Frontiers of Information Technology & Electronic Engineering
>> 2019,
Volume 20,
Issue 10
doi:
10.1631/FITEE.1900155
Frontiers of Information Technology & Electronic Engineering
Unusual phenomenon of optimizing the Griewank function with the increase of dimension
Affiliation(s): School of Computer Science and Technology, Huaiyin Normal University, Huai'an 223000, China; School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; Jiangsu Key Laboratory of Media Design and Software Technology, Jiangnan University, Wuxi 214122, China; School of Computer Science and Technology, Southwest Minzu University, Chengdu 610225, China; less
Accepted: 2019-11-11
Available online: 2019-11-11
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Abstract
The function is a typical multimodal benchmark function, composed of a quadratic convex function and an oscillatory nonconvex function. The comparative importance of ’s two major parts alters in different dimensions. Different from most test functions, an unusual phenomenon appears when optimizing the function. The function first becomes more difficult and then becomes easier to optimize with the increase of dimension. In this study, from the methodology perspective, this phenomenon is explained by structural, mathematical, and quantum analyses. Furthermore, frequency transformation and amplitude transformation are implemented on the function to make a generalization. The (MQHOA) with is used to verify its characteristics. Experimental results indicate that the function’s is the main reason for this phenomenon. The quantum tunneling mechanism mentioned in this paper is an effective method which can be generalized to analyze the generation and variation of solutions for numerous swarm optimization algorithms.
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