A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization
Ignacio Segovia-Domínguez, S. Ivvan Valdez, Arturo Hernández-Aguirre · 2014
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.