Six-Hump Camelback

Implementation of the bi-fidelity Six-hump Camel-back 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:

\[f_h(x_1, x_2) = 4x_1^2 - 2.1x_1^4 + \dfrac{x_1^6}{3} + x_1x_2 - 4x_2^2 + 4x_2^4\]

\[f_l(x_1, x_2) = f_h(0.7x_1, 0.7x_2) + x_1x_2 - 15\]

l_bound = [-2, -2]

Lower bound for Six-hump Camelback function

six_hump_camelback = MultiFidelityFunction(Six Hump Camelback, [2. 2.], [-2. -2.], fidelity_names=['high', 'low'])

2D Six-hump Camelback function with fidelities ‘high’ and ‘low’

six_hump_camelback_hf(xx)

SIX-HUMP CAMEL-BACK FUNCTION

INPUT: xx = [x1, x2]

six_hump_camelback_lf(xx)

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

INPUT: xx = [x1, x2]

u_bound = [2, 2]

upper bound for Six-hump Camelback function