Student's t Distribution based Estimation of Distribution Algorithms for Derivative-free Global Optimization
This work addresses derivative-free global optimization problems for researchers and practitioners, but it is incremental as it modifies an existing method by changing the distribution type.
The authors tackled derivative-free global optimization by proposing ESTDA and EMSTDA, which use Student's t distributions instead of Gaussian ones in estimation of distribution algorithms, and empirical results showed they provide remarkably better performance than Gaussian counterparts.
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.