Hierarchical Problem Solving and the Bayesian Optimization Algorithm

The paper discusses three major issues. First, it discusses why it makes sense to approach problems in a hierarchical fashion. It defines the class of hierarchically decomposable functions that can be used to test the algorithms that approach problems in this fashion. Finally, the Bayesian optimization algorithm (BOA) is extended in order to solve the proposed class of problems.

[1]  John H. Holland,et al.  Hidden Order: How Adaptation Builds Complexity , 1995 .

[2]  Nir Friedman,et al.  Learning Bayesian Networks with Local Structure , 1996, UAI.

[3]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

[4]  Daniel E. Goldberg The design of innovation: Lessons from genetic algorithms , 1998 .

[5]  D. Madigan,et al.  Proceedings : KDD-99 : the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, August 15-18, 1999, San Diego, California, USA , 1999 .

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  John R. Koza,et al.  Hidden Order: How Adaptation Builds Complexity. , 1995, Artificial Life.

[8]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[9]  David E. Goldberg,et al.  Linkage Problem, Distribution Estimation, and Bayesian Networks , 2000, Evolutionary Computation.

[10]  Samir W. Mahfoud Niching methods for genetic algorithms , 1996 .

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

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

[13]  P. Nordin Genetic Programming III - Darwinian Invention and Problem Solving , 1999 .

[14]  Andrew W. Moore,et al.  Bayesian networks for lossless dataset compression , 1999, KDD '99.

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

[16]  David E. Goldberg,et al.  Probabilistic Crowding: Deterministic Crowding with Probabilistic Replacement , 1999 .

[17]  Nir Friedman,et al.  On the Sample Complexity of Learning Bayesian Networks , 1996, UAI.

[18]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[19]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[20]  David Maxwell Chickering,et al.  Learning Bayesian networks: The combination of knowledge and statistical data , 1995, Mach. Learn..