# makeBraninFunction: Branin RCOS function In smoof: Single and Multi-Objective Optimization Test Functions

## Description

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

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

where a = 1, b = \frac{5.1}{4π^2}, c = \frac{5}{π}, d = 6, e = 10 and f = \frac{1}{8π}. 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

 1 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

 1 2 3 4 library(ggplot2) fn = makeBraninFunction() print(fn) print(autoplot(fn, show.optimum = TRUE)) 

smoof documentation built on Feb. 18, 2020, 5:11 p.m.