# American Institute of Mathematical Sciences

2012, 2(1): 57-67. doi: 10.3934/naco.2012.2.57

## Global optimization via differential evolution with automatic termination

 1 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan 2 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501

Received  April 2011 Revised  July 2011 Published  March 2012

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.
Citation: Bun Theang Ong, Masao Fukushima. Global optimization via differential evolution with automatic termination. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 57-67. doi: 10.3934/naco.2012.2.57
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