Source code for skopt.benchmarks

# -*- coding: utf-8 -*-
"""A collection of benchmark problems."""

import numpy as np


[docs]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
[docs]def bench1_with_time(x): """Same as bench1 but returns the computation time (constant).""" return x[0] ** 2, 2.22
[docs]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
[docs]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))
[docs]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
[docs]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
[docs]def branin(x, a=1, b=5.1 / (4 * np.pi**2), c=5. / np.pi, r=6, s=10, t=1. / (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)))