Bayesian Classifiers in Optimization: An EDA-like Approach

This chapter introduces a new Evolutionary Computation method which applies Bayesian classifiers in the construction of a probabilistic graphical model that will be used to evolve a population of individuals. On the other hand, the satisfiability problem (SAT) is a central problem in the theory of computation as a representative example of NP-complete problems. We have verified the performance of this new method for the SAT problem. We compare three different solution representations suggested in the literature. Finally, we apply local search methods for this problem.

[1]  Michael J. Pazzani,et al.  Searching for Dependencies in Bayesian Classifiers , 1995, AISTATS.

[2]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[3]  Marvin Minsky,et al.  Steps toward Artificial Intelligence , 1995, Proceedings of the IRE.

[4]  A. Eiben,et al.  Solving 3-SAT by GAs adapting constraint weights , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[5]  Shotaro Akaho Statistical Learning in Optimization: Gaussian Modeling for Population Search , 1998, ICONIP.

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

[7]  Jens Gottlieb,et al.  Representations, Fitness Functions and Genetic Operators for the Satisfiability Problem , 1997, Artificial Evolution.

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

[9]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[10]  Pat Langley,et al.  Induction of Selective Bayesian Classifiers , 1994, UAI.

[11]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[12]  Kenneth A. De Jong,et al.  Using Genetic Algorithms to Solve NP-Complete Problems , 1989, ICGA.

[13]  Jin-Kao Hao,et al.  A Clausal Genetic Representation and its Evolutionary Procedures for Satisfiability Problems , 1995, ICANNGA.

[14]  Thomas Stützle,et al.  SATLIB: An Online Resource for Research on SAT , 2000 .

[15]  Elena Marchiori,et al.  Evolutionary Algorithms for the Satisfiability Problem , 2002, Evolutionary Computation.

[16]  Pedro Larrañaga,et al.  Evolutionary computation based on Bayesian classifiers , 2004 .

[17]  Xavier Llorà,et al.  Wise Breeding GA via Machine Learning Techniques for Function Optimization , 2003, GECCO.

[18]  Andrew W. Moore,et al.  Learning Evaluation Functions for Global Optimization and Boolean Satisfiability , 1998, AAAI/IAAI.

[19]  Igor Kononenko,et al.  Semi-Naive Bayesian Classifier , 1991, EWSL.

[20]  Hiroshi Motoda,et al.  Feature Selection for Knowledge Discovery and Data Mining , 1998, The Springer International Series in Engineering and Computer Science.

[21]  Ron Kohavi,et al.  Wrappers for Feature Subset Selection , 1997, Artif. Intell..

[22]  Pedro Larrañaga,et al.  Feature Subset Selection by Bayesian network-based optimization , 2000, Artif. Intell..

[23]  Elena Marchiori,et al.  A flipping genetic algorithm for hard 3-SAT problems , 1999 .

[24]  Ryszard S. Michalski,et al.  LEARNABLE EVOLUTION MODEL: Evolutionary Processes Guided by Machine Learning , 2004, Machine Learning.