smoof (version 1.6.0.3)

makeBraninFunction: Branin RCOS function

Description

Popular 2-dimensional single-objective test function based on the formula: $$f(\mathbf{x})=a{({\mathbf{x}}_2-b{\mathbf{x}}_1^2+c{\mathbf{x}}_{\mathbf{1}}-d)}^2+e(1-f)\cos ({\mathbf{x}}_1)+e,$$ 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))