A Note on the Extended Rosenbrock Function

By Yun Shang, Y. Qiu. Evolutionary Computation, 2006

341 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/32415fbca3cc7e2e2370086ad658709b2cdaf0bf

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Citations in the corpus

Benchmark Functions for the CEC'2010 Special Session and Competition on Large-Scale (2009, background): “Introducing imbalance between the contribution of various subcomponents, subcomponents with nonuniform sizes, and conforming and conflicting overlapping functions are among the major new features proposed in this report.”
A Novel Artificial Bee Colony Algorithm Based on Modified Search Equation and Orthogonal Learning (2013, background): “f10 is the Rosenbrock function which is unimodal for D = 2 and 3 but may have multiple minima in high dimension cases [40].”
A Python surrogate modeling framework with derivatives (2019, background): “Rosenbrock [39] The Rosenbrock function is a continuous, nonlinear, and nonconvex function and usually used in optimization.”
Population size reduction for the differential evolution algorithm (2008, background): “Function f5 is multimodal [25] and the remaining functions (f9–f13) are also multimodal.”
Differential Evolution Using a Neighborhood-Based Mutation Operator (2009, background): “Functions f1 − f5 are unimodal (there is some recent evidence [49] that f5 is multimodal for D > 3).”
A comparative study of differential evolution variants for global optimization (2006, methodology): “Please note that we consider the Rosenbrock function as a multimodal function based on the results summarized in [17].”
Orthogonal Learning Particle Swarm Optimization (2009, background): “The first group includes four unimodal functions, where f1 and f2 are simple unimodal, f3 (Rosenbrock) is unimodal in a 2-D or 3-D search space but can be treated as a multimodal function in high-dimensional cases [52]–[54], and”
JADE: Adaptive Differential Evolution With Optional External Archive (2009, background): “…unimodal functions. f 5 is the Rosenbrock function which is unimodal for D = 2 and 3 but may have multiple minima in high dimension cases [39]. f 6 is a discontinuous step function, and f 7 is a noisy quartic function. f 8 – f 13 are multimodal and the number of their local minima…”
Differential Evolution With Ranking-Based Mutation Operators (2013, background): “4In [39], the authors pointed out that the extended Rosenbrock function f05 is actually multimodal when D > 3.”
Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization (2008, background): “For example, the Rosenbrock function is a unimodal function in two dimensions, but it turns into a multimodal function when the number of dimensions increases [37].”