Global optimization via differential evolution with automatic termination

Abstract

Evolutionary Algorithms (EAs) provide a very powerful tool for solving optimization problems. In the last decades, numerous studies have been focusing on improving the performance of EAs. However, there is a lack of studies that tackle the question of the termination criteria. Indeed, EAs still need termination criteria prespecified by the user. In this paper, we propose to combine the Differential Evolution (DE) method with novel elements, i.e., the ``Gene Matrix'' (GM), the ``Space Decomposition'' (SD) and ``Space Rotation'' (SR) mechanisms, in order to equip DE with an automatic termination criterion without resort to predefined conditions. We name this algorithm ``Differential Evolution with Automatic Termination'' (DEAT). Numerical experiments using a test bed of widely used benchmark functions in 10, 50 and 100 dimensions show the effectiveness of the proposed method.