A Note on the Extended Rosenbrock Function

Yun-Wei Shang, Yu-Huang Qiu
2006 Evolutionary Computation  
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 highdimensional 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
more » ... higher dimensions although no theoretical analysis was provided. This paper shows that the n-dimensional (n = 4∼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.
doi:10.1162/evco.2006.14.1.119 pmid:16536893 fatcat:6tcb6zaoarbnjnlesigbtiuep4