makeRosenbrockFunction {smoof}

Rosenbrock Function

Description

Also known as the “De Jong's function 2” or the “(Rosenbrock) banana/valley function” due to its shape. The global optimum is located within a large flat valley and thus it is hard for optimization algorithms to find it. The following formula underlies the implementation:

f(\mathbf{x}) = \sum_{i=1}^{n-1} 100 \cdot (\mathbf{x}_{i+1} - \mathbf{x}_i^2)^2 + (1 - \mathbf{x}_i)^2.

The domain is given by the constraints \mathbf{x}_i \in [-30, 30], i = 1, \ldots, n.

Usage

makeRosenbrockFunction(dimensions)

Arguments

dimensions

[integer(1)]
Size of corresponding parameter space.

Value

[smoof_single_objective_function]

References

H. H. Rosenbrock, An Automatic Method for Finding the Greatest or least Value of a Function, Computer Journal, vol. 3, no. 3, pp. 175-184, 1960.