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Population model-based optimization

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  • Xi Chen
  • Enlu Zhou

Abstract

Model-based optimization methods are a class of stochastic search methods that iteratively find candidate solutions by generating samples from a parameterized probabilistic model on the solution space. In order to better capture the multi-modality of the objective functions than the traditional model-based methods which use only a single model, we propose a framework of using a population of models at every iteration with an adaptive mechanism to propagate the population over iterations. The adaptive mechanism is derived from estimating the optimal parameter of the probabilistic model in a Bayesian manner, and thus provides a proper way to determine the diversity in the population of the models. We provide theoretical justification on the convergence of this framework by showing that the posterior distribution of the parameter asymptotically converges to a degenerate distribution concentrating on the optimal parameter. Under this framework, we develop two practical algorithms by incorporating sequential Monte Carlo methods, and carry out numerical experiments to illustrate their performance. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Xi Chen & Enlu Zhou, 2015. "Population model-based optimization," Journal of Global Optimization, Springer, vol. 63(1), pages 125-148, September.
  • Handle: RePEc:spr:jglopt:v:63:y:2015:i:1:p:125-148
    DOI: 10.1007/s10898-015-0288-1
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    References listed on IDEAS

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    1. Jiaqiao Hu & Hyeong Chang & Michael Fu & Steven Marcus, 2011. "Dynamic sample budget allocation in model-based optimization," Journal of Global Optimization, Springer, vol. 50(4), pages 575-596, August.
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    4. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
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