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A note on the extended Rosenbrock function
Shang, YW; Qiu, YH
AbstractThe Rosenbrock function is a well-known benchmark for numerical optimization problems, which is frequently used to assess the performance of Evolutionary Algorithms. The classical Rosenbrock function, which is a two-dimensional unimodal function, has been extended to higher dimensions in recent years. Many researchers take the high-dimensional Rosenbrock function as a unimodal function by instinct. In 2001 and 2002, Hansen and Deb found that the Rosenbrock function is not a unimodal function for higher dimensions although no theoretical analysis was provided. This paper shows that the n-dimensional (n = 4 similar to 30) Rosenbrock function has 2 minima, and analysis is proposed to verify this. The local minima in some cases are presented. In addition, this paper demonstrates that one of the "local minima" for the 20-variable Rosenbrock function found by Deb might not in fact be a local minimum.
KeywordNumerical Optimization Problems Benchmark Function Multimodal Function Local Minimum
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Theory & Methods
WOS IDWOS:000236046800008
Citation statistics
Cited Times:166[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
AffiliationChinese Acad Sci, Inst Automat, Lab Complex Syst & Intelligence Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Shang, YW,Qiu, YH. A note on the extended Rosenbrock function[J]. EVOLUTIONARY COMPUTATION,2006,14(1):119-126.
APA Shang, YW,&Qiu, YH.(2006).A note on the extended Rosenbrock function.EVOLUTIONARY COMPUTATION,14(1),119-126.
MLA Shang, YW,et al."A note on the extended Rosenbrock function".EVOLUTIONARY COMPUTATION 14.1(2006):119-126.
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