Analyzing probabilistic models in hierarchical BOA

  • Authors:
  • Mark Hauschild;Martin Pelikan;Kumara Sastry;Claudio Lima

  • Affiliations:
  • Missouri Estimation of Distribution Algorithms Laboratory, Department of Mathematics and Computer Science, University of Missouri at St. Louis, St. Louis, MO;Missouri Estimation of Distribution Algorithms Laboratory, Department of Mathematics and Computer Science, University of Missouri at St. Louis, St. Louis, MO;Illinois Genetic Algorithms Laboratory, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL;Informatics Laboratory, UALG-ILAB, Department of Electronics and Computer Science Engineering, University of Algarve, Faro, Portugal

  • Venue:
  • IEEE Transactions on Evolutionary Computation - Special issue on evolutionary algorithms based on probabilistic models
  • Year:
  • 2009

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Abstract

The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on four important classes of test problems: concatenated traps, random additively decomposable problems, hierarchical traps and two-dimensional Ising spin glasses with periodic boundary conditions. We argue that although the probabilistic models in hBOA can encode complex probability distributions, analyzing these models is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying optimization problem, the models do not change significantly in consequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem.