Global optimization via differential evolution with automatic termination

Bun Theang Ong; Masao Fukushima

doi:10.3934/naco.2012.2.57

Article Contents

2012, Volume 2, Issue 1: 57-67. Doi: 10.3934/naco.2012.2.57

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Global optimization via differential evolution with automatic termination

Bun Theang Ong^1, and
Masao Fukushima^2,

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

Received: April 2011

Revised: July 2011

Published: February 2012

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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.

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Mathematics Subject Classification: Primary: 90C26, 90C59.

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