Student's t Distribution based Estimation of Distribution Algorithms for Derivative-free Global Optimization

TL;DR

This paper introduces ESTDA and EMSTDA, novel estimation of distribution algorithms using Student's t distributions for derivative-free global optimization, showing superior performance over Gaussian-based methods.

Contribution

The paper proposes using Student's t distributions in EDAs and extends to mixtures for better exploration, a novel approach in derivative-free optimization.

Findings

ESTDA and EMSTDA outperform Gaussian-based EDAs on benchmark functions.

Student's t distribution enhances exploration due to heavier tails.

Mixture models improve performance on multimodal problems.

Abstract

In this paper, we are concerned with a branch of evolutionary algorithms termed estimation of distribution (EDA), which has been successfully used to tackle derivative-free global optimization problems. For existent EDA algorithms, it is a common practice to use a Gaussian distribution or a mixture of Gaussian components to represent the statistical property of available promising solutions found so far. Observing that the Student's t distribution has heavier and longer tails than the Gaussian, which may be beneficial for exploring the solution space, we propose a novel EDA algorithm termed ESTDA, in which the Student's t distribution, rather than Gaussian, is employed. To address hard multimodal and deceptive problems, we extend ESTDA further by substituting a single Student's t distribution with a mixture of Student's t distributions. The resulting algorithm is named as estimation of mixture of Student's t distribution algorithm (EMSTDA). Both ESTDA and EMSTDA are evaluated through extensive and in-depth numerical experiments using over a dozen of benchmark objective functions. Empirical results demonstrate that the proposed algorithms provide remarkably better performance than their Gaussian counterparts.