A note on the extended Rosenbrock function.
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.
Shang
Yun-Wei
YW
Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China. yunwei.shang@mail.ia.ac.cn
Qiu
Yu-Huang
YH
D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D005828:Genetics, Population; D008957:Models, Genetic; D012680:Sensitivity and Specificity