Adjustable Branin

Implementation of the adjustable bi-fidelity Branin function as defined in:

Toal, D.J.J. Some considerations regarding the use of multi- fidelity Kriging in the construction of surrogate models. Struct Multidisc Optim 51, 1223–1245 (2015) doi:10.1007/s00158-014-1209-5

Function definitions:

\[f_h(x_1, x_2) = \Bigg(x_2 - (5.1\dfrac{x_1^2}{4\pi^2}) + \dfrac{5x_1}{\pi} - 6\Bigg)^2 + \Bigg(10\cos(x_1) (1 - \dfrac{1}{8\pi}\Bigg) + 10\]

\[f_l(x_1, x_2) = f_h(x_1, x_2) - (a+0.5)\Bigg( \Bigg(x_2 - (5.1\dfrac{x_1^2}{4\pi^2}) + \dfrac{5x_1}{\pi} - 6\Bigg)^2 \Bigg)\]

where \(a \in [0, 1]\) is the adjustable parameter.

Note that \(f_h\) is equal to the non-adjustable \(f_b\) defined in mf2.branin.

adjustable_branin_lf(xx, a)