Combinatonal Optimization by Learning and Simulation of Bayesian Networks

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation of Distribution Algorithms (EDA). EDA are a new tool for evolutionary computation in which populations of individuals are created by estimation and simulation of the joint probability distribution of the selected individuals. We propose new approaches to EDA for combinatorial optimization based on the theory of probabilistic graphical models. Experimental results are also presented.

[1]  Pedro Larrañaga,et al.  Structure Learning of Bayesian Networks by Genetic Algorithms , 1994 .

[2]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[3]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

[4]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[5]  Pedro Larrañaga,et al.  Analysis of the behaviour of genetic algorithms when learning Bayesian network structure from data , 1997, Pattern Recognit. Lett..

[6]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[7]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[8]  G. Harik.  Linkage Learning via Probabilistic Modeling in the ECGA , 1999 .

[9]  Heinz Mühlenbein,et al.  Schemata, Distributions and Graphical Models in Evolutionary Optimization , 1999, J. Heuristics.

[10]  Wray L. Buntine.  Theory Refinement on Bayesian Networks , 1991, UAI.

[11]  Wray L. Buntine.  A Guide to the Literature on Learning Probabilistic Networks from Data , 1996, IEEE Trans. Knowl. Data Eng..

[12]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

[13]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[14]  H. Akaike.  A new look at the statistical model identification , 1974 .

[15]  David E. Goldberg,et al.  The compact genetic algorithm , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[16]  Pedro Larrañaga,et al.  Learning Bayesian network structures by searching for the best ordering with genetic algorithms , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[17]  P. Spirtes,et al.  An Algorithm for Fast Recovery of Sparse Causal Graphs , 1991 .

[18]  Gregory F. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 1992 .

[19]  S. Baluja,et al.  Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space , 1997 .

[20]  Gilbert Syswerda,et al.  Simulated Crossover in Genetic Algorithms , 1992, FOGA.

[21]  Darrell Whitley,et al.  Genitor: a different genetic algorithm , 1988 .

[22]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, Conference on Uncertainty in Artificial Intelligence.

[23]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[24]  Enrique F. Castillo,et al.  Expert Systems and Probabilistic Network Models , 1996, Monographs in Computer Science.

[25]  David E. Goldberg,et al.  The compact genetic algorithm , 1999, IEEE Trans. Evol. Comput..

[26]  Michael I. Jordan,et al.  Probabilistic Networks and Expert Systems , 1999 .

[27]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[28]  Heinz Mühlenbein.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[29]  David Heckerman,et al.  Learning Bayesian Networks: Search Methods and Experimental Results , 1995 .

[30]  José Manuel Gutiérrez,et al.  Expert Systems and Probabiistic Network Models , 1996 .

[31]  Finn Verner Jensen,et al.  An introduction to Bayesian networks , 1996 .