makeBraninFunction {smoof}

Branin RCOS function

Description

Popular 2-dimensional single-objective test function based on the formula:

f(\mathbf{x}) = a \left(\mathbf{x}_2 - b \mathbf{x}_1^2 + c \mathbf{x_1} - d\right)^2 + e\left(1 - f\right)\cos(\mathbf{x}_1) + e,

where a = 1, b = \frac{5.1}{4\pi^2}, c = \frac{5}{\pi}, d = 6, e = 10 and f = \frac{1}{8\pi}. The box constraints are given by \mathbf{x}_1 \in [-5, 10] and \mathbf{x}_2 \in [0, 15]. The function has three global minima.

Usage

makeBraninFunction()

Value

[smoof_single_objective_function]

References

F. H. Branin. Widely convergent method for finding multiple solutions of simultaneous nonlinear equations. IBM J. Res. Dev. 16, 504-522, 1972.

Examples

library(ggplot2)
fn = makeBraninFunction()
print(fn)
print(autoplot(fn, show.optimum = TRUE))