poli.objective_repository.toy_continuous_problem.definitions#

Defines several continuous toy problems.

This script defines all the artificial landscapes with signature [np.ndarray] -> np.ndarray. You might see that the signs have been flipped from [1] or [2]. This is because we’re dealing with maximizations instead of minimizations.

[1] Ali R. Al-Roomi (2015). Unconstrained Single-Objective Benchmark

Functions Repository [https://www.al-roomi.org/benchmarks/unconstrained]. Halifax, Nova Scotia, Canada: Dalhousie University, Electrical and Computer Engineering.

[2] Surjanovic, S. and Bingham, D. Virtual Library of Simulation Experiments:

Test Functions and Datasets. [https://www.sfu.ca/~ssurjano/optimization.html]

Functions

ackley_function_01(x)

alpine_01(x)

alpine_02(x)

bent_cigar(x)

branin_2d(x)

The 2D Branin function.

brown(x)

camelback_2d(x)

Taken directly from the LineBO repository [1].

chung_reynolds(x)

cosine_mixture(x)

cross_in_tray(xy)

Cross-in-tray has several local maxima in a quilt-like pattern.

deb_01(x)

deb_02(x)

deflected_corrugated_spring(x[, alpha, k])

easom(xy)

Easom is very flat, with a maxima at (pi, pi).

egg_holder(xy)

The egg holder is especially difficult.

hartmann_6d(x)

The 6 dimensional Hartmann function.

levy(x)

Compute the Levy function.

rosenbrock(x[, a, b])

Compute the Rosenbrock function.

shifted_sphere(x)

The usual squared norm, but shifted away from the origin by a bit.

styblinski_tang(x[, normalize])

This function is maximized at (-2.903534, ..., -2.903534), with a value of -39.16599 * d.