Structure Learning of Bayesian Networks by Estimation of Distribution Algorithms with Transpose Mutation

 

D.W. Kim¹, S. Ko¹, B.Y. Kang*²

 

¹ School of Computer Science and Engineering, Chung-Ang University, Seoul 156-756, Korea.

² School of Mechanical Engineering, Kyungpook National University, Daegu 702-701, Korea. * kby09@knu.ac.kr.

 

ABSTRACT

Estimation of distribution algorithms (EDAs) constitute a new branch of evolutionary optimization algorithms that were developed as a natural alternative to genetic algorithms (GAs). Several studies have demonstrated that the heuristic scheme of EDAs is effective and efficient for many optimization problems. Recently, it has been reported that the incorporation of mutation into EDAs increases the diversity of genetic information in the population, thereby avoiding premature convergence into a suboptimal solution. In this study, we propose a new mutation operator, a transpose mutation, designed for Bayesian structure learning. It enhances the diversity of the offspring and it increases the possibility of inferring the correct arc direction by considering the arc directions in candidate solutions as bi-directional, using the matrix transpose operator. As compared to the conventional EDAs, the transpose mutation-adopted EDAs are superior and effective algorithms for learning Bayesian networks.

Keywords: Estimation of distribution algorithms, Mutation, Bayesian network, Structure learning, Optimization.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

[1] R. Armañanzas et al., "A Review of Estimation of Distribution Algorithms in Bioinformatics," BioData Mining, vol. 1, no. 6, 2008.         [ Links ]

[2] B. Bernábe-Loranca et al., "A Multiobjective Approach for the Heuristic Optimization of Compactness and Homogeneity in the Optimal Zoning," Journal of Applied Research and Technology, vol. 10, no. 3, pp. 447-457, 2012.         [ Links ]

[3] R. González-Ramírez et al., "A Hybrid Metaheuristic Approach to Optimize the Districting Design of a Parcel Company," Journal of Applied Research and Technology, vol. 9, no. 1, pp. 19-35, 2011.         [ Links ]

[4] A. Afkar et al., "Geometry Optimization of Double Wishbone Suspension System via Genetic Algorithm for Handling Improvement," Journal of Vibroengineering, vol. 14, no. 14, pp. 827-837, 2012.         [ Links ]

[5] H. Taleshbahrami and H. Saffari, "Optimization of the C3mr Cycle with Genetic Algorithm," Transactions of the Canadian Society for Mechanical Engineering, vol. 34, no. 3/4, pp. 433-448, 2010.         [ Links ]

[6] F. Yaman and A.E. Yilmaz, "Impacts of Genetic Algorithm Parameters on the Solution Performance for the Uniform Circular Antenna Array Pattern Synthesis Problem," Journal of Applied Research and Technology, vol. 8, no. 3, pp. 378-393, 2010.         [ Links ]

[7] R. Blanco et al., "Learning Bayesian Networks in the Space of Structures by Estimation of Distribution Algorithms," International Journal of Intelligent Systems, vol. 18, pp. 205-220, 2003.         [ Links ]

[8] H. Handa, "Estimation of Distribution Algorithms with Mutation," Lecture Notes in Computer Science, vol. 3448, pp. 112-121, 2005.         [ Links ]

[9] T. Gosling et al., "Population based Incremental Learning with Guided Mutation versus Genetic Algorithms: Iterated Prisoners Dilemma," IEEE Congress on Evolutionary Computation, Edinburgh, 2005, pp. 958-965.         [ Links ]

[10] E.M. Heien et al., "Investigation of Mutation Operators for the Bayesian Optimization Algorithm," Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, London, 2007, p. 625.         [ Links ]

[11] M. Pelikan and K. Sastry, "Initial-Population Bias in the Univariate Estimation of Distribution Algorithm," MEDAL Report No. 2009001, University of Missouri-St. Louise, 2009.         [ Links ]

[12] Y. Chen et al., "Genetic Relation Algorithm with Guided Mutation for the Large-Scale Portfolio Optimization," Expert Systems with Applications, vol. 38, no. 4, pp. 3353-3363, 2011.         [ Links ]

[13] H. Mühlenbein, "The Equation for Response to Selection and Its Use for Prediction," Evolutionary Computation, vol. 5, no. 3, pp. 303-346, 1997.         [ Links ]

[14] S. Baluja, "Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning," Technical Report No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA, 1994.         [ Links ]

[15] G.R. Harik et al., "The Compact Genetic Algorithm," IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 287-297, 1999.         [ Links ]

[16] J.S. De Bonet et al., "MIMIC: Finding Optima by Estimating Probability Densities," Advances in Neural Information Processing Systems, vol. 9, pp. 424-430, 1997.         [ Links ]

[17] M. Pelikan and H. Mühlenbein, "The Bivariate Marginal Distribution Algorithm," in Books Editor, R. Roy et al (eds), Advances in Soft Computing-Engineering Design and Manufacturing, Springer-Verlag, 1999, pp. 521-535.         [ Links ]

[18] S. Baluja and S. Davies, "Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space," Proceedings of the International Conference on Machine Learning, Nashville, 1997, pp. 30-38.         [ Links ]

[19] G. Harik, "Linkage Learning in via Probabilistic Modeling in the ECGA," Technical Report 99010, IlliGAL, 1999.         [ Links ]

[20] P. Larrañaga et al., "Combinatorial Optimization by Learning and Simulation of Networks," UAI'00 Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, California, 2000, pp. 343-352.         [ Links ]

[21] M. Pelikan et al., "Linkage Problem, Distribution Estimation and Bayesian Networks," Evolutionary Computation, vol. 8, no. 3, pp. 311-340, 2000.         [ Links ]

[22] R.E. Neapolitan, "Learning Bayesian Networks," Prentice Hall, 2004.         [ Links ]

[23] D. Koller and N. Friedman, "Probabilistic Graphical Models: Principles and Techniques," The MIT Press, 2009.         [ Links ]

[24] T. Romero et al., "Learning Bayesian Networks in the Space of Orderings with Estimation of Distribution Algorithms," International Journal of Pattern Recognition and Artificial Intelligence, vol. 18, no. 4, pp. 607-625, 2004.         [ Links ]

[25] Z. Michalewicz and D.B. Fogel, "How to Solve it: Modern Heuristics," Springer, 2004.         [ Links ]

[26] J.W. Smith et al., "Using the ADAP Learning Algorithm to Forecast the Onset of Diabetes Mellitus," Proceedings of the Symposium on Computer Applications and Medical Care, 1998, pp. 261-265.         [ Links ]

[27] S.L. Lauritzen and D.J. Speigelhalter, "Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems," Journal of the Royal Statistical Society: Series B, vol. 50, no. 2, pp. 157-224, 1988.         [ Links ]