Booth

Implementation of the bi-fidelity Booth function as defined in:

Dong, H., Song, B., Wang, P. et al. Multi-fidelity information fusion based on prediction of kriging. Struct Multidisc Optim 51, 1267–1280 (2015) doi:10.1007/s00158-014-1213-9

Function definitions:

\[f_h(x_1, x_2) = (x_1 + 2x_2 - 7)^2 + (2x_1 + x_2 - 5)^2\]

\[f_l(x_1, x_2) = f_h(0.4x_1, x_2) + 1.7x_1x_2 - x_1 + 2x_2\]

booth = MultiFidelityFunction(Booth, [10. 10.], [-10. -10.], fidelity_names=['high', 'low'])

2D Booth function with fidelities ‘high’ and ‘low’

booth_hf(xx)

BOOTH FUNCTION

INPUT: xx = [x1, x2]

booth_lf(xx)

BOOTH FUNCTION, LOWER FIDELITY CODE Calls: booth_hf This function, from Dong et al. (2015), is used as the “low-accuracy code” version of the function booth_hf.

INPUT: xx = [x1, x2]

l_bound = [-10, -10]

Lower bound for Booth function

u_bound = [10, 10]

Upper bound for Booth function