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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahn, C.W., Kim, K.P., Ramakrishna, R.S.: A Memory-Efficient Elitist Genetic Algorithm, pp. 552–559. Springer (2004)
Alden, M.A.: MARLEDA: Effective Distribution Estimation Through Markov Random Fields. PhD thesis. Faculty of the Graduate Schoool. University of Texas at Austin, USA (December 2007)
Baluja, S.: Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Pittsburgh, PA (1994)
Baluja, S.: An empirical comparison of seven iterative and evolutionary function optimization heuristics. Technical Report CMU-CS-95-193. Carnegie Mellon University (1995)
Baluja, S., Davies, S.: Using optimal dependency-trees for combinatorial optimization: Learning the structure of the search space. In: Proceedings of the 14th International Conference on Machine Learning, pp. 30–38. Morgan Kaufmann (1997)
Besag, J.: Spatial interactions and the statistical analysis of lattice systems. Journal of the Royal Statistical Society B-36, 192–236 (1974)
Bosman, P.A.: Design and Application of Iterated Density-Estimation Evolutionary Algorithms. PhD thesis. Universiteit Utrecht. Utrecht, The Netherlands (2003)
Bosman, P.A., Thierens, D.: Expanding from Discrete to Continuous Estimation of Distribution Algorithms: The IDEA. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 767–776. Springer, Heidelberg (2000)
Bosman, P.A., Thierens, D.: Multi-objective optimization with diversity preserving mixture-based iterated density estimation evolutionary algorithms. International Journal of Approximate Reasoning 31(3), 259–289 (2002)
Brown, D.F., Garmendia-Doval, A.B., McCall, J.A.W.: Markov Random Field Modelling of Royal Road Genetic Algorithms. In: Collet, P., et al. (eds.) EA 2001. LNCS, vol. 2310, pp. 65–78. Springer, Heidelberg (2002)
Brownlee, A.E.I.: Multivariate Markov networks for fitness modelling in an estimation of distribution algorithm. PhD thesis. The Robert Gordon University. School of Computing, Aberdeen, UK (2009)
Brownlee, A.E.I., McCall, J., Shakya, S.K., Zhang, Q.: Structure learning and optimisation in a Markov-network based estimation of distribution algorithm. In: Proceedings of the 2009 Congress on Evolutionary Computation CEC-2009, pp. 447–454. IEEE Press, Norway (2009)
de Bonet, J.S., Isbell Jr., C.L., Viola, P.: MIMIC: Finding optima by estimating probability densities. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9. The MIT Press (1997)
Etxeberria, R., Larrañaga, P.: Global optimization using Bayesian networks. In: Ochoa, A., Soto, M.R., Santana, R. (eds.) Proceedings of the Second Symposium on Artificial Intelligence (CIMAF 1999), Havana, Cuba, pp. 151–173 (1999)
Gámez, J.A., Mateo, J.L., Puerta, J.M.: EDNA: Estimation of Dependency Networks Algorithm. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2007. LNCS, vol. 4527, pp. 427–436. Springer, Heidelberg (2007)
Gámez, J.A., Mateo, J.L., Puerta, J.M.: Improved EDNA estimation of dependency networks algorithm using combining function with bivariate probability distributions. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, GECCO 2008, pp. 407–414. ACM, New York (2008)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. In: Fischler, M.A., Firschein, O. (eds.) Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 564–584. Kaufmann, Los Altos (1987)
Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley (1989)
González, C., Rodríguez, J.D., Lozano, J., Larrañaga, P.: Analysis of the Univariate Marginal Distribution Algorithm modeled by Markov chains. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, pp. 510–517. Springer, Heidelberg (2003)
Grefenstette, J.J.: Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man, and Cybernetics 16, 122–128 (1986)
Harik, Cantu-Paz, Goldberg, Miller: The gambler’s ruin problem, genetic algorithms, and the sizing of populations. In: IEEECEP: Proceedings of The IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence (1997)
Harik, G.: Linkage learning via probabilistic modeling in the ECGA. Technical Report IlliGAL Report No. 99010. University of Illinois at Urbana-Champaign (1999)
Harik, G.R., Lobo, F.G., Goldberg, D.E.: The compact genetic algorithm. IEEE-EC 3(4), 287 (1999)
Hauschild, M., Pelikan, M., Lima, C., Sastry, K.: Analyzing probabilistic models in hierarchical BOA on traps and spin glasses. In: Thierens, D., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2007, vol. I, pp. 523–530. ACM Press, London (2007)
Heckerman, D., Chickering, D.M., Meek, C., Rounthwaite, R., Kadie, C.M.: Dependency networks for inference, collaborative filtering, and data visualization. Journal of Machine Learning Research 1, 49–75 (2000)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Khan, N.: Bayesian optimization algorithms for multi-objective and hierarchically difficult problems. Master’s thesis. University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL (2003)
Khan, N., Goldberg, D.E., Pelikan, M.: Multi-objective Bayesian optimization algorithm. IlliGAL Report No. 2002009. University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL (2002)
Kindermann, R., Snell, J.L.: Markov Random Fields and Their Applications. AMS (1980)
Larrañaga, P., Etxeberria, R., Lozano, J.A., Peña, J.M.: Optimization by learning and simulation of Bayesian and Gaussian networks. Technical Report EHU-KZAA-IK-4/99. University of the Basque Country (1999)
Larrañaga, P., Etxeberria, R., Lozano, J.A., Peña, J.M.: Optimization by learning and simulation of Bayesian and Gaussian networks. Technical Report EHU-KZAA-IK-4/99. Department of Computer Science and Artificial Intelligence. University of the Basque Country (1999)
Larrañaga, P., Etxeberria, R., Lozano, J.A., Peña, J.M.: Combinatorial optimization by learning and simulation of Bayesian networks. In: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, Stanford, pp. 343–352 (2000)
Larrañaga, P., Etxeberria, R., Lozano, J.A., Peña, J.M.: Optimization in continuous domains by learning and simulation of Gaussian networks. In: Wu, A.S. (ed.) Proceedings of the 2000 Genetic and Evolutionary Computation Conference Workshop Program, pp. 201–204 (2000)
Larrañaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers (2002)
Lauritzen, S.L.: Graphical Models. Oxford University Press (1996)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society B 50, 157–224 (1988)
Li, S.Z.: Markov Random Field modeling in computer vision. Springer (1995)
Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.): Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer (2006)
Malagó, L., Matteo, M., Gabriele, V.: Introducing l1-regularized logistic regression in Markov networks based EDAs. In: Proceedings of the 2011 Congress on Evolutionary Computation CEC 2011, pp. 1581–1588. IEEE (2011)
Metropolis, N.: Equations of state calculations by fast computational machine. Journal of Chemical Physics 21, 1087–1091 (1953)
Mühlenbein, H.: The equation for response to selection and its use for prediction. Evolutionary Computation 5(3), 303–346 (1998)
Mühlenbein, H.: Convergence of estimation of distribution algorithms (2009) (submmited for publication )
Mühlenbein, H., Mahnig, T.: FDA - A scalable evolutionary algorithm for the optimization of additively decomposed functions. Evolutionary Computation 7(4), 353–376 (1999)
Mühlenbein, H., Mahnig, T., Ochoa, A.: Schemata, distributions and graphical models in evolutionary optimization. Journal of Heuristics 5(2), 215–247 (1999)
Mühlenbein, H., Paaß, G.: From Recombination of Genes to the Estimation of Distributions: I. Binary Parameters. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996)
Murray, I., Ghahramani, Z.: Bayesian Learning in Undirected Graphical Models: Approximate MCMC algorithms. In: Twentieth Conference on Uncertainty in Artificial Intelligence (UAI 2004), Banff, Canada, July 8-11, pp. 392–399 (2004)
Ochoa, A., Soto, M.R., Santana, R., Madera, J., Jorge, N.: The factorized distribution algorithm and the junction tree: A learning perspective. In: Ochoa, A., Soto, M.R., Santana, R. (eds.) Proceedings of the Second Symposium on Artificial Intelligence (CIMAF 1999), pp. 368–377. Editorial Academia, Havana (1999)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)
Pelikan, M.: Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer (2005)
Pelikan, M., Goldberg, D.E.: Hierarchical problem solving by the Bayesian optimization algorithm. IlliGAL Report No. 2000002. Illinois Genetic Algorithms Laboratory. University of Illinois at Urbana-Champaign, Urbana, IL (2000)
Pelikan, M., Goldberg, D.E., Cantú-Paz, E.: BOA: The Bayesian Optimization Algorithm. In: Banzhaf, W., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference GECCO 1999, vol. I, pp. 525–532. Morgan Kaufmann Publishers, San Francisco (1999)
Pelikan, M., Goldberg, D.E., Lobo, F.: A survey of optimization by building and using probabilistic models. Computational Optimization and Applications 21(1), 5–20 (2002)
Pelikan, M., Mühlenbein, H.: The bivariate marginal distribution algorithm. In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing - Engineering Design and Manufacturing, pp. 521–535. Springer, London (1999)
Santana, R.: A Markov Network Based Factorized Distribution Algorithm for Optimization. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS (LNAI), vol. 2837, pp. 337–348. Springer, Heidelberg (2003)
Santana, R.: Estimation of distribution algorithms with Kikuchi approximations. Evolutionary Computation 13(1), 67–97 (2005)
Santana, R., Bielza, C., Larrañaga, P., Lozano, J.A., Echegoyen, C., Mendiburu, A., Armañanzas, R., Shakya, S.: Mateda-2.0: A MATLAB package for the implementation and analysis of estimation of distribution algorithms. Journal of Statistical Software 35(7), 1–30 (2010)
Schlüter, F., Bromberg, F.: Independence-based MAP for Markov networks structure discovery. In: Proceedings of the 23rd IEEE International Conference on Tools with Artificial Intelligence (2011) (in press)
Sebag, M., Ducoulombier, A.: Extending Population-Based Incremental Learning to Continuous Search Spaces. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 418–427. Springer, Heidelberg (1998)
Shakya, S.: DEUM: A Framework for an Estimation of Distribution Algorithm based on Markov Random Fields. PhD thesis. The Robert Gordon University, Aberdeen, UK (April 2006)
Shakya, S., McCall, J.: Optimisation by Estimation of Distribution with DEUM framework based on Markov Random Fields. International Journal of Automation and Computing 4, 262–272 (2007)
Shakya, S., McCall, J., Brown, D.: Updating the probability vector using MRF technique for a univariate EDA. In: Onaindia, E., Staab, S. (eds.) Proceedings of the Second Starting AI Researchers’ Symposium. Frontiers in Artificial Intelligence and Applications, vol. 109, pp. 15–25. IOS press, Valencia (2004)
Shakya, S., McCall, J., Brown, D.: Estimating the distribution in an EDA. In: Ribeiro, B., Albrechet, R.F., Dobnikar, A., Pearson, D.W., Steele, N.C. (eds.) Proceedings of the International Conference on Adaptive and Natural Computing Algorithms (ICANNGA 2005), Coimbra, Portugal, pp. 202–205. Springer, Heidelberg (2005)
Shakya, S., McCall, J., Brown, D.: Using a Markov Network Model in a Univariate EDA: An Emperical Cost-Benefit Analysis. In: Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2005), pp. 727–734. ACM, Washington, D.C. (2005)
Shakya, S., McCall, J., Brown, D.: Solving the Ising spin glass problem using a bivariate EDA based on Markov Random Fields. In: Proceedings of IEEE Congress on Evolutionary Computation (IEEE CEC 2006), pp. 3250–3257. IEEE press, Vancouver (2006)
Shakya, S., Santana, R.: An EDA based on local Markov property and Gibbs sampling. In: Keijzer, M. (ed.) Proceedings of the 2008 Genetic and Evolutionary Computation Conference (GECCO), pp. 475–476. ACM, New York (2008)
Shakya, S., Santana, R.: A markovianity based optimisation algorithm. Genetic Programming and Evolvable Machines (2011) ( in press)
Shakya, S.K., Brownlee, A.E.I., McCall, J., Fournier, W., Owusu, G.: A fully multivariate DEUM algorithm. In: Proceedings of the 2009 Congress on Evolutionary Computation, CEC 2009, pp. 479–486. IEEE Press, Norway (2009)
Valentini, G.: A novel approach to model selection in distribution estimation using Markov networks. PhD thesis, Milan, Italy (2011)
Valentini, G., Malago, L., Matteucci, M.: Evoptool: An extensible toolkit for evolutionary optimization algorithms comparison. In: Proceedings of the 2010 IEEE Congress on Evolutionary Computation (CEC 2010), pp. 1–8. IEEE (2010)
Wright, A.H., Pulavarty, S.: Estimation of distribution algorithm based on linkage discovery and factorization. In: Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2005), pp. 695–703. ACM, Washington, D.C. (2005)
Yedidia, J.S., Freeman, W.T., Weiss, Y.: Constructing free-energy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory 51, 2282–2312 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Shakya, S., Santana, R. (2012). A Review of Estimation of Distribution Algorithms and Markov Networks. In: Shakya, S., Santana, R. (eds) Markov Networks in Evolutionary Computation. Adaptation, Learning, and Optimization, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28900-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-28900-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28899-9
Online ISBN: 978-3-642-28900-2
eBook Packages: EngineeringEngineering (R0)