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A note on the extended Rosenbrock function.

Yun-Wei Shang·Yu-Huang Qiu
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Abstract

The 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 approximately 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.

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AlgorithmsBiological EvolutionComputer SimulationGenetics, PopulationModels, GeneticSensitivity and SpecificityJournal ArticleResearch Support, Non-U.S. Gov't

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Yun-Wei Shang, Yu-Huang Qiu. 2006. A note on the extended Rosenbrock function.. https://doi.org/10.1162/evco.2006.14.1.119

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