A note on the extended Rosenbrock function

Evolutionary Computation
Yun-Wei Shang, Yu-Huang Qiu

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.

References

May 31, 2001·Evolutionary Computation·N Hansen, A Ostermeier
Nov 27, 2002·Evolutionary Computation·Kalyanmoy DebDhiraj Joshi

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Citations

Aug 28, 2009·Evolutionary Computation·Schalk Kok, Carl Sandrock
May 9, 2012·Evolutionary Computation·Minh Nghia LeBernhard Sendhoff
Oct 23, 2012·IEEE Transactions on Cybernetics·Wei-feng GaoLing-ling Huang
Sep 28, 2012·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·Hui WangMahamed G H Omran
Sep 10, 2013·IEEE Transactions on Cybernetics·Wei-Jie YuJun Zhang
Jun 13, 2013·IEEE Transactions on Cybernetics·Wenyin Gong, Zhihua Cai
Sep 15, 2010·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·Wenyin GongHui Li
Apr 29, 2010·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·Swagatam DasBijaya K Panigrahi
Jan 17, 2015·IEEE Transactions on Cybernetics·Wei-Feng GaoCai Dai
Sep 18, 2015·Computational Intelligence and Neuroscience·Zhaolu GuoZhijian Wu
Oct 12, 2016·Journal of Computational Neuroscience·Brandon S CoventryEdward L Bartlett
Oct 9, 2021·Frontiers in Physiology·Sarthak ChatterjeeSérgio Pequito

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