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Echegoyen C, Mendiburu A, Santana R and Lozano JA (2012), "Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis", IEEE Transactions on Evolutionary Computation. Vol. 16(2), pp. 173-189.

[Abstract] [BibTeX] [URL]
Abstract: The successful application of estimation of distribution algorithms (EDAs) to solve different kinds of problems has reinforced their candidature as promising black-box optimization tools. However, their internal behavior is still not completely understood and therefore it is necessary to work in this direction in order to advance their development. This paper presents a methodology of analysis which provides new information about the behavior of EDAs by quantitatively analyzing the probabilistic models learned during the search. We particularly focus on calculating the probabilities of the optimal solutions, the most probable solution given by the model and the best individual of the population at each step of the algorithm. We carry out the analysis by optimizing functions of different nature such as Trap5, two variants of Ising spin glass and Max-SAT. By using different structures in the probabilistic models, we also analyze the impact of the structural model accuracy in the quantitative behavior of EDAs. In addition, the objective function values of our analyzed key solutions are contrasted with their probability values in order to study the connection between function and probabilistic models. The results not only show information about the internal behavior of EDAs, but also about the quality of the optimization process and setup of the parameters, the relationship between the probabilistic model and the fitness function, and even about the problem itself. Furthermore, the results allow us to discover common patterns of behavior in EDAs and propose new ideas in the development of this type of algorithms.
BibTeX: 
@article{Echegoyen_et_al:2012a,
  author = {C. Echegoyen and A. Mendiburu and R. Santana and J. A. Lozano},
  title = {Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis},
  journal = {IEEE Transactions on Evolutionary Computation},
  year = {2012},
  volume = {16},
  number = {2},
  pages = {173-189},
  url = {http://dx.doi.org/10.1109/TEVC.2010.2102037}
}
Echegoyen C, Mendiburu A, Santana R and Lozano JA (2012), "Clases de equivalencia en algoritmos de estimación de distribuciones", In Proceedings of the VIII Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB-2012). Albacete

[Abstract] [BibTeX] [URL]
Abstract: Entender la relación que surge entre un algoritmo de búsqueda y el espacio de problemas es una cuestión fundamental en el campo de la optimización. En este trabajo nos centramos en la elaboración de taxonomías de problemas para algoritmos de estıtimación de distribuciones (EDAs). Mediante la utilización del modelo de población infinita y asumiendo selección basada en el ranqueo de las soluciones, agrupamos las funciones inyectivas segun el comportamiento del EDA. Para llevar a cabo esta clasificación, se define una relación de equivalencia entre funciones que permite particionar el espacio de funciones en clases de equivalencia para las cuales el algoritmo tiene un comportamiento similar. Considerar diferentes modelos probabilísticos en el EDA genera diferentes particiones del conjunto de posibles problemas. Como consecuencia natural de las definiciones, todas las funciones objetivo están en la misma clase de equivalencia cuando el algoritmo no impone restricciones sobre el modelo probabilístico. Con el fin de crear una primera taxonomía de problemas, nos centramos en la partición que se produce cuando se considera un modelo probabilístico que asume independencia entre las variables. Para ello, primero fijamos las condiciones suficientes para decidir si dos funciones son equivalentes y segundo, obtenemos los operadores para describir y contar los miembros de una clase. En general, el presente trabajo sienta las bases para continuar el estudio del comportamiento de los EDAs y su relación con los problemas de optimización.
BibTeX: 
@inproceedings{Echegoyen_et_al:2012b,
  author = {C. Echegoyen and A. Mendiburu and R. Santana and J. A. Lozano},
  title = {Clases de equivalencia en algoritmos de estimación de distribuciones},
  booktitle = {Proceedings of the VIII Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB-2012)},
  year = {2012},
  url = {http://simd.albacete.org/maeb2012/papers/paper_85.pdf}
}
Karshenas H, Santana R, Bielza C and Larrañaga P (2012), "Continuous estimation of distribution algorithms based on factorized Gaussian Markov networks", In Markov Networks in Evolutionary Computation. , pp. 157-173. Springer.

[Abstract] [BibTeX] [URL]
Abstract: Because of their intrinsic properties, the majority of the estimation of distribution algorithms proposed for continuous optimization problems are based on the Gaussian distribution assumption for the variables. This paper looks over the relation between the general multivariate Gaussian distribution and the popular undirected graphical model of Markov networks and discusses how they can be employed in estimation of distribution algorithms for continuous optimization. A number of learning and sampling techniques for thesemodels, including the promising regularized model learning, are also reviewed and their application for function optimization in the context of estimation of distribution algorithms is studied.
BibTeX: 
@incollection{Karshenas_et_al:2012,
  author = {H. Karshenas and R. Santana and C. Bielza and P. Larrañaga},
  editor = {S. Shakya and R. Santana},
  title = {Continuous estimation of distribution algorithms based on factorized Gaussian Markov networks},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {157-173},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_10}
}
Karshenas H, Santana R, Bielza C and Larrañaga P (2012), "Multi-objective optimization based on joint probabilistic modeling of objectives and variables". Research Report at: Department of Artificial Intelligence, Faculty of Informatics, Technical University of Madrid. (UPM-FI/DIA/2012-2)

[Abstract] [BibTeX] [URL]
Abstract: This paper proposes a new multi-objective estimation of distribution algorithm (EDA) based on joint modeling of objectives and variables. This EDA uses the multi-dimensional Bayesian network as its probabilistic model. In this way it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learnt between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm to find better trade-off solutions to the multi-objective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multi-objective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is applied to the set of walking fish group (WFG) problems, and its optimization performance is compared with an evolutionary algorithm and another multi-objective EDA. The experimental results show that the proposed algorithm performs significantly better on many of the problems and for different objective space dimensions, and achieves comparable results on some compared with the other algorithms.
BibTeX: 
@techreport{Karshenas_et_al:2012b,
  author = {H. Karshenas and R. Santana and C. Bielza and P. Larrañaga},
  title = {Multi-objective optimization based on joint probabilistic modeling of objectives and variables},
  school = {Department of Artificial Intelligence, Faculty of Informatics, Technical University of Madrid},
  year = {2012},
  number = {UPM-FI/DIA/2012-2},
  url = {https://link.springer.com/chapter/10.1007/978-3-642-19893-9_21}
}
Larrañaga P, Karshenas H, Bielza C and Santana R (2012), "A review on probabilistic graphical models in evolutionary computation", Journal of Heuristics. Vol. 18(5), pp. 795-819.

[Abstract] [BibTeX] [URL]
Abstract: Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.
BibTeX: 
@article{Larranaga_et_al:2012,
  author = {P. Larrañaga and H. Karshenas and C. Bielza and R. Santana},
  title = {A review on probabilistic graphical models in evolutionary computation},
  journal = {Journal of Heuristics},
  year = {2012},
  volume = {18},
  number = {5},
  pages = {795--819},
  url = {http://dx.doi.org/10.1007/s10732-012-9208-4}
}
Mendiburu A, Santana R and Lozano JA (2012), "Fast fitness improvements in Estimation of Distribution Algorithms using belief propagation", In Markov Networks in Evolutionary Computation. , pp. 141-155. Springer.

[Abstract] [BibTeX] [URL]
Abstract: Factor graphs can serve to represent Markov networks and Bayesian networks models. They can also be employed to implement efficient inference procedures such as belief propagation. In this paper we introduce a flexible implementation of belief propagation on factor graphs in the context of estimation of distribution algorithms (EDAs). By using a transformation from Bayesian networks to factor graphs, we show the way in which belief propagation can be inserted within the Estimation of Bayesian Networks Algorithm (EBNA). The objective of the proposed variation is to increase the search capabilities by extracting information of the, computationally costly to learn, Bayesian network. Belief Propagation applied to graphs with cycles allows to find (with a low computational cost), in many scenarios, the point with the highest probability of a Bayesian network. We carry out some experiments to show how this modification can increase the potentialities of Estimation of Distribution Algorithms.
BibTeX: 
@incollection{Mendiburu_et_al:2012,
  author = {A. Mendiburu and R. Santana and J. A. Lozano},
  editor = {R. Santana and S. Shakya},
  title = {Fast fitness improvements in Estimation of Distribution Algorithms using belief propagation},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {141-155},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_9}
}
Santana R and Shakya S (2012), "Probabilistic Graphical Models and Markov Networks", In Markov Networks in Evolutionary Computation. , pp. 3-19. Springer.

[Abstract] [BibTeX] [URL]
Abstract: This chapter introduces probabilistic graphical models and explain their use for modelling probabilistic relationships between variables in the context of optimisation with EDAs. We focus on Markov networks models and review different algorithms used to learn and sample Markov networks. Other probabilistic graphical models are also reviewed and their differences with Markov networks are analysed.
BibTeX: 
@incollection{Santana_and_Shakya:2012a,
  author = {R. Santana and S. Shakya},
  editor = {S. Shakya and R. Santana},
  title = {Probabilistic Graphical Models and Markov Networks},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {3-19},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_1}
}
Santana R, Bielza C and Larrañaga P (2012), "Regularized logistic regression and multi-objective variable selection for classifying MEG data", Biological Cybernetics. Vol. 106(6-7), pp. 389-405.

[Abstract] [BibTeX] [URL]
Abstract: This paper addresses the question of maximizing classifier accuracy for classifying task-related mental activity from Magnetoencelophalography (MEG) data. We propose the use of different sources of information and introduce an automatic channel selection procedure. To determine an informative set of channels, our approach combines a variety of machine learning algorithms: feature subset selection methods, classifiers based on regularized logistic regression, information fusion, and multiobjective optimization based on probabilistic modeling of the search space. The experimental results show that our proposal is able to improve classification accuracy compared to approaches whose classifiers use only one type of MEG information or for which the set of channels is fixed a priori.
BibTeX: 
@article{Santana_et_al:2012,
  author = {R. Santana and C. Bielza and P. Larrañaga},
  title = {Regularized logistic regression and multi-objective variable selection for classifying MEG data},
  journal = {Biological Cybernetics},
  year = {2012},
  volume = {106},
  number = {6-7},
  pages = {389-405},
  url = {http://dx.doi.org/10.1007/s00422-012-0506-6}
}
Santana R, Bonnet L, Légeny J and Lécuyer A (2012), "Introducing the use of model-based evolutionary algorithms for EEG-based motor imagery classification", In Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012. Philadelphia, US , pp. 1159-1166. ACM Press.

[Abstract] [BibTeX] [URL]
Abstract: Brain computer interfaces (BCIs) allow the direct human-computer interaction without the need of motor intervention. To properly and efficiently decode brain signals into computer commands the application of machine-learning techniques is required. Evolutionary algorithms have been increasingly applied in different steps of BCI implementations. In this paper we introduce the use of the covariance matrix adaptation evolution strategy (CMA-ES) for BCI systems based on motor imagery. The optimization algorithm is used to evolve linear classifiers able to outperform other traditional classifiers. We also analyze the role of modeling variables interactions for additional insight in the understanding of the BCI paradigms.
BibTeX: 
@inproceedings{Santana_et_al:2012c,
  author = {R. Santana and L. Bonnet and J. Légeny and A. Lécuyer},
  title = {Introducing the use of model-based evolutionary algorithms for EEG-based motor imagery classification},
  booktitle = {Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012},
  publisher = {ACM Press},
  year = {2012},
  pages = {1159--1166},
  url = {http://dl.acm.org/citation.cfm?id=2330323}
}
Santana R, Bielza C and Larrañaga P (2012), "Maximizing the number of polychronous groups in spiking networks", In Companion Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012. Philadelphia, US , pp. 1499-1500. ACM Press.

[Abstract] [BibTeX] [URL]
Abstract: In this paper we investigate the effect of biasing the axonal connection delay values in the number of polychronous groups produced for a spiking neuron network model. We use an estimation of distribution algorithm (EDA) that learns tree models to search for optimal delay configurations. Our results indicate that the introduced approach can be used to considerably increase the number of such groups.
BibTeX: 
@inproceedings{Santana_et_al:2012d,
  author = {R. Santana and C. Bielza and P. Larrañaga},
  title = {Maximizing the number of polychronous groups in spiking networks},
  booktitle = {Companion Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012},
  publisher = {ACM Press},
  year = {2012},
  pages = {1499--1500},
  url = {http://dl.acm.org/citation.cfm?id=2331012}
}
Santana R, Mendiburu A and Lozano JA (2012), "Evolving NK-complexity for evolutionary solvers", In Companion Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012. Philadelphia, US , pp. 1473-1474. ACM Press.

[Abstract] [BibTeX] [URL]
Abstract: In this paper we empirically investigate the structural characteristics that can help to predict the complexity of NK-landscape instances for estimation of distribution algorithms (EDAs). We evolve instances that maximize the EDA complexity in terms of its success rate. Similarly, instances that minimize the algorithm complexity are evolved. We then identify network measures, computed from the structures of the NK-landscape instances, that have a statistically significant difference between the set of easy and hard instances. The features identified are consistently significant for different values of N and K.
BibTeX: 
@inproceedings{Santana_et_al:2012e,
  author = {R. Santana and A. Mendiburu and J. A. Lozano},
  title = {Evolving NK-complexity for evolutionary solvers},
  booktitle = {Companion Proceedings of the 2012 Genetic and Evolutionary Computation Conference GECCO-2012},
  publisher = {ACM Press},
  year = {2012},
  pages = {1473--1474},
  url = {http://dl.acm.org/citation.cfm?id=2330997}
}
Santana R, Mendiburu A and Lozano JA (2012), "Structural transfer using EDAs: An application to multi-marker tagging SNP selection", In Proceedings of the 2012 Congress on Evolutionary Computation CEC-2012. Brisbane, Australia , pp. 3484-3491. IEEE Press.

[Abstract] [BibTeX] [URL]
Abstract: In this paper we investigate the question of transfer learning in evolutionary optimization using estimation of distribution algorithms. We propose a framework for transfer learning between related optimization problems by means of structural transfer. Different methods for incrementing or replacing the (possibly unavailable) structural information of the target optimization problem are presented. As a test case we solve the multi-marker tagging single-nucleotide polymorphism (SNP) selection problem, a real world problem from genetics. The introduced variants of structural transfer are validated in the computation of tagging SNPs on a database of 1167 individuals from 58 human populations worldwide. Our experimental results show significant improvements over EDAs that do not incorporate information from related problems.
BibTeX: 
@inproceedings{Santana_et_al:2012f,
  author = {R. Santana and A. Mendiburu and J. A. Lozano},
  title = {Structural transfer using EDAs: An application to multi-marker tagging SNP selection},
  booktitle = {Proceedings of the 2012 Congress on Evolutionary Computation CEC-2012},
  publisher = {IEEE Press},
  year = {2012},
  pages = {3484-3491},
  note = {Best Paper Award of 2012 Congress on Evolutionary Computation},
  url = {http://dx.doi.org/10.1109/CEC.2012.6252963}
}
Santana R, Mendiburu A and Lozano JA (2012), "An analysis of the use of probabilistic modeling for synaptic connectivity prediction from genomic data", In Proceedings of the 2012 Congress on Evolutionary Computation CEC-2012. Brisbane, Australia , pp. 3221-3228. IEEE Press.

[Abstract] [BibTeX] [URL]
Abstract: The identification of the specific genes that influence particular phenotypes is a common problem in genetic studies. In this paper we address the problem of determining the influence of gene joint expression in synapse predictability. The question is posed as an optimization problem in which the conditional entropy of gene subsets with respect to the synaptic connectivity phenotype is minimized. We investigate the use of single- and multi-objective estimation of distribution algorithms and focus on real data from C. elegans synaptic connectivity. We show that the introduced algorithms are able to compute gene sets that allow an accurate synapse predictability. However, the multi-objective approach can simultaneously search for gene sets with different number of genes. Our results also indicate that optimization problems defined on constrained binary spaces remain challenging for the conception of competitive estimation of distribution algorithm.
BibTeX: 
@inproceedings{Santana_et_al:2012g,
  author = {R. Santana and A. Mendiburu and J. A. Lozano},
  title = {An analysis of the use of probabilistic modeling for synaptic connectivity prediction from genomic data},
  booktitle = {Proceedings of the 2012 Congress on Evolutionary Computation CEC-2012},
  publisher = {IEEE Press},
  year = {2012},
  pages = {3221--3228},
  url = {http://dx.doi.org/10.1109/CEC.2012.6252997}
}
Santana R, Bielza C and Larrañaga P (2012), "Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models", BMC Neuroscience. Vol. 13(Suppl 1), pp. P100. BioMed Central.

[Abstract] [BibTeX] [URL]
Abstract: In this paper we propose a probabilistic approach based on the computation of the Boltzmann distribution and the mutual information of conductance interactions to learn higher-order, not necessarily pair-wise, potential co-regulation mechanisms from a database of the crustacean stomatogastric ganglion pyloric circuit models.
BibTeX: 
@article{Santana_et_al:2012h,
  author = {Santana, R. and Bielza, C. and Larrañaga, P.},
  title = {Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models},
  journal = {BMC Neuroscience},
  publisher = {BioMed Central},
  year = {2012},
  volume = {13},
  number = {Suppl 1},
  pages = {P100},
  url = {http://dx.doi.org/10.1186/1471-2202-13-S1-P100}
}
Santana R, Mendiburu A and Lozano JA (2012), "New methods for generating populations in Markov network based EDAs: Decimation strategies and model-based template recombination". Research Report at: Department of Computer Science and Artificial Intelligence, University of the Basque Country., December, 2012. (EHU-KZAA-TR:2012-05)

[Abstract] [BibTeX] [URL]
Abstract: Methods for generating a new population are a fundamental component of estimation of distribution algorithms (EDAs). They serve to transfer the information contained in the probabilistic model to the new generated population. In EDAs based on Markov networks, methods for generating new populations usually discard information contained in the model to gain in efficiency. Other methods like Gibbs sampling use information about all interactions in the model but are computationally very costly. In this paper we propose new methods for generating new solutions in EDAs based on Markov networks. We introduce approaches based on inference methods for computing the most probable configurations and model-based template recombination. We show that the application of different variants of inference methods can increase the EDAs convergence rate and reduce the number of function evaluations needed to find the optimum of binary and non-binary discrete functions.
BibTeX: 
@techreport{Santana_et_al:2012i,
  author = {R. Santana and A. Mendiburu and J. A. Lozano},
  title = {New methods for generating populations in Markov network based EDAs: Decimation strategies and model-based template recombination},
  school = {Department of Computer Science and Artificial Intelligence, University of the Basque Country},
  year = {2012},
  number = {EHU-KZAA-TR:2012-05},
  url = {http://hdl.handle.net/10810/9180}
}
Santana R, Mendiburu A and Lozano JA (2012), "Using network measures to test evolved NK-landscapes". Thesis at: Department of Computer Science and Artificial Intelligence, University of the Basque Country., July, 2012. (EHU-KZAA-TR:2012-03)

[Abstract] [BibTeX] [URL]
Abstract:In this paper we empirically investigate which are the structural characteristics that can help to predict the complexity of NK-landscape instances for estimation of distribution algorithms. To this end, we evolve instances that maximize the estimation of distribution algorithm complexity in terms of its success rate. Similarly, instances that minimize the algorithm complexity are evolved. We then identify network measures, computed from the structures of the NK-landscape instances, that have a statistically significant difference between the set of easy and hard instances. The features identified are consistently significant for different values of N and K.
BibTeX: 
@techreport{Santana_et_al:2012j,
  author = {R. Santana and A. Mendiburu and J. A. Lozano},
  title = {Using network measures to test evolved NK-landscapes},
  school = {Department of Computer Science and Artificial Intelligence, University of the Basque Country},
  year = {2012},
  number = {EHU-KZAA-TR:2012-03},
  url = {http://hdl.handle.net/10810/8282}  
}
Santana R (2012), "MN-EDA and the Use of Clique-Based Factorisations in EDAs", In Markov Networks in Evolutionary Computation. , pp. 73-87. Springer.

[Abstract] [BibTeX] [URL]
Abstract: This chapter discusses the important role played by factorisations in the study of EDAs and presents the Markov network estimation of distribution algorithm (MN-EDA) as a classical example of the EDAs based on the use of undirected graphs. The chapter also reviews recent work on the use of clique-based decompositions and other approximations methods inspired in the field of statistical physics with direct application to EDAs.
BibTeX: 
@incollection{Santana:2012,
  author = {R. Santana},
  editor = {S. Shakya and R. Santana},
  title = {MN-EDA and the Use of Clique-Based Factorisations in EDAs},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {73-87},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_5}
}
Shakya S and Santana R (2012), "A Review of Estimation of Distribution Algorithms and Markov Networks", In Markov Networks in Evolutionary Computation. , pp. 21-37. Springer.

[Abstract] [BibTeX] [URL]
Abstract: This chapter reviews some of the popular EDAs based on Markov Networks. It starts by giving introduction to general EDAs and describes the motivation behind their emergence. It then categorises EDAs according to the type of probabilistic models they use (directed model based, undirected model based and common model based) and briefly lists some of the popular EDAs in each categories. It then further focuses on undirected model based EDAs, describes their general workflow and the history, and briefly reviews some of the popular EDAs based on undirected models. It also outlines some of the current research work in this area.
BibTeX: 
@incollection{Shakya_and_Santana:2012a,
  author = {S. Shakya and R. Santana},
  editor = {S. Shakya and R. Santana},
  title = {A Review of Estimation of Distribution Algorithms and Markov Networks},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {21-37},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_2}
}
Shakya S and Santana R (2012), "MOA - Markovian Optimisation Algorithm", In Markov Networks in Evolutionary Computation. , pp. 39-53. Springer.

[Abstract] [BibTeX] [URL]
Abstract: In this chapter we describe Markovian Optimisation Algorithm (MOA), one of the recent developments in MN based EDA. It uses the local Markov property to model the dependency and directly sample from it without needing to approximate a complex join probability distribution model. MOA has a much simpler workflow in comparison to its global property based counter parts, since expensive processes to finding cliques, and building and estimating clique potential functions are avoided. The chapter is intended as an introductory chapter, and describes the motivation and the workflow of MOA. It also reviews some of the results obtained with it.
BibTeX: 
@incollection{Shakya_and_Santana:2012b,
  author = {S. Shakya and R. Santana},
  editor = {S. Shakya and R. Santana},
  title = {MOA - Markovian Optimisation Algorithm},
  booktitle = {Markov Networks in Evolutionary Computation},
  publisher = {Springer},
  year = {2012},
  pages = {39-53},
  url = {http://dx.doi.org/10.1007/978-3-642-28900-2_3}
}
Shakya S, Santana R and Lozano JA (2012), "A Markovianity based optimisation algorithm", Genetic Programming and Evolvable Machines. Vol. 13(2), pp. 159-195.

[Abstract] [BibTeX] [URL]
Abstract: 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.
BibTeX: 
@article{Shakya_et_al:2011,
  author = {S. Shakya and R. Santana and J. A. Lozano},
  title = {A Markovianity based optimisation algorithm},
  journal = {Genetic Programming and Evolvable Machines},
  year = {2012},
  volume = {13},
  number = {2},
  pages = {159--195},
  url = {http://dx.doi.org/10.1007/s10710-011-9149-y}
}