| """A collection of benchmark problems.""" |
|
|
| import numpy as np |
|
|
|
|
| def bench1(x): |
| """A benchmark function for test purposes. |
| |
| f(x) = x ** 2 |
| |
| It has a single minima with f(x*) = 0 at x* = 0. |
| """ |
| return x[0] ** 2 |
|
|
|
|
| def bench1_with_time(x): |
| """Same as bench1 but returns the computation time (constant).""" |
| return x[0] ** 2, 2.22 |
|
|
|
|
| def bench2(x): |
| """A benchmark function for test purposes. |
| |
| f(x) = x ** 2 if x < 0 |
| (x-5) ** 2 - 5 otherwise. |
| |
| It has a global minima with f(x*) = -5 at x* = 5. |
| """ |
| if x[0] < 0: |
| return x[0] ** 2 |
| else: |
| return (x[0] - 5) ** 2 - 5 |
|
|
|
|
| def bench3(x): |
| """A benchmark function for test purposes. |
| |
| f(x) = sin(5*x) * (1 - tanh(x ** 2)) |
| |
| It has a global minima with f(x*) ~= -0.9 at x* ~= -0.3. |
| """ |
| return np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2)) |
|
|
|
|
| def bench4(x): |
| """A benchmark function for test purposes. |
| |
| f(x) = float(x) ** 2 |
| |
| where x is a string. It has a single minima with f(x*) = 0 at x* = |
| "0". This benchmark is used for checking support of categorical |
| variables. |
| """ |
| return float(x[0]) ** 2 |
|
|
|
|
| def bench5(x): |
| """A benchmark function for test purposes. |
| |
| f(x) = float(x[0]) ** 2 + x[1] ** 2 |
| |
| where x is a string. It has a single minima with f(x) = 0 at x[0] = |
| "0" and x[1] = "0" This benchmark is used for checking support of |
| mixed spaces. |
| """ |
| return float(x[0]) ** 2 + x[1] ** 2 |
|
|
|
|
| def branin( |
| x, a=1, b=5.1 / (4 * np.pi**2), c=5.0 / np.pi, r=6, s=10, t=1.0 / (8 * np.pi) |
| ): |
| """Branin-Hoo function is defined on the square :math:`x1 \\in [-5, 10], x2 \\in [0, |
| 15]`. |
| |
| It has three minima with f(x*) = 0.397887 at x* = (-pi, 12.275), |
| (+pi, 2.275), and (9.42478, 2.475). |
| |
| More details: <http://www.sfu.ca/~ssurjano/branin.html> |
| """ |
| return ( |
| a * (x[1] - b * x[0] ** 2 + c * x[0] - r) ** 2 + s * (1 - t) * np.cos(x[0]) + s |
| ) |
|
|
|
|
| def hart6( |
| x, |
| alpha=np.asarray([1.0, 1.2, 3.0, 3.2]), |
| P=10**-4 |
| * np.asarray( |
| [ |
| [1312, 1696, 5569, 124, 8283, 5886], |
| [2329, 4135, 8307, 3736, 1004, 9991], |
| [2348, 1451, 3522, 2883, 3047, 6650], |
| [4047, 8828, 8732, 5743, 1091, 381], |
| ] |
| ), |
| A=np.asarray( |
| [ |
| [10, 3, 17, 3.50, 1.7, 8], |
| [0.05, 10, 17, 0.1, 8, 14], |
| [3, 3.5, 1.7, 10, 17, 8], |
| [17, 8, 0.05, 10, 0.1, 14], |
| ] |
| ), |
| ): |
| """The six dimensional Hartmann function is defined on the unit hypercube. |
| |
| It has six local minima and one global minimum f(x*) = -3.32237 at |
| x* = (0.20169, 0.15001, 0.476874, 0.275332, 0.311652, 0.6573). |
| |
| More details: <http://www.sfu.ca/~ssurjano/hart6.html> |
| """ |
| return -np.sum(alpha * np.exp(-np.sum(A * (np.array(x) - P) ** 2, axis=1))) |
|
|
