Symmetric-Approximation Energy-Based Estimation of Distribution (SEED) Algorithm for Solving Continuous High-Dimensional Global Optimization Problems

Abstract

The Symmetric-approximation Energy-based Estimation of Distribution (SEED) is a continuous optimization algorithm based on the univariate Estimation of Distribution Algorithms (EDAs). Generally speaking, SEED uses Boltzmann selection and a symmetric divergence measure to guide the evolutionary process toward the optimum by constructing and sampling explicit probabilistic models of promising candidate solutions. SEED has been compared with other univariate EDAs, showing better results for low-dimensional continuous problems, and converging faster than the compared algorithms. In this paper, we propose to use SEED for solving continuous high-dimensional global optimization problems, and the results are compared with those of other representative evolutionary algorithms from the state-of-the-art such as Differential Evolution and Particle Swarm Optimization. To stress the algorithms, the search domain is extended from $x\in {\left[-1000, 1000\right]}^{n}$ for several benchmark functions whose dimension ranges from 500 to 10,000. Finally, to know the best performing algorithm, the convergence results of all algorithms are statistically compared using the Page’s Trend Test.