1160 lines
39 KiB
Python
1160 lines
39 KiB
Python
import logging
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import sys
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import numpy
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import numpy as np
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import time
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from multiprocessing import Pool
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from numpy.testing import assert_allclose, IS_PYPY
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import pytest
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from pytest import raises as assert_raises, warns
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from scipy.optimize import (shgo, Bounds, minimize_scalar, minimize, rosen,
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rosen_der, rosen_hess, NonlinearConstraint)
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from scipy.optimize._constraints import new_constraint_to_old
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from scipy.optimize._shgo import SHGO
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class StructTestFunction:
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def __init__(self, bounds, expected_x, expected_fun=None,
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expected_xl=None, expected_funl=None):
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self.bounds = bounds
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self.expected_x = expected_x
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self.expected_fun = expected_fun
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self.expected_xl = expected_xl
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self.expected_funl = expected_funl
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def wrap_constraints(g):
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cons = []
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if g is not None:
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if not isinstance(g, (tuple, list)):
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g = (g,)
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else:
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pass
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for g in g:
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cons.append({'type': 'ineq',
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'fun': g})
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cons = tuple(cons)
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else:
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cons = None
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return cons
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class StructTest1(StructTestFunction):
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def f(self, x):
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return x[0] ** 2 + x[1] ** 2
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def g(x):
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return -(numpy.sum(x, axis=0) - 6.0)
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cons = wrap_constraints(g)
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test1_1 = StructTest1(bounds=[(-1, 6), (-1, 6)],
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expected_x=[0, 0])
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test1_2 = StructTest1(bounds=[(0, 1), (0, 1)],
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expected_x=[0, 0])
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test1_3 = StructTest1(bounds=[(None, None), (None, None)],
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expected_x=[0, 0])
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class StructTest2(StructTestFunction):
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"""
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Scalar function with several minima to test all minimiser retrievals
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"""
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def f(self, x):
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return (x - 30) * numpy.sin(x)
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def g(x):
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return 58 - numpy.sum(x, axis=0)
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cons = wrap_constraints(g)
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test2_1 = StructTest2(bounds=[(0, 60)],
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expected_x=[1.53567906],
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expected_fun=-28.44677132,
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# Important: test that funl return is in the correct
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# order
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expected_xl=numpy.array([[1.53567906],
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[55.01782167],
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[7.80894889],
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[48.74797493],
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[14.07445705],
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[42.4913859],
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[20.31743841],
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[36.28607535],
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[26.43039605],
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[30.76371366]]),
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expected_funl=numpy.array([-28.44677132, -24.99785984,
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-22.16855376, -18.72136195,
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-15.89423937, -12.45154942,
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-9.63133158, -6.20801301,
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-3.43727232, -0.46353338])
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)
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test2_2 = StructTest2(bounds=[(0, 4.5)],
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expected_x=[1.53567906],
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expected_fun=[-28.44677132],
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expected_xl=numpy.array([[1.53567906]]),
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expected_funl=numpy.array([-28.44677132])
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)
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class StructTest3(StructTestFunction):
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"""
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Hock and Schittkowski 18 problem (HS18). Hoch and Schittkowski (1981)
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http://www.ai7.uni-bayreuth.de/test_problem_coll.pdf
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Minimize: f = 0.01 * (x_1)**2 + (x_2)**2
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Subject to: x_1 * x_2 - 25.0 >= 0,
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(x_1)**2 + (x_2)**2 - 25.0 >= 0,
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2 <= x_1 <= 50,
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0 <= x_2 <= 50.
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Approx. Answer:
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f([(250)**0.5 , (2.5)**0.5]) = 5.0
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"""
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# amended to test vectorisation of constraints
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def f(self, x):
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return 0.01 * (x[0]) ** 2 + (x[1]) ** 2
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def g1(x):
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return x[0] * x[1] - 25.0
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def g2(x):
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return x[0] ** 2 + x[1] ** 2 - 25.0
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# g = (g1, g2)
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# cons = wrap_constraints(g)
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def g(x):
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return x[0] * x[1] - 25.0, x[0] ** 2 + x[1] ** 2 - 25.0
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# this checks that shgo can be sent new-style constraints
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__nlc = NonlinearConstraint(g, 0, np.inf)
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cons = (__nlc,)
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test3_1 = StructTest3(bounds=[(2, 50), (0, 50)],
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expected_x=[250 ** 0.5, 2.5 ** 0.5],
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expected_fun=5.0
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)
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class StructTest4(StructTestFunction):
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"""
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Hock and Schittkowski 11 problem (HS11). Hoch and Schittkowski (1981)
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NOTE: Did not find in original reference to HS collection, refer to
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Henderson (2015) problem 7 instead. 02.03.2016
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"""
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def f(self, x):
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return ((x[0] - 10) ** 2 + 5 * (x[1] - 12) ** 2 + x[2] ** 4
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+ 3 * (x[3] - 11) ** 2 + 10 * x[4] ** 6 + 7 * x[5] ** 2 + x[
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6] ** 4
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- 4 * x[5] * x[6] - 10 * x[5] - 8 * x[6]
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)
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def g1(x):
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return -(2 * x[0] ** 2 + 3 * x[1] ** 4 + x[2] + 4 * x[3] ** 2
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+ 5 * x[4] - 127)
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def g2(x):
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return -(7 * x[0] + 3 * x[1] + 10 * x[2] ** 2 + x[3] - x[4] - 282.0)
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def g3(x):
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return -(23 * x[0] + x[1] ** 2 + 6 * x[5] ** 2 - 8 * x[6] - 196)
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def g4(x):
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return -(4 * x[0] ** 2 + x[1] ** 2 - 3 * x[0] * x[1] + 2 * x[2] ** 2
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+ 5 * x[5] - 11 * x[6])
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g = (g1, g2, g3, g4)
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cons = wrap_constraints(g)
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test4_1 = StructTest4(bounds=[(-10, 10), ] * 7,
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expected_x=[2.330499, 1.951372, -0.4775414,
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4.365726, -0.6244870, 1.038131, 1.594227],
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expected_fun=680.6300573
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)
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class StructTest5(StructTestFunction):
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def f(self, x):
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return (-(x[1] + 47.0)
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* numpy.sin(numpy.sqrt(abs(x[0] / 2.0 + (x[1] + 47.0))))
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- x[0] * numpy.sin(numpy.sqrt(abs(x[0] - (x[1] + 47.0))))
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)
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g = None
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cons = wrap_constraints(g)
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test5_1 = StructTest5(bounds=[(-512, 512), (-512, 512)],
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expected_fun=[-959.64066272085051],
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expected_x=[512., 404.23180542])
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class StructTestLJ(StructTestFunction):
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"""
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LennardJones objective function. Used to test symmetry constraints
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settings.
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"""
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def f(self, x, *args):
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print(f'x = {x}')
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self.N = args[0]
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k = int(self.N / 3)
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s = 0.0
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for i in range(k - 1):
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for j in range(i + 1, k):
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a = 3 * i
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b = 3 * j
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xd = x[a] - x[b]
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yd = x[a + 1] - x[b + 1]
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zd = x[a + 2] - x[b + 2]
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ed = xd * xd + yd * yd + zd * zd
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ud = ed * ed * ed
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if ed > 0.0:
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s += (1.0 / ud - 2.0) / ud
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return s
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g = None
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cons = wrap_constraints(g)
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N = 6
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boundsLJ = list(zip([-4.0] * 6, [4.0] * 6))
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testLJ = StructTestLJ(bounds=boundsLJ,
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expected_fun=[-1.0],
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expected_x=None,
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# expected_x=[-2.71247337e-08,
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# -2.71247337e-08,
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# -2.50000222e+00,
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# -2.71247337e-08,
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# -2.71247337e-08,
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# -1.50000222e+00]
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)
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class StructTestS(StructTestFunction):
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def f(self, x):
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return ((x[0] - 0.5) ** 2 + (x[1] - 0.5) ** 2
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+ (x[2] - 0.5) ** 2 + (x[3] - 0.5) ** 2)
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g = None
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cons = wrap_constraints(g)
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test_s = StructTestS(bounds=[(0, 2.0), ] * 4,
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expected_fun=0.0,
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expected_x=numpy.ones(4) - 0.5
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)
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class StructTestTable(StructTestFunction):
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def f(self, x):
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if x[0] == 3.0 and x[1] == 3.0:
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return 50
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else:
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return 100
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g = None
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cons = wrap_constraints(g)
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test_table = StructTestTable(bounds=[(-10, 10), (-10, 10)],
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expected_fun=[50],
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expected_x=[3.0, 3.0])
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class StructTestInfeasible(StructTestFunction):
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"""
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Test function with no feasible domain.
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"""
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def f(self, x, *args):
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return x[0] ** 2 + x[1] ** 2
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def g1(x):
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return x[0] + x[1] - 1
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def g2(x):
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return -(x[0] + x[1] - 1)
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def g3(x):
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return -x[0] + x[1] - 1
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def g4(x):
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return -(-x[0] + x[1] - 1)
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g = (g1, g2, g3, g4)
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cons = wrap_constraints(g)
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test_infeasible = StructTestInfeasible(bounds=[(2, 50), (-1, 1)],
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expected_fun=None,
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expected_x=None
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)
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@pytest.mark.skip("Not a test")
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def run_test(test, args=(), test_atol=1e-5, n=100, iters=None,
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callback=None, minimizer_kwargs=None, options=None,
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sampling_method='sobol', workers=1):
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res = shgo(test.f, test.bounds, args=args, constraints=test.cons,
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n=n, iters=iters, callback=callback,
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minimizer_kwargs=minimizer_kwargs, options=options,
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sampling_method=sampling_method, workers=workers)
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print(f'res = {res}')
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logging.info(f'res = {res}')
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if test.expected_x is not None:
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numpy.testing.assert_allclose(res.x, test.expected_x,
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rtol=test_atol,
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atol=test_atol)
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# (Optional tests)
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if test.expected_fun is not None:
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numpy.testing.assert_allclose(res.fun,
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test.expected_fun,
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atol=test_atol)
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if test.expected_xl is not None:
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numpy.testing.assert_allclose(res.xl,
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test.expected_xl,
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atol=test_atol)
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if test.expected_funl is not None:
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numpy.testing.assert_allclose(res.funl,
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test.expected_funl,
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atol=test_atol)
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return
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# Base test functions:
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class TestShgoSobolTestFunctions:
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"""
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Global optimisation tests with Sobol sampling:
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"""
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# Sobol algorithm
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def test_f1_1_sobol(self):
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"""Multivariate test function 1:
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x[0]**2 + x[1]**2 with bounds=[(-1, 6), (-1, 6)]"""
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run_test(test1_1)
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def test_f1_2_sobol(self):
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"""Multivariate test function 1:
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x[0]**2 + x[1]**2 with bounds=[(0, 1), (0, 1)]"""
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run_test(test1_2)
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def test_f1_3_sobol(self):
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"""Multivariate test function 1:
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x[0]**2 + x[1]**2 with bounds=[(None, None),(None, None)]"""
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options = {'disp': True}
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run_test(test1_3, options=options)
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def test_f2_1_sobol(self):
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"""Univariate test function on
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f(x) = (x - 30) * sin(x) with bounds=[(0, 60)]"""
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run_test(test2_1)
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def test_f2_2_sobol(self):
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"""Univariate test function on
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f(x) = (x - 30) * sin(x) bounds=[(0, 4.5)]"""
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run_test(test2_2)
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def test_f3_sobol(self):
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"""NLP: Hock and Schittkowski problem 18"""
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run_test(test3_1)
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@pytest.mark.slow
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def test_f4_sobol(self):
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"""NLP: (High dimensional) Hock and Schittkowski 11 problem (HS11)"""
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options = {'infty_constraints': False}
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# run_test(test4_1, n=990, options=options)
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run_test(test4_1, n=990 * 2, options=options)
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def test_f5_1_sobol(self):
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"""NLP: Eggholder, multimodal"""
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# run_test(test5_1, n=30)
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run_test(test5_1, n=60)
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def test_f5_2_sobol(self):
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"""NLP: Eggholder, multimodal"""
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# run_test(test5_1, n=60, iters=5)
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run_test(test5_1, n=60, iters=5)
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# def test_t911(self):
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# """1D tabletop function"""
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# run_test(test11_1)
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class TestShgoSimplicialTestFunctions:
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"""
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Global optimisation tests with Simplicial sampling:
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"""
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def test_f1_1_simplicial(self):
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"""Multivariate test function 1:
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x[0]**2 + x[1]**2 with bounds=[(-1, 6), (-1, 6)]"""
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run_test(test1_1, n=1, sampling_method='simplicial')
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def test_f1_2_simplicial(self):
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"""Multivariate test function 1:
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x[0]**2 + x[1]**2 with bounds=[(0, 1), (0, 1)]"""
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run_test(test1_2, n=1, sampling_method='simplicial')
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def test_f1_3_simplicial(self):
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"""Multivariate test function 1: x[0]**2 + x[1]**2
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with bounds=[(None, None),(None, None)]"""
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run_test(test1_3, n=5, sampling_method='simplicial')
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def test_f2_1_simplicial(self):
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"""Univariate test function on
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f(x) = (x - 30) * sin(x) with bounds=[(0, 60)]"""
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options = {'minimize_every_iter': False}
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run_test(test2_1, n=200, iters=7, options=options,
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sampling_method='simplicial')
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def test_f2_2_simplicial(self):
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"""Univariate test function on
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f(x) = (x - 30) * sin(x) bounds=[(0, 4.5)]"""
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run_test(test2_2, n=1, sampling_method='simplicial')
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def test_f3_simplicial(self):
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"""NLP: Hock and Schittkowski problem 18"""
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run_test(test3_1, n=1, sampling_method='simplicial')
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@pytest.mark.slow
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def test_f4_simplicial(self):
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"""NLP: (High dimensional) Hock and Schittkowski 11 problem (HS11)"""
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run_test(test4_1, n=1, sampling_method='simplicial')
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def test_lj_symmetry_old(self):
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"""LJ: Symmetry-constrained test function"""
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options = {'symmetry': True,
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'disp': True}
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args = (6,) # Number of atoms
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run_test(testLJ, args=args, n=300,
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options=options, iters=1,
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sampling_method='simplicial')
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def test_f5_1_lj_symmetry(self):
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"""LJ: Symmetry constrained test function"""
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options = {'symmetry': [0, ] * 6,
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'disp': True}
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args = (6,) # No. of atoms
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run_test(testLJ, args=args, n=300,
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options=options, iters=1,
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sampling_method='simplicial')
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def test_f5_2_cons_symmetry(self):
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"""Symmetry constrained test function"""
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options = {'symmetry': [0, 0],
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'disp': True}
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run_test(test1_1, n=200,
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options=options, iters=1,
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sampling_method='simplicial')
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def test_f5_3_cons_symmetry(self):
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"""Assymmetrically constrained test function"""
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options = {'symmetry': [0, 0, 0, 3],
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'disp': True}
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run_test(test_s, n=10000,
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options=options,
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iters=1,
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sampling_method='simplicial')
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@pytest.mark.skip("Not a test")
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def test_f0_min_variance(self):
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"""Return a minimum on a perfectly symmetric problem, based on
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gh10429"""
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avg = 0.5 # Given average value of x
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cons = {'type': 'eq', 'fun': lambda x: numpy.mean(x) - avg}
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# Minimize the variance of x under the given constraint
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res = shgo(numpy.var, bounds=6 * [(0, 1)], constraints=cons)
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assert res.success
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assert_allclose(res.fun, 0, atol=1e-15)
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assert_allclose(res.x, 0.5)
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@pytest.mark.skip("Not a test")
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def test_f0_min_variance_1D(self):
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"""Return a minimum on a perfectly symmetric 1D problem, based on
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gh10538"""
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def fun(x):
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return x * (x - 1.0) * (x - 0.5)
|
|
|
|
bounds = [(0, 1)]
|
|
res = shgo(fun, bounds=bounds)
|
|
ref = minimize_scalar(fun, bounds=bounds[0])
|
|
assert res.success
|
|
assert_allclose(res.fun, ref.fun)
|
|
assert_allclose(res.x, ref.x, rtol=1e-6)
|
|
|
|
# Argument test functions
|
|
class TestShgoArguments:
|
|
def test_1_1_simpl_iter(self):
|
|
"""Iterative simplicial sampling on TestFunction 1 (multivariate)"""
|
|
run_test(test1_2, n=None, iters=2, sampling_method='simplicial')
|
|
|
|
def test_1_2_simpl_iter(self):
|
|
"""Iterative simplicial on TestFunction 2 (univariate)"""
|
|
options = {'minimize_every_iter': False}
|
|
run_test(test2_1, n=None, iters=9, options=options,
|
|
sampling_method='simplicial')
|
|
|
|
def test_2_1_sobol_iter(self):
|
|
"""Iterative Sobol sampling on TestFunction 1 (multivariate)"""
|
|
run_test(test1_2, n=None, iters=1, sampling_method='sobol')
|
|
|
|
def test_2_2_sobol_iter(self):
|
|
"""Iterative Sobol sampling on TestFunction 2 (univariate)"""
|
|
res = shgo(test2_1.f, test2_1.bounds, constraints=test2_1.cons,
|
|
n=None, iters=1, sampling_method='sobol')
|
|
|
|
numpy.testing.assert_allclose(res.x, test2_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
numpy.testing.assert_allclose(res.fun, test2_1.expected_fun, atol=1e-5)
|
|
|
|
def test_3_1_disp_simplicial(self):
|
|
"""Iterative sampling on TestFunction 1 and 2 (multi and univariate)
|
|
"""
|
|
|
|
def callback_func(x):
|
|
print("Local minimization callback test")
|
|
|
|
for test in [test1_1, test2_1]:
|
|
shgo(test.f, test.bounds, iters=1,
|
|
sampling_method='simplicial',
|
|
callback=callback_func, options={'disp': True})
|
|
shgo(test.f, test.bounds, n=1, sampling_method='simplicial',
|
|
callback=callback_func, options={'disp': True})
|
|
|
|
def test_3_2_disp_sobol(self):
|
|
"""Iterative sampling on TestFunction 1 and 2 (multi and univariate)"""
|
|
|
|
def callback_func(x):
|
|
print("Local minimization callback test")
|
|
|
|
for test in [test1_1, test2_1]:
|
|
shgo(test.f, test.bounds, iters=1, sampling_method='sobol',
|
|
callback=callback_func, options={'disp': True})
|
|
|
|
shgo(test.f, test.bounds, n=1, sampling_method='simplicial',
|
|
callback=callback_func, options={'disp': True})
|
|
|
|
def test_args_gh14589(self):
|
|
"""Using `args` used to cause `shgo` to fail; see #14589, #15986,
|
|
#16506"""
|
|
res = shgo(func=lambda x, y, z: x * z + y, bounds=[(0, 3)], args=(1, 2)
|
|
)
|
|
ref = shgo(func=lambda x: 2 * x + 1, bounds=[(0, 3)])
|
|
assert_allclose(res.fun, ref.fun)
|
|
assert_allclose(res.x, ref.x)
|
|
|
|
@pytest.mark.slow
|
|
def test_4_1_known_f_min(self):
|
|
"""Test known function minima stopping criteria"""
|
|
# Specify known function value
|
|
options = {'f_min': test4_1.expected_fun,
|
|
'f_tol': 1e-6,
|
|
'minimize_every_iter': True}
|
|
# TODO: Make default n higher for faster tests
|
|
run_test(test4_1, n=None, test_atol=1e-5, options=options,
|
|
sampling_method='simplicial')
|
|
|
|
@pytest.mark.slow
|
|
def test_4_2_known_f_min(self):
|
|
"""Test Global mode limiting local evaluations"""
|
|
options = { # Specify known function value
|
|
'f_min': test4_1.expected_fun,
|
|
'f_tol': 1e-6,
|
|
# Specify number of local iterations to perform
|
|
'minimize_every_iter': True,
|
|
'local_iter': 1}
|
|
|
|
run_test(test4_1, n=None, test_atol=1e-5, options=options,
|
|
sampling_method='simplicial')
|
|
|
|
def test_4_4_known_f_min(self):
|
|
"""Test Global mode limiting local evaluations for 1D funcs"""
|
|
options = { # Specify known function value
|
|
'f_min': test2_1.expected_fun,
|
|
'f_tol': 1e-6,
|
|
# Specify number of local iterations to perform+
|
|
'minimize_every_iter': True,
|
|
'local_iter': 1,
|
|
'infty_constraints': False}
|
|
|
|
res = shgo(test2_1.f, test2_1.bounds, constraints=test2_1.cons,
|
|
n=None, iters=None, options=options,
|
|
sampling_method='sobol')
|
|
numpy.testing.assert_allclose(res.x, test2_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
|
|
def test_5_1_simplicial_argless(self):
|
|
"""Test Default simplicial sampling settings on TestFunction 1"""
|
|
res = shgo(test1_1.f, test1_1.bounds, constraints=test1_1.cons)
|
|
numpy.testing.assert_allclose(res.x, test1_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
|
|
def test_5_2_sobol_argless(self):
|
|
"""Test Default sobol sampling settings on TestFunction 1"""
|
|
res = shgo(test1_1.f, test1_1.bounds, constraints=test1_1.cons,
|
|
sampling_method='sobol')
|
|
numpy.testing.assert_allclose(res.x, test1_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
|
|
def test_6_1_simplicial_max_iter(self):
|
|
"""Test that maximum iteration option works on TestFunction 3"""
|
|
options = {'max_iter': 2}
|
|
res = shgo(test3_1.f, test3_1.bounds, constraints=test3_1.cons,
|
|
options=options, sampling_method='simplicial')
|
|
numpy.testing.assert_allclose(res.x, test3_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
numpy.testing.assert_allclose(res.fun, test3_1.expected_fun, atol=1e-5)
|
|
|
|
def test_6_2_simplicial_min_iter(self):
|
|
"""Test that maximum iteration option works on TestFunction 3"""
|
|
options = {'min_iter': 2}
|
|
res = shgo(test3_1.f, test3_1.bounds, constraints=test3_1.cons,
|
|
options=options, sampling_method='simplicial')
|
|
numpy.testing.assert_allclose(res.x, test3_1.expected_x, rtol=1e-5,
|
|
atol=1e-5)
|
|
numpy.testing.assert_allclose(res.fun, test3_1.expected_fun, atol=1e-5)
|
|
|
|
def test_7_1_minkwargs(self):
|
|
"""Test the minimizer_kwargs arguments for solvers with constraints"""
|
|
# Test solvers
|
|
for solver in ['COBYLA', 'SLSQP']:
|
|
# Note that passing global constraints to SLSQP is tested in other
|
|
# unittests which run test4_1 normally
|
|
minimizer_kwargs = {'method': solver,
|
|
'constraints': test3_1.cons}
|
|
run_test(test3_1, n=100, test_atol=1e-3,
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
sampling_method='sobol')
|
|
|
|
def test_7_2_minkwargs(self):
|
|
"""Test the minimizer_kwargs default inits"""
|
|
minimizer_kwargs = {'ftol': 1e-5}
|
|
options = {'disp': True} # For coverage purposes
|
|
SHGO(test3_1.f, test3_1.bounds, constraints=test3_1.cons[0],
|
|
minimizer_kwargs=minimizer_kwargs, options=options)
|
|
|
|
def test_7_3_minkwargs(self):
|
|
"""Test minimizer_kwargs arguments for solvers without constraints"""
|
|
for solver in ['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Newton-CG',
|
|
'L-BFGS-B', 'TNC', 'dogleg', 'trust-ncg', 'trust-exact',
|
|
'trust-krylov']:
|
|
def jac(x):
|
|
return numpy.array([2 * x[0], 2 * x[1]]).T
|
|
|
|
def hess(x):
|
|
return numpy.array([[2, 0], [0, 2]])
|
|
|
|
minimizer_kwargs = {'method': solver,
|
|
'jac': jac,
|
|
'hess': hess}
|
|
logging.info(f"Solver = {solver}")
|
|
logging.info("=" * 100)
|
|
run_test(test1_1, n=100, test_atol=1e-3,
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
sampling_method='sobol')
|
|
|
|
def test_8_homology_group_diff(self):
|
|
options = {'minhgrd': 1,
|
|
'minimize_every_iter': True}
|
|
|
|
run_test(test1_1, n=None, iters=None, options=options,
|
|
sampling_method='simplicial')
|
|
|
|
def test_9_cons_g(self):
|
|
"""Test single function constraint passing"""
|
|
SHGO(test3_1.f, test3_1.bounds, constraints=test3_1.cons[0])
|
|
|
|
@pytest.mark.xfail(IS_PYPY and sys.platform == 'win32',
|
|
reason="Failing and fix in PyPy not planned (see gh-18632)")
|
|
def test_10_finite_time(self):
|
|
"""Test single function constraint passing"""
|
|
options = {'maxtime': 1e-15}
|
|
|
|
def f(x):
|
|
time.sleep(1e-14)
|
|
return 0.0
|
|
|
|
res = shgo(f, test1_1.bounds, iters=5, options=options)
|
|
# Assert that only 1 rather than 5 requested iterations ran:
|
|
assert res.nit == 1
|
|
|
|
def test_11_f_min_0(self):
|
|
"""Test to cover the case where f_lowest == 0"""
|
|
options = {'f_min': 0.0,
|
|
'disp': True}
|
|
res = shgo(test1_2.f, test1_2.bounds, n=10, iters=None,
|
|
options=options, sampling_method='sobol')
|
|
numpy.testing.assert_equal(0, res.x[0])
|
|
numpy.testing.assert_equal(0, res.x[1])
|
|
|
|
# @nottest
|
|
@pytest.mark.skip(reason="no way of currently testing this")
|
|
def test_12_sobol_inf_cons(self):
|
|
"""Test to cover the case where f_lowest == 0"""
|
|
# TODO: This test doesn't cover anything new, it is unknown what the
|
|
# original test was intended for as it was never complete. Delete or
|
|
# replace in the future.
|
|
options = {'maxtime': 1e-15,
|
|
'f_min': 0.0}
|
|
res = shgo(test1_2.f, test1_2.bounds, n=1, iters=None,
|
|
options=options, sampling_method='sobol')
|
|
numpy.testing.assert_equal(0.0, res.fun)
|
|
|
|
def test_13_high_sobol(self):
|
|
"""Test init of high-dimensional sobol sequences"""
|
|
|
|
def f(x):
|
|
return 0
|
|
|
|
bounds = [(None, None), ] * 41
|
|
SHGOc = SHGO(f, bounds, sampling_method='sobol')
|
|
# SHGOc.sobol_points(2, 50)
|
|
SHGOc.sampling_function(2, 50)
|
|
|
|
def test_14_local_iter(self):
|
|
"""Test limited local iterations for a pseudo-global mode"""
|
|
options = {'local_iter': 4}
|
|
run_test(test5_1, n=60, options=options)
|
|
|
|
def test_15_min_every_iter(self):
|
|
"""Test minimize every iter options and cover function cache"""
|
|
options = {'minimize_every_iter': True}
|
|
run_test(test1_1, n=1, iters=7, options=options,
|
|
sampling_method='sobol')
|
|
|
|
def test_16_disp_bounds_minimizer(self, capsys):
|
|
"""Test disp=True with minimizers that do not support bounds """
|
|
options = {'disp': True}
|
|
minimizer_kwargs = {'method': 'nelder-mead'}
|
|
run_test(test1_2, sampling_method='simplicial',
|
|
options=options, minimizer_kwargs=minimizer_kwargs)
|
|
|
|
def test_17_custom_sampling(self):
|
|
"""Test the functionality to add custom sampling methods to shgo"""
|
|
|
|
def sample(n, d):
|
|
return numpy.random.uniform(size=(n, d))
|
|
|
|
run_test(test1_1, n=30, sampling_method=sample)
|
|
|
|
def test_18_bounds_class(self):
|
|
# test that new and old bounds yield same result
|
|
def f(x):
|
|
return numpy.square(x).sum()
|
|
|
|
lb = [-6., 1., -5.]
|
|
ub = [-1., 3., 5.]
|
|
bounds_old = list(zip(lb, ub))
|
|
bounds_new = Bounds(lb, ub)
|
|
|
|
res_old_bounds = shgo(f, bounds_old)
|
|
res_new_bounds = shgo(f, bounds_new)
|
|
|
|
assert res_new_bounds.nfev == res_old_bounds.nfev
|
|
assert res_new_bounds.message == res_old_bounds.message
|
|
assert res_new_bounds.success == res_old_bounds.success
|
|
x_opt = numpy.array([-1., 1., 0.])
|
|
numpy.testing.assert_allclose(res_new_bounds.x, x_opt)
|
|
numpy.testing.assert_allclose(res_new_bounds.x,
|
|
res_old_bounds.x)
|
|
|
|
def test_19_parallelization(self):
|
|
"""Test the functionality to add custom sampling methods to shgo"""
|
|
|
|
with Pool(2) as p:
|
|
run_test(test1_1, n=30, workers=p.map) # Constrained
|
|
run_test(test1_1, n=30, workers=map) # Constrained
|
|
with Pool(2) as p:
|
|
run_test(test_s, n=30, workers=p.map) # Unconstrained
|
|
run_test(test_s, n=30, workers=map) # Unconstrained
|
|
|
|
def test_20_constrained_args(self):
|
|
"""Test that constraints can be passed to arguments"""
|
|
|
|
def eggholder(x):
|
|
return (-(x[1] + 47.0)
|
|
* numpy.sin(numpy.sqrt(abs(x[0] / 2.0 + (x[1] + 47.0))))
|
|
- x[0] * numpy.sin(numpy.sqrt(abs(x[0] - (x[1] + 47.0))))
|
|
)
|
|
|
|
def f(x): # (cattle-feed)
|
|
return 24.55 * x[0] + 26.75 * x[1] + 39 * x[2] + 40.50 * x[3]
|
|
|
|
bounds = [(0, 1.0), ] * 4
|
|
|
|
def g1_modified(x, i):
|
|
return i * 2.3 * x[0] + i * 5.6 * x[1] + 11.1 * x[2] + 1.3 * x[
|
|
3] - 5 # >=0
|
|
|
|
def g2(x):
|
|
return (12 * x[0] + 11.9 * x[1] + 41.8 * x[2] + 52.1 * x[3] - 21
|
|
- 1.645 * numpy.sqrt(0.28 * x[0] ** 2 + 0.19 * x[1] ** 2
|
|
+ 20.5 * x[2] ** 2 + 0.62 * x[3] ** 2)
|
|
) # >=0
|
|
|
|
def h1(x):
|
|
return x[0] + x[1] + x[2] + x[3] - 1 # == 0
|
|
|
|
cons = ({'type': 'ineq', 'fun': g1_modified, "args": (0,)},
|
|
{'type': 'ineq', 'fun': g2},
|
|
{'type': 'eq', 'fun': h1})
|
|
|
|
shgo(f, bounds, n=300, iters=1, constraints=cons)
|
|
# using constrain with arguments AND sampling method sobol
|
|
shgo(f, bounds, n=300, iters=1, constraints=cons,
|
|
sampling_method='sobol')
|
|
|
|
def test_21_1_jac_true(self):
|
|
"""Test that shgo can handle objective functions that return the
|
|
gradient alongside the objective value. Fixes gh-13547"""
|
|
# previous
|
|
def func(x):
|
|
return numpy.sum(numpy.power(x, 2)), 2 * x
|
|
|
|
shgo(
|
|
func,
|
|
bounds=[[-1, 1], [1, 2]],
|
|
n=100, iters=5,
|
|
sampling_method="sobol",
|
|
minimizer_kwargs={'method': 'SLSQP', 'jac': True}
|
|
)
|
|
|
|
# new
|
|
def func(x):
|
|
return numpy.sum(x ** 2), 2 * x
|
|
|
|
bounds = [[-1, 1], [1, 2], [-1, 1], [1, 2], [0, 3]]
|
|
|
|
res = shgo(func, bounds=bounds, sampling_method="sobol",
|
|
minimizer_kwargs={'method': 'SLSQP', 'jac': True})
|
|
ref = minimize(func, x0=[1, 1, 1, 1, 1], bounds=bounds,
|
|
jac=True)
|
|
assert res.success
|
|
assert_allclose(res.fun, ref.fun)
|
|
assert_allclose(res.x, ref.x, atol=1e-15)
|
|
|
|
@pytest.mark.parametrize('derivative', ['jac', 'hess', 'hessp'])
|
|
def test_21_2_derivative_options(self, derivative):
|
|
"""shgo used to raise an error when passing `options` with 'jac'
|
|
# see gh-12963. check that this is resolved
|
|
"""
|
|
|
|
def objective(x):
|
|
return 3 * x[0] * x[0] + 2 * x[0] + 5
|
|
|
|
def gradient(x):
|
|
return 6 * x[0] + 2
|
|
|
|
def hess(x):
|
|
return 6
|
|
|
|
def hessp(x, p):
|
|
return 6 * p
|
|
|
|
derivative_funcs = {'jac': gradient, 'hess': hess, 'hessp': hessp}
|
|
options = {derivative: derivative_funcs[derivative]}
|
|
minimizer_kwargs = {'method': 'trust-constr'}
|
|
|
|
bounds = [(-100, 100)]
|
|
res = shgo(objective, bounds, minimizer_kwargs=minimizer_kwargs,
|
|
options=options)
|
|
ref = minimize(objective, x0=[0], bounds=bounds, **minimizer_kwargs,
|
|
**options)
|
|
|
|
assert res.success
|
|
numpy.testing.assert_allclose(res.fun, ref.fun)
|
|
numpy.testing.assert_allclose(res.x, ref.x)
|
|
|
|
def test_21_3_hess_options_rosen(self):
|
|
"""Ensure the Hessian gets passed correctly to the local minimizer
|
|
routine. Previous report gh-14533.
|
|
"""
|
|
bounds = [(0, 1.6), (0, 1.6), (0, 1.4), (0, 1.4), (0, 1.4)]
|
|
options = {'jac': rosen_der, 'hess': rosen_hess}
|
|
minimizer_kwargs = {'method': 'Newton-CG'}
|
|
res = shgo(rosen, bounds, minimizer_kwargs=minimizer_kwargs,
|
|
options=options)
|
|
ref = minimize(rosen, numpy.zeros(5), method='Newton-CG',
|
|
**options)
|
|
assert res.success
|
|
assert_allclose(res.fun, ref.fun)
|
|
assert_allclose(res.x, ref.x, atol=1e-15)
|
|
|
|
def test_21_arg_tuple_sobol(self):
|
|
"""shgo used to raise an error when passing `args` with Sobol sampling
|
|
# see gh-12114. check that this is resolved"""
|
|
|
|
def fun(x, k):
|
|
return x[0] ** k
|
|
|
|
constraints = ({'type': 'ineq', 'fun': lambda x: x[0] - 1})
|
|
|
|
bounds = [(0, 10)]
|
|
res = shgo(fun, bounds, args=(1,), constraints=constraints,
|
|
sampling_method='sobol')
|
|
ref = minimize(fun, numpy.zeros(1), bounds=bounds, args=(1,),
|
|
constraints=constraints)
|
|
assert res.success
|
|
assert_allclose(res.fun, ref.fun)
|
|
assert_allclose(res.x, ref.x)
|
|
|
|
|
|
# Failure test functions
|
|
class TestShgoFailures:
|
|
def test_1_maxiter(self):
|
|
"""Test failure on insufficient iterations"""
|
|
options = {'maxiter': 2}
|
|
res = shgo(test4_1.f, test4_1.bounds, n=2, iters=None,
|
|
options=options, sampling_method='sobol')
|
|
|
|
numpy.testing.assert_equal(False, res.success)
|
|
# numpy.testing.assert_equal(4, res.nfev)
|
|
numpy.testing.assert_equal(4, res.tnev)
|
|
|
|
def test_2_sampling(self):
|
|
"""Rejection of unknown sampling method"""
|
|
assert_raises(ValueError, shgo, test1_1.f, test1_1.bounds,
|
|
sampling_method='not_Sobol')
|
|
|
|
def test_3_1_no_min_pool_sobol(self):
|
|
"""Check that the routine stops when no minimiser is found
|
|
after maximum specified function evaluations"""
|
|
options = {'maxfev': 10,
|
|
# 'maxev': 10,
|
|
'disp': True}
|
|
res = shgo(test_table.f, test_table.bounds, n=3, options=options,
|
|
sampling_method='sobol')
|
|
numpy.testing.assert_equal(False, res.success)
|
|
# numpy.testing.assert_equal(9, res.nfev)
|
|
numpy.testing.assert_equal(12, res.nfev)
|
|
|
|
def test_3_2_no_min_pool_simplicial(self):
|
|
"""Check that the routine stops when no minimiser is found
|
|
after maximum specified sampling evaluations"""
|
|
options = {'maxev': 10,
|
|
'disp': True}
|
|
res = shgo(test_table.f, test_table.bounds, n=3, options=options,
|
|
sampling_method='simplicial')
|
|
numpy.testing.assert_equal(False, res.success)
|
|
|
|
def test_4_1_bound_err(self):
|
|
"""Specified bounds ub > lb"""
|
|
bounds = [(6, 3), (3, 5)]
|
|
assert_raises(ValueError, shgo, test1_1.f, bounds)
|
|
|
|
def test_4_2_bound_err(self):
|
|
"""Specified bounds are of the form (lb, ub)"""
|
|
bounds = [(3, 5, 5), (3, 5)]
|
|
assert_raises(ValueError, shgo, test1_1.f, bounds)
|
|
|
|
def test_5_1_1_infeasible_sobol(self):
|
|
"""Ensures the algorithm terminates on infeasible problems
|
|
after maxev is exceeded. Use infty constraints option"""
|
|
options = {'maxev': 100,
|
|
'disp': True}
|
|
|
|
res = shgo(test_infeasible.f, test_infeasible.bounds,
|
|
constraints=test_infeasible.cons, n=100, options=options,
|
|
sampling_method='sobol')
|
|
|
|
numpy.testing.assert_equal(False, res.success)
|
|
|
|
def test_5_1_2_infeasible_sobol(self):
|
|
"""Ensures the algorithm terminates on infeasible problems
|
|
after maxev is exceeded. Do not use infty constraints option"""
|
|
options = {'maxev': 100,
|
|
'disp': True,
|
|
'infty_constraints': False}
|
|
|
|
res = shgo(test_infeasible.f, test_infeasible.bounds,
|
|
constraints=test_infeasible.cons, n=100, options=options,
|
|
sampling_method='sobol')
|
|
|
|
numpy.testing.assert_equal(False, res.success)
|
|
|
|
def test_5_2_infeasible_simplicial(self):
|
|
"""Ensures the algorithm terminates on infeasible problems
|
|
after maxev is exceeded."""
|
|
options = {'maxev': 1000,
|
|
'disp': False}
|
|
|
|
res = shgo(test_infeasible.f, test_infeasible.bounds,
|
|
constraints=test_infeasible.cons, n=100, options=options,
|
|
sampling_method='simplicial')
|
|
|
|
numpy.testing.assert_equal(False, res.success)
|
|
|
|
def test_6_1_lower_known_f_min(self):
|
|
"""Test Global mode limiting local evaluations with f* too high"""
|
|
options = { # Specify known function value
|
|
'f_min': test2_1.expected_fun + 2.0,
|
|
'f_tol': 1e-6,
|
|
# Specify number of local iterations to perform+
|
|
'minimize_every_iter': True,
|
|
'local_iter': 1,
|
|
'infty_constraints': False}
|
|
args = (test2_1.f, test2_1.bounds)
|
|
kwargs = {'constraints': test2_1.cons,
|
|
'n': None,
|
|
'iters': None,
|
|
'options': options,
|
|
'sampling_method': 'sobol'
|
|
}
|
|
warns(UserWarning, shgo, *args, **kwargs)
|
|
|
|
def test(self):
|
|
from scipy.optimize import rosen, shgo
|
|
bounds = [(0, 2), (0, 2), (0, 2), (0, 2), (0, 2)]
|
|
|
|
def fun(x):
|
|
fun.nfev += 1
|
|
return rosen(x)
|
|
|
|
fun.nfev = 0
|
|
|
|
result = shgo(fun, bounds)
|
|
print(result.x, result.fun, fun.nfev) # 50
|
|
|
|
|
|
# Returns
|
|
class TestShgoReturns:
|
|
def test_1_nfev_simplicial(self):
|
|
bounds = [(0, 2), (0, 2), (0, 2), (0, 2), (0, 2)]
|
|
|
|
def fun(x):
|
|
fun.nfev += 1
|
|
return rosen(x)
|
|
|
|
fun.nfev = 0
|
|
|
|
result = shgo(fun, bounds)
|
|
numpy.testing.assert_equal(fun.nfev, result.nfev)
|
|
|
|
def test_1_nfev_sobol(self):
|
|
bounds = [(0, 2), (0, 2), (0, 2), (0, 2), (0, 2)]
|
|
|
|
def fun(x):
|
|
fun.nfev += 1
|
|
return rosen(x)
|
|
|
|
fun.nfev = 0
|
|
|
|
result = shgo(fun, bounds, sampling_method='sobol')
|
|
numpy.testing.assert_equal(fun.nfev, result.nfev)
|
|
|
|
|
|
def test_vector_constraint():
|
|
# gh15514
|
|
def quad(x):
|
|
x = np.asarray(x)
|
|
return [np.sum(x ** 2)]
|
|
|
|
nlc = NonlinearConstraint(quad, [2.2], [3])
|
|
oldc = new_constraint_to_old(nlc, np.array([1.0, 1.0]))
|
|
|
|
res = shgo(rosen, [(0, 10), (0, 10)], constraints=oldc, sampling_method='sobol')
|
|
assert np.all(np.sum((res.x)**2) >= 2.2)
|
|
assert np.all(np.sum((res.x) ** 2) <= 3.0)
|
|
assert res.success
|
|
|
|
|
|
@pytest.mark.filterwarnings("ignore:delta_grad")
|
|
def test_trust_constr():
|
|
def quad(x):
|
|
x = np.asarray(x)
|
|
return [np.sum(x ** 2)]
|
|
|
|
nlc = NonlinearConstraint(quad, [2.6], [3])
|
|
minimizer_kwargs = {'method': 'trust-constr'}
|
|
# note that we don't supply the constraints in minimizer_kwargs,
|
|
# so if the final result obeys the constraints we know that shgo
|
|
# passed them on to 'trust-constr'
|
|
res = shgo(
|
|
rosen,
|
|
[(0, 10), (0, 10)],
|
|
constraints=nlc,
|
|
sampling_method='sobol',
|
|
minimizer_kwargs=minimizer_kwargs
|
|
)
|
|
assert np.all(np.sum((res.x)**2) >= 2.6)
|
|
assert np.all(np.sum((res.x) ** 2) <= 3.0)
|
|
assert res.success
|
|
|
|
|
|
def test_equality_constraints():
|
|
# gh16260
|
|
bounds = [(0.9, 4.0)] * 2 # Constrain probabilities to 0 and 1.
|
|
|
|
def faulty(x):
|
|
return x[0] + x[1]
|
|
|
|
nlc = NonlinearConstraint(faulty, 3.9, 3.9)
|
|
res = shgo(rosen, bounds=bounds, constraints=nlc)
|
|
assert_allclose(np.sum(res.x), 3.9)
|
|
|
|
def faulty(x):
|
|
return x[0] + x[1] - 3.9
|
|
|
|
constraints = {'type': 'eq', 'fun': faulty}
|
|
res = shgo(rosen, bounds=bounds, constraints=constraints)
|
|
assert_allclose(np.sum(res.x), 3.9)
|
|
|
|
bounds = [(0, 1.0)] * 4
|
|
# sum of variable should equal 1.
|
|
def faulty(x):
|
|
return x[0] + x[1] + x[2] + x[3] - 1
|
|
|
|
# options = {'minimize_every_iter': True, 'local_iter':10}
|
|
constraints = {'type': 'eq', 'fun': faulty}
|
|
res = shgo(
|
|
lambda x: - np.prod(x),
|
|
bounds=bounds,
|
|
constraints=constraints,
|
|
sampling_method='sobol'
|
|
)
|
|
assert_allclose(np.sum(res.x), 1.0)
|
|
|
|
def test_gh16971():
|
|
def cons(x):
|
|
return np.sum(x**2) - 0
|
|
|
|
c = {'fun': cons, 'type': 'ineq'}
|
|
minimizer_kwargs = {
|
|
'method': 'COBYLA',
|
|
'options': {'rhobeg': 5, 'tol': 5e-1, 'catol': 0.05}
|
|
}
|
|
|
|
s = SHGO(
|
|
rosen, [(0, 10)]*2, constraints=c, minimizer_kwargs=minimizer_kwargs
|
|
)
|
|
|
|
assert s.minimizer_kwargs['method'].lower() == 'cobyla'
|
|
assert s.minimizer_kwargs['options']['catol'] == 0.05
|