A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization

Ignacio Segovia-Domínguez, S. Ivvan Valdez, Arturo Hernández-Aguirre

2014

Abstract

This paper introduces an approach for continuous optimization using an Estimation of Distribution Algorithm (EDA), based on the Boltzmann distribution. When using the objective function as energy function, the Boltzmann function favors the most promising regions, making the probability exponentially proportional to the objective function. Using the Boltzmann distribution directly for sampling is not possible because it requires the computation of the objective function values in the complete search space. This work presents an approximation to the Boltzmann function by a multivariate Normal distribution. Formulae for computing the mean and covariance matrix are derived by minimizing the Kullback-Leibler divergence. The proposed EDA is competitive and often superior to similar algorithms as it is shown by statistical results reported here.

Paper Citation

in Harvard Style

Segovia-Domínguez I., Valdez S. and Hernández-Aguirre A. (2014). A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014) ISBN 978-989-758-052-9, pages 251-258. DOI: 10.5220/0005079902510258

in Bibtex Style

@conference{ecta14,
author={Ignacio Segovia-Domínguez and S. Ivvan Valdez and Arturo Hernández-Aguirre},
title={A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)},
year={2014},
pages={251-258},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005079902510258},
isbn={978-989-758-052-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)
TI - A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization
SN - 978-989-758-052-9
AU - Segovia-Domínguez I.
AU - Valdez S.
AU - Hernández-Aguirre A.
PY - 2014
SP - 251
EP - 258
DO - 10.5220/0005079902510258