# Sporadic model building for efficiency enhancement of the hierarchical BOA

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## Abstract

Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes *sporadic model building*, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant *model-building speedup*, which decreases the asymptotic time complexity of model building in hBOA by a factor of \(\Uptheta(n^{0.26})\) to \(\Uptheta(n^{0.5}),\) where *n* is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, if model building is the bottleneck, the *evaluation slowdown* is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structure-building period, which is the only parameter of the proposed sporadic model-building approach. The paper then tests the proposed method and the rule for setting the structure-building period on the problem of finding ground states of 2D and 3D Ising spin glasses.

## Keywords

Bayesian optimization algorithm Hierarchical BOA Estimation of distribution algorithms Efficiency enhancement Sporadic model building## Notes

### Acknowledgments

This work was supported by the National Science Foundation under NSF CAREER grant ECS-0547013 (at UMSL) and ITR grant DMR-03-25939 (at Materials Computation Center, UIUC), by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant FA9550-06-1-0096, and by the University of Missouri in St. Louis through the High Performance Computing Collaboratory sponsored by Information Technology Services, and the Research Award and Research Board programs. The experiments presented in this work were done using the hBOA software developed by Martin Pelikan and David E. Goldberg at the University of Illinois at Urbana-Champaign. Most experiments were completed at the Beowulf cluster at the University of Missouri at St. Louis. The U.S. Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation thereon.

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