of evolutionary optimization algorithms based on probability distribution model. This article extends the basic EDAs for tackling multi-objective optimization problems by incorporating multivariate Gaussian copulas for constructing probability distribution model, and using the concept of preference order. In the algorithm, the multivariate Gaussian copula is used to construct probability distribution model in EDAs. By estimating Kendall's τ and using the relationship of correlation matrix and Kendall's τ, correlation matrix R in Gaussian copula are firstly estimated from the current population, and then is used to generate offsprings. Preference order is used to identify the best individuals in order to guide the search process. The population with the current population and current offsprings population is sorted based on preference order, and the best individuals are selected to form the next population. The algorithm is tested to compare with NSGA-II, GDE, MOEP and MOPSO based on convergence metric and diversity metric using a set of benchmark functions. The experimental results show that the algorithm is effective on the benchmark functions.

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Optimization by estimation of distribution with DEUM framework based on Markov random fields

Cited by 66 publications

References 19 publications

A Markovianity based optimisation algorithm

A Markovianity based optimisation algorithm

Mateda-2.0: AMATLABPackage for the Implementation and Analysis of Estimation of Distribution Algorithms

EDA-Based Multi-objective Optimization Using Preference Order Ranking and Multivariate Gaussian Copula

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