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.
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
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., 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 (with discussions). Journal of the Royal Statistical Society 36, 192–236 (1974)
Echegoyen, C., Lozano, J.A., Santana, R., Larrañaga, P.: Exact Bayesian network learning in estimation of distribution algorithms. In: Proceedings of the 2007 Congress on Evolutionary Computation CEC 2007, pp. 1051–1058. IEEE Press (2007)
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)
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)
Henrion, M.: Propagating uncertainty in Bayesian networks by probabilistic logic sampling. In: Lemmer, J.F., Kanal, L.N. (eds.) Uncertainty in Artificial Intelligence 2, pp. 149–163. North-Holland, Amsterdam (1988)
Kikuchi, R.: A Theory of Cooperative Phenomena. Physical Review 81, 988–1003 (1951)
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., 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)
Metropolis, N.: Equations of state calculations by fast computational machine. Journal of Chemical Physics 21, 1087–1091 (1953)
Mitchell, M.: An Introduction To Genetic Algorithms. MIT Press, Cambridge (1997)
Mühlenbein, H., Mahnig, T., Ochoa, A.R.: 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)
Murphy, K.: Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, University of California, Berkeley (2002)
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 (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), Havana, Cuba, March 1999, pp. 368–377 (1999)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman Publishers, Palo Alto (1988)
Pelikan, M.: Bayesian optimization algorithm: From single level to hierarchy. PhD thesis, University of Illinois at Urbana-Champaign, Urbana, IL, Also IlliGAL Report No. 2002023 (2002)
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, San Francisco (1999)
Pelikan, M., Sastry, K., Butz, M.V., Goldberg, D.E.: Hierarchical BOA on random decomposable problems. IlliGAL Report No. 2006002, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL (January 2006)
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, 67–98 (2005)
Santana, R., Bielza, C., Larrañaga, P., Lozano, J.A., Echegoyen, C., Mendiburu, A., Armanñanzas, R., Shakya, S.: MATEDA 2.0: Estimation of distribution algorithms in MATLAB. Journal of Statistical Software 35(7), 1–30 (2010)
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., Brownlee, A., McCall, J., Fournier, F., Owusu, G.: DEUM – A Fully Multivariate EDA Based on Markov Networks. In: Chen, Y.-p. (ed.) Exploitation of Linkage Learning. ALO, vol. 3, pp. 71–93. Springer, Heidelberg (2010)
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.: 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: Proceedings of Genetic and Evolutionary Computation COnference (GECCO 2008). ACM Press, Atlanta (2008)
Shakya, S., Santana, R.: A markovianity based optimisation algorithm. Technical Report Technical Report EHU-KZAA-IK-3/08, Department of Computer Science and Artificial Intelligence, University of the Basque Country (September 2008)
Shakya, S., Santana, R.: A markovianity based optimisation algorithm. Genetic Programming and Evolvable Machines (2011) (in press)
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). MOA - Markovian Optimisation Algorithm. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-28900-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28899-9
Online ISBN: 978-3-642-28900-2
eBook Packages: EngineeringEngineering (R0)