1202 lines
48 KiB
Python
1202 lines
48 KiB
Python
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"""
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Unit tests for the differential global minimization algorithm.
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"""
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import multiprocessing
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import platform
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from scipy.optimize._differentialevolution import (DifferentialEvolutionSolver,
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_ConstraintWrapper)
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from scipy.optimize import differential_evolution
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from scipy.optimize._constraints import (Bounds, NonlinearConstraint,
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LinearConstraint)
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from scipy.optimize import rosen
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from scipy.sparse import csr_matrix
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from scipy._lib._pep440 import Version
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import numpy as np
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from numpy.testing import (assert_equal, assert_allclose,
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assert_almost_equal, assert_array_equal,
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assert_string_equal, assert_, suppress_warnings)
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from pytest import raises as assert_raises, warns
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import pytest
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class TestDifferentialEvolutionSolver(object):
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def setup_method(self):
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self.old_seterr = np.seterr(invalid='raise')
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self.limits = np.array([[0., 0.],
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[2., 2.]])
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self.bounds = [(0., 2.), (0., 2.)]
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self.dummy_solver = DifferentialEvolutionSolver(self.quadratic,
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[(0, 100)])
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# dummy_solver2 will be used to test mutation strategies
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self.dummy_solver2 = DifferentialEvolutionSolver(self.quadratic,
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[(0, 1)],
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popsize=7,
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mutation=0.5)
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# create a population that's only 7 members long
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# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
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population = np.atleast_2d(np.arange(0.1, 0.8, 0.1)).T
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self.dummy_solver2.population = population
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def teardown_method(self):
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np.seterr(**self.old_seterr)
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def quadratic(self, x):
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return x[0]**2
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def test__strategy_resolves(self):
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# test that the correct mutation function is resolved by
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# different requested strategy arguments
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='best1exp')
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assert_equal(solver.strategy, 'best1exp')
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assert_equal(solver.mutation_func.__name__, '_best1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='best1bin')
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assert_equal(solver.strategy, 'best1bin')
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assert_equal(solver.mutation_func.__name__, '_best1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='rand1bin')
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assert_equal(solver.strategy, 'rand1bin')
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assert_equal(solver.mutation_func.__name__, '_rand1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='rand1exp')
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assert_equal(solver.strategy, 'rand1exp')
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assert_equal(solver.mutation_func.__name__, '_rand1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='rand2exp')
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assert_equal(solver.strategy, 'rand2exp')
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assert_equal(solver.mutation_func.__name__, '_rand2')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='best2bin')
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assert_equal(solver.strategy, 'best2bin')
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assert_equal(solver.mutation_func.__name__, '_best2')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='rand2bin')
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assert_equal(solver.strategy, 'rand2bin')
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assert_equal(solver.mutation_func.__name__, '_rand2')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='rand2exp')
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assert_equal(solver.strategy, 'rand2exp')
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assert_equal(solver.mutation_func.__name__, '_rand2')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='randtobest1bin')
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assert_equal(solver.strategy, 'randtobest1bin')
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assert_equal(solver.mutation_func.__name__, '_randtobest1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='randtobest1exp')
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assert_equal(solver.strategy, 'randtobest1exp')
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assert_equal(solver.mutation_func.__name__, '_randtobest1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='currenttobest1bin')
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assert_equal(solver.strategy, 'currenttobest1bin')
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assert_equal(solver.mutation_func.__name__, '_currenttobest1')
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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strategy='currenttobest1exp')
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assert_equal(solver.strategy, 'currenttobest1exp')
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assert_equal(solver.mutation_func.__name__, '_currenttobest1')
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def test__mutate1(self):
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# strategies */1/*, i.e. rand/1/bin, best/1/exp, etc.
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result = np.array([0.05])
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trial = self.dummy_solver2._best1((2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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result = np.array([0.25])
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trial = self.dummy_solver2._rand1((2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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def test__mutate2(self):
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# strategies */2/*, i.e. rand/2/bin, best/2/exp, etc.
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# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
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result = np.array([-0.1])
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trial = self.dummy_solver2._best2((2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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result = np.array([0.1])
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trial = self.dummy_solver2._rand2((2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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def test__randtobest1(self):
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# strategies randtobest/1/*
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result = np.array([0.15])
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trial = self.dummy_solver2._randtobest1((2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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def test__currenttobest1(self):
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# strategies currenttobest/1/*
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result = np.array([0.1])
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trial = self.dummy_solver2._currenttobest1(1, (2, 3, 4, 5, 6))
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assert_allclose(trial, result)
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def test_can_init_with_dithering(self):
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mutation = (0.5, 1)
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solver = DifferentialEvolutionSolver(self.quadratic,
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self.bounds,
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mutation=mutation)
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assert_equal(solver.dither, list(mutation))
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def test_invalid_mutation_values_arent_accepted(self):
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func = rosen
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mutation = (0.5, 3)
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assert_raises(ValueError,
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DifferentialEvolutionSolver,
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func,
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self.bounds,
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mutation=mutation)
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mutation = (-1, 1)
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assert_raises(ValueError,
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DifferentialEvolutionSolver,
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func,
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self.bounds,
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mutation=mutation)
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mutation = (0.1, np.nan)
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assert_raises(ValueError,
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DifferentialEvolutionSolver,
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func,
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self.bounds,
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mutation=mutation)
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mutation = 0.5
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solver = DifferentialEvolutionSolver(func,
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self.bounds,
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mutation=mutation)
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assert_equal(0.5, solver.scale)
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assert_equal(None, solver.dither)
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def test__scale_parameters(self):
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trial = np.array([0.3])
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assert_equal(30, self.dummy_solver._scale_parameters(trial))
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# it should also work with the limits reversed
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self.dummy_solver.limits = np.array([[100], [0.]])
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assert_equal(30, self.dummy_solver._scale_parameters(trial))
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def test__unscale_parameters(self):
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trial = np.array([30])
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assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
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# it should also work with the limits reversed
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self.dummy_solver.limits = np.array([[100], [0.]])
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assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
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def test__ensure_constraint(self):
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trial = np.array([1.1, -100, 0.9, 2., 300., -0.00001])
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self.dummy_solver._ensure_constraint(trial)
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assert_equal(trial[2], 0.9)
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assert_(np.logical_and(trial >= 0, trial <= 1).all())
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def test_differential_evolution(self):
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# test that the Jmin of DifferentialEvolutionSolver
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# is the same as the function evaluation
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solver = DifferentialEvolutionSolver(self.quadratic, [(-2, 2)])
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result = solver.solve()
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assert_almost_equal(result.fun, self.quadratic(result.x))
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def test_best_solution_retrieval(self):
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# test that the getter property method for the best solution works.
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solver = DifferentialEvolutionSolver(self.quadratic, [(-2, 2)])
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result = solver.solve()
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assert_almost_equal(result.x, solver.x)
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def test_callback_terminates(self):
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# test that if the callback returns true, then the minimization halts
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bounds = [(0, 2), (0, 2)]
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expected_msg = 'callback function requested stop early by returning True'
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def callback_python_true(param, convergence=0.):
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return True
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result = differential_evolution(rosen, bounds, callback=callback_python_true)
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assert_string_equal(result.message, expected_msg)
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def callback_evaluates_true(param, convergence=0.):
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# DE should stop if bool(self.callback) is True
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return [10]
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result = differential_evolution(rosen, bounds, callback=callback_evaluates_true)
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assert_string_equal(result.message, expected_msg)
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def callback_evaluates_false(param, convergence=0.):
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return []
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result = differential_evolution(rosen, bounds, callback=callback_evaluates_false)
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assert result.success
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def test_args_tuple_is_passed(self):
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# test that the args tuple is passed to the cost function properly.
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bounds = [(-10, 10)]
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args = (1., 2., 3.)
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def quadratic(x, *args):
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if type(args) != tuple:
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raise ValueError('args should be a tuple')
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return args[0] + args[1] * x + args[2] * x**2.
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result = differential_evolution(quadratic,
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bounds,
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args=args,
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polish=True)
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assert_almost_equal(result.fun, 2 / 3.)
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def test_init_with_invalid_strategy(self):
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# test that passing an invalid strategy raises ValueError
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func = rosen
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bounds = [(-3, 3)]
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assert_raises(ValueError,
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differential_evolution,
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func,
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bounds,
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strategy='abc')
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def test_bounds_checking(self):
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# test that the bounds checking works
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func = rosen
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bounds = [(-3)]
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assert_raises(ValueError,
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differential_evolution,
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func,
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bounds)
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bounds = [(-3, 3), (3, 4, 5)]
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assert_raises(ValueError,
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differential_evolution,
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func,
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bounds)
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# test that we can use a new-type Bounds object
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result = differential_evolution(rosen, Bounds([0, 0], [2, 2]))
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assert_almost_equal(result.x, (1., 1.))
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def test_select_samples(self):
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# select_samples should return 5 separate random numbers.
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limits = np.arange(12., dtype='float64').reshape(2, 6)
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bounds = list(zip(limits[0, :], limits[1, :]))
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solver = DifferentialEvolutionSolver(None, bounds, popsize=1)
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candidate = 0
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r1, r2, r3, r4, r5 = solver._select_samples(candidate, 5)
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assert_equal(
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len(np.unique(np.array([candidate, r1, r2, r3, r4, r5]))), 6)
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def test_maxiter_stops_solve(self):
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# test that if the maximum number of iterations is exceeded
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# the solver stops.
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solver = DifferentialEvolutionSolver(rosen, self.bounds, maxiter=1)
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result = solver.solve()
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assert_equal(result.success, False)
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assert_equal(result.message,
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'Maximum number of iterations has been exceeded.')
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def test_maxfun_stops_solve(self):
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# test that if the maximum number of function evaluations is exceeded
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# during initialisation the solver stops
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solver = DifferentialEvolutionSolver(rosen, self.bounds, maxfun=1,
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polish=False)
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result = solver.solve()
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assert_equal(result.nfev, 2)
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assert_equal(result.success, False)
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assert_equal(result.message,
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'Maximum number of function evaluations has '
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'been exceeded.')
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# test that if the maximum number of function evaluations is exceeded
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# during the actual minimisation, then the solver stops.
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# Have to turn polishing off, as this will still occur even if maxfun
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# is reached. For popsize=5 and len(bounds)=2, then there are only 10
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# function evaluations during initialisation.
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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popsize=5,
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polish=False,
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maxfun=40)
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result = solver.solve()
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assert_equal(result.nfev, 41)
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assert_equal(result.success, False)
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assert_equal(result.message,
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'Maximum number of function evaluations has '
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'been exceeded.')
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# now repeat for updating='deferred version
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solver = DifferentialEvolutionSolver(rosen,
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self.bounds,
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popsize=5,
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polish=False,
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maxfun=40,
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updating='deferred')
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|
result = solver.solve()
|
||
|
|
|
||
|
|
assert_equal(result.nfev, 40)
|
||
|
|
assert_equal(result.success, False)
|
||
|
|
assert_equal(result.message,
|
||
|
|
'Maximum number of function evaluations has '
|
||
|
|
'been reached.')
|
||
|
|
|
||
|
|
def test_quadratic(self):
|
||
|
|
# test the quadratic function from object
|
||
|
|
solver = DifferentialEvolutionSolver(self.quadratic,
|
||
|
|
[(-100, 100)],
|
||
|
|
tol=0.02)
|
||
|
|
solver.solve()
|
||
|
|
assert_equal(np.argmin(solver.population_energies), 0)
|
||
|
|
|
||
|
|
def test_quadratic_from_diff_ev(self):
|
||
|
|
# test the quadratic function from differential_evolution function
|
||
|
|
differential_evolution(self.quadratic,
|
||
|
|
[(-100, 100)],
|
||
|
|
tol=0.02)
|
||
|
|
|
||
|
|
def test_seed_gives_repeatability(self):
|
||
|
|
result = differential_evolution(self.quadratic,
|
||
|
|
[(-100, 100)],
|
||
|
|
polish=False,
|
||
|
|
seed=1,
|
||
|
|
tol=0.5)
|
||
|
|
result2 = differential_evolution(self.quadratic,
|
||
|
|
[(-100, 100)],
|
||
|
|
polish=False,
|
||
|
|
seed=1,
|
||
|
|
tol=0.5)
|
||
|
|
assert_equal(result.x, result2.x)
|
||
|
|
assert_equal(result.nfev, result2.nfev)
|
||
|
|
|
||
|
|
@pytest.mark.skipif(Version(np.__version__) < Version('1.17'),
|
||
|
|
reason='Generator not available for numpy, < 1.17')
|
||
|
|
def test_random_generator(self):
|
||
|
|
# check that np.random.Generator can be used (numpy >= 1.17)
|
||
|
|
# obtain a np.random.Generator object
|
||
|
|
rng = np.random.default_rng()
|
||
|
|
|
||
|
|
inits = ['random', 'latinhypercube']
|
||
|
|
for init in inits:
|
||
|
|
differential_evolution(self.quadratic,
|
||
|
|
[(-100, 100)],
|
||
|
|
polish=False,
|
||
|
|
seed=rng,
|
||
|
|
tol=0.5,
|
||
|
|
init=init)
|
||
|
|
|
||
|
|
def test_exp_runs(self):
|
||
|
|
# test whether exponential mutation loop runs
|
||
|
|
solver = DifferentialEvolutionSolver(rosen,
|
||
|
|
self.bounds,
|
||
|
|
strategy='best1exp',
|
||
|
|
maxiter=1)
|
||
|
|
|
||
|
|
solver.solve()
|
||
|
|
|
||
|
|
def test_gh_4511_regression(self):
|
||
|
|
# This modification of the differential evolution docstring example
|
||
|
|
# uses a custom popsize that had triggered an off-by-one error.
|
||
|
|
# Because we do not care about solving the optimization problem in
|
||
|
|
# this test, we use maxiter=1 to reduce the testing time.
|
||
|
|
bounds = [(-5, 5), (-5, 5)]
|
||
|
|
# result = differential_evolution(rosen, bounds, popsize=1815,
|
||
|
|
# maxiter=1)
|
||
|
|
|
||
|
|
# the original issue arose because of rounding error in arange, with
|
||
|
|
# linspace being a much better solution. 1815 is quite a large popsize
|
||
|
|
# to use and results in a long test time (~13s). I used the original
|
||
|
|
# issue to figure out the lowest number of samples that would cause
|
||
|
|
# this rounding error to occur, 49.
|
||
|
|
differential_evolution(rosen, bounds, popsize=49, maxiter=1)
|
||
|
|
|
||
|
|
def test_calculate_population_energies(self):
|
||
|
|
# if popsize is 3, then the overall generation has size (6,)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds, popsize=3)
|
||
|
|
solver._calculate_population_energies(solver.population)
|
||
|
|
solver._promote_lowest_energy()
|
||
|
|
assert_equal(np.argmin(solver.population_energies), 0)
|
||
|
|
|
||
|
|
# initial calculation of the energies should require 6 nfev.
|
||
|
|
assert_equal(solver._nfev, 6)
|
||
|
|
|
||
|
|
def test_iteration(self):
|
||
|
|
# test that DifferentialEvolutionSolver is iterable
|
||
|
|
# if popsize is 3, then the overall generation has size (6,)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds, popsize=3,
|
||
|
|
maxfun=12)
|
||
|
|
x, fun = next(solver)
|
||
|
|
assert_equal(np.size(x, 0), 2)
|
||
|
|
|
||
|
|
# 6 nfev are required for initial calculation of energies, 6 nfev are
|
||
|
|
# required for the evolution of the 6 population members.
|
||
|
|
assert_equal(solver._nfev, 12)
|
||
|
|
|
||
|
|
# the next generation should halt because it exceeds maxfun
|
||
|
|
assert_raises(StopIteration, next, solver)
|
||
|
|
|
||
|
|
# check a proper minimisation can be done by an iterable solver
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds)
|
||
|
|
_, fun_prev = next(solver)
|
||
|
|
for i, soln in enumerate(solver):
|
||
|
|
x_current, fun_current = soln
|
||
|
|
assert(fun_prev >= fun_current)
|
||
|
|
_, fun_prev = x_current, fun_current
|
||
|
|
# need to have this otherwise the solver would never stop.
|
||
|
|
if i == 50:
|
||
|
|
break
|
||
|
|
|
||
|
|
def test_convergence(self):
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds, tol=0.2,
|
||
|
|
polish=False)
|
||
|
|
solver.solve()
|
||
|
|
assert_(solver.convergence < 0.2)
|
||
|
|
|
||
|
|
def test_maxiter_none_GH5731(self):
|
||
|
|
# Pre 0.17 the previous default for maxiter and maxfun was None.
|
||
|
|
# the numerical defaults are now 1000 and np.inf. However, some scripts
|
||
|
|
# will still supply None for both of those, this will raise a TypeError
|
||
|
|
# in the solve method.
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxiter=None,
|
||
|
|
maxfun=None)
|
||
|
|
solver.solve()
|
||
|
|
|
||
|
|
def test_population_initiation(self):
|
||
|
|
# test the different modes of population initiation
|
||
|
|
|
||
|
|
# init must be either 'latinhypercube' or 'random'
|
||
|
|
# raising ValueError is something else is passed in
|
||
|
|
assert_raises(ValueError,
|
||
|
|
DifferentialEvolutionSolver,
|
||
|
|
*(rosen, self.bounds),
|
||
|
|
**{'init': 'rubbish'})
|
||
|
|
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds)
|
||
|
|
|
||
|
|
# check that population initiation:
|
||
|
|
# 1) resets _nfev to 0
|
||
|
|
# 2) all population energies are np.inf
|
||
|
|
solver.init_population_random()
|
||
|
|
assert_equal(solver._nfev, 0)
|
||
|
|
assert_(np.all(np.isinf(solver.population_energies)))
|
||
|
|
|
||
|
|
solver.init_population_lhs()
|
||
|
|
assert_equal(solver._nfev, 0)
|
||
|
|
assert_(np.all(np.isinf(solver.population_energies)))
|
||
|
|
|
||
|
|
# we should be able to initialize with our own array
|
||
|
|
population = np.linspace(-1, 3, 10).reshape(5, 2)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds,
|
||
|
|
init=population,
|
||
|
|
strategy='best2bin',
|
||
|
|
atol=0.01, seed=1, popsize=5)
|
||
|
|
|
||
|
|
assert_equal(solver._nfev, 0)
|
||
|
|
assert_(np.all(np.isinf(solver.population_energies)))
|
||
|
|
assert_(solver.num_population_members == 5)
|
||
|
|
assert_(solver.population_shape == (5, 2))
|
||
|
|
|
||
|
|
# check that the population was initialized correctly
|
||
|
|
unscaled_population = np.clip(solver._unscale_parameters(population),
|
||
|
|
0, 1)
|
||
|
|
assert_almost_equal(solver.population[:5], unscaled_population)
|
||
|
|
|
||
|
|
# population values need to be clipped to bounds
|
||
|
|
assert_almost_equal(np.min(solver.population[:5]), 0)
|
||
|
|
assert_almost_equal(np.max(solver.population[:5]), 1)
|
||
|
|
|
||
|
|
# shouldn't be able to initialize with an array if it's the wrong shape
|
||
|
|
# this would have too many parameters
|
||
|
|
population = np.linspace(-1, 3, 15).reshape(5, 3)
|
||
|
|
assert_raises(ValueError,
|
||
|
|
DifferentialEvolutionSolver,
|
||
|
|
*(rosen, self.bounds),
|
||
|
|
**{'init': population})
|
||
|
|
|
||
|
|
def test_infinite_objective_function(self):
|
||
|
|
# Test that there are no problems if the objective function
|
||
|
|
# returns inf on some runs
|
||
|
|
def sometimes_inf(x):
|
||
|
|
if x[0] < .5:
|
||
|
|
return np.inf
|
||
|
|
return x[1]
|
||
|
|
bounds = [(0, 1), (0, 1)]
|
||
|
|
differential_evolution(sometimes_inf, bounds=bounds, disp=False)
|
||
|
|
|
||
|
|
def test_deferred_updating(self):
|
||
|
|
# check setting of deferred updating, with default workers
|
||
|
|
bounds = [(0., 2.), (0., 2.)]
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, bounds, updating='deferred')
|
||
|
|
assert_(solver._updating == 'deferred')
|
||
|
|
assert_(solver._mapwrapper._mapfunc is map)
|
||
|
|
solver.solve()
|
||
|
|
|
||
|
|
def test_immediate_updating(self):
|
||
|
|
# check setting of immediate updating, with default workers
|
||
|
|
bounds = [(0., 2.), (0., 2.)]
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, bounds)
|
||
|
|
assert_(solver._updating == 'immediate')
|
||
|
|
|
||
|
|
# should raise a UserWarning because the updating='immediate'
|
||
|
|
# is being overridden by the workers keyword
|
||
|
|
with warns(UserWarning):
|
||
|
|
with DifferentialEvolutionSolver(rosen, bounds, workers=2) as solver:
|
||
|
|
pass
|
||
|
|
assert_(solver._updating == 'deferred')
|
||
|
|
|
||
|
|
def test_parallel(self):
|
||
|
|
# smoke test for parallelization with deferred updating
|
||
|
|
bounds = [(0., 2.), (0., 2.)]
|
||
|
|
with multiprocessing.Pool(2) as p, DifferentialEvolutionSolver(
|
||
|
|
rosen, bounds, updating='deferred', workers=p.map) as solver:
|
||
|
|
assert_(solver._mapwrapper.pool is not None)
|
||
|
|
assert_(solver._updating == 'deferred')
|
||
|
|
solver.solve()
|
||
|
|
|
||
|
|
with DifferentialEvolutionSolver(rosen, bounds, updating='deferred',
|
||
|
|
workers=2) as solver:
|
||
|
|
assert_(solver._mapwrapper.pool is not None)
|
||
|
|
assert_(solver._updating == 'deferred')
|
||
|
|
solver.solve()
|
||
|
|
|
||
|
|
def test_converged(self):
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)])
|
||
|
|
solver.solve()
|
||
|
|
assert_(solver.converged())
|
||
|
|
|
||
|
|
def test_constraint_violation_fn(self):
|
||
|
|
def constr_f(x):
|
||
|
|
return [x[0] + x[1]]
|
||
|
|
|
||
|
|
def constr_f2(x):
|
||
|
|
return [x[0]**2 + x[1], x[0] - x[1]]
|
||
|
|
|
||
|
|
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
|
||
|
|
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc))
|
||
|
|
|
||
|
|
cv = solver._constraint_violation_fn([1.0, 1.0])
|
||
|
|
assert_almost_equal(cv, 0.1)
|
||
|
|
|
||
|
|
nlc2 = NonlinearConstraint(constr_f2, -np.inf, 1.8)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc, nlc2))
|
||
|
|
|
||
|
|
# for multiple constraints the constraint violations should
|
||
|
|
# be concatenated.
|
||
|
|
cv = solver._constraint_violation_fn([1.2, 1.])
|
||
|
|
assert_almost_equal(cv, [0.3, 0.64, 0])
|
||
|
|
|
||
|
|
cv = solver._constraint_violation_fn([2., 2.])
|
||
|
|
assert_almost_equal(cv, [2.1, 4.2, 0])
|
||
|
|
|
||
|
|
# should accept valid values
|
||
|
|
cv = solver._constraint_violation_fn([0.5, 0.5])
|
||
|
|
assert_almost_equal(cv, [0., 0., 0.])
|
||
|
|
|
||
|
|
def test_constraint_population_feasibilities(self):
|
||
|
|
def constr_f(x):
|
||
|
|
return [x[0] + x[1]]
|
||
|
|
|
||
|
|
def constr_f2(x):
|
||
|
|
return [x[0]**2 + x[1], x[0] - x[1]]
|
||
|
|
|
||
|
|
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
|
||
|
|
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc))
|
||
|
|
|
||
|
|
# are population feasibilities correct
|
||
|
|
# [0.5, 0.5] corresponds to scaled values of [1., 1.]
|
||
|
|
feas, cv = solver._calculate_population_feasibilities(
|
||
|
|
np.array([[0.5, 0.5], [1., 1.]]))
|
||
|
|
assert_equal(feas, [False, False])
|
||
|
|
assert_almost_equal(cv, np.array([[0.1], [2.1]]))
|
||
|
|
assert cv.shape == (2, 1)
|
||
|
|
|
||
|
|
nlc2 = NonlinearConstraint(constr_f2, -np.inf, 1.8)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc, nlc2))
|
||
|
|
|
||
|
|
feas, cv = solver._calculate_population_feasibilities(
|
||
|
|
np.array([[0.5, 0.5], [0.6, 0.5]]))
|
||
|
|
assert_equal(feas, [False, False])
|
||
|
|
assert_almost_equal(cv, np.array([[0.1, 0.2, 0], [0.3, 0.64, 0]]))
|
||
|
|
|
||
|
|
feas, cv = solver._calculate_population_feasibilities(
|
||
|
|
np.array([[0.5, 0.5], [1., 1.]]))
|
||
|
|
assert_equal(feas, [False, False])
|
||
|
|
assert_almost_equal(cv, np.array([[0.1, 0.2, 0], [2.1, 4.2, 0]]))
|
||
|
|
assert cv.shape == (2, 3)
|
||
|
|
|
||
|
|
feas, cv = solver._calculate_population_feasibilities(
|
||
|
|
np.array([[0.25, 0.25], [1., 1.]]))
|
||
|
|
assert_equal(feas, [True, False])
|
||
|
|
assert_almost_equal(cv, np.array([[0.0, 0.0, 0.], [2.1, 4.2, 0]]))
|
||
|
|
assert cv.shape == (2, 3)
|
||
|
|
|
||
|
|
def test_constraint_solve(self):
|
||
|
|
def constr_f(x):
|
||
|
|
return np.array([x[0] + x[1]])
|
||
|
|
|
||
|
|
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
|
||
|
|
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc))
|
||
|
|
|
||
|
|
# trust-constr warns if the constraint function is linear
|
||
|
|
with warns(UserWarning):
|
||
|
|
res = solver.solve()
|
||
|
|
|
||
|
|
assert constr_f(res.x) <= 1.9
|
||
|
|
assert res.success
|
||
|
|
|
||
|
|
def test_impossible_constraint(self):
|
||
|
|
def constr_f(x):
|
||
|
|
return np.array([x[0] + x[1]])
|
||
|
|
|
||
|
|
nlc = NonlinearConstraint(constr_f, -np.inf, -1)
|
||
|
|
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc), popsize=3,
|
||
|
|
seed=1)
|
||
|
|
|
||
|
|
# a UserWarning is issued because the 'trust-constr' polishing is
|
||
|
|
# attempted on the least infeasible solution found.
|
||
|
|
with warns(UserWarning):
|
||
|
|
res = solver.solve()
|
||
|
|
|
||
|
|
assert res.maxcv > 0
|
||
|
|
assert not res.success
|
||
|
|
|
||
|
|
# test _promote_lowest_energy works when none of the population is
|
||
|
|
# feasible. In this case, the solution with the lowest constraint
|
||
|
|
# violation should be promoted.
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc), polish=False)
|
||
|
|
next(solver)
|
||
|
|
assert not solver.feasible.all()
|
||
|
|
assert not np.isfinite(solver.population_energies).all()
|
||
|
|
|
||
|
|
# now swap two of the entries in the population
|
||
|
|
l = 20
|
||
|
|
cv = solver.constraint_violation[0]
|
||
|
|
|
||
|
|
solver.population_energies[[0, l]] = solver.population_energies[[l, 0]]
|
||
|
|
solver.population[[0, l], :] = solver.population[[l, 0], :]
|
||
|
|
solver.constraint_violation[[0, l], :] = (
|
||
|
|
solver.constraint_violation[[l, 0], :])
|
||
|
|
|
||
|
|
solver._promote_lowest_energy()
|
||
|
|
assert_equal(solver.constraint_violation[0], cv)
|
||
|
|
|
||
|
|
def test_accept_trial(self):
|
||
|
|
# _accept_trial(self, energy_trial, feasible_trial, cv_trial,
|
||
|
|
# energy_orig, feasible_orig, cv_orig)
|
||
|
|
def constr_f(x):
|
||
|
|
return [x[0] + x[1]]
|
||
|
|
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
|
||
|
|
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
|
||
|
|
constraints=(nlc))
|
||
|
|
fn = solver._accept_trial
|
||
|
|
# both solutions are feasible, select lower energy
|
||
|
|
assert fn(0.1, True, np.array([0.]), 1.0, True, np.array([0.]))
|
||
|
|
assert (fn(1.0, True, np.array([0.]), 0.1, True, np.array([0.]))
|
||
|
|
== False)
|
||
|
|
assert fn(0.1, True, np.array([0.]), 0.1, True, np.array([0.]))
|
||
|
|
|
||
|
|
# trial is feasible, original is not
|
||
|
|
assert fn(9.9, True, np.array([0.]), 1.0, False, np.array([1.]))
|
||
|
|
|
||
|
|
# trial and original are infeasible
|
||
|
|
# cv_trial have to be <= cv_original to be better
|
||
|
|
assert (fn(0.1, False, np.array([0.5, 0.5]),
|
||
|
|
1.0, False, np.array([1., 1.0])))
|
||
|
|
assert (fn(0.1, False, np.array([0.5, 0.5]),
|
||
|
|
1.0, False, np.array([1., 0.50])))
|
||
|
|
assert (fn(1.0, False, np.array([0.5, 0.5]),
|
||
|
|
1.0, False, np.array([1., 0.4])) == False)
|
||
|
|
|
||
|
|
def test_constraint_wrapper(self):
|
||
|
|
lb = np.array([0, 20, 30])
|
||
|
|
ub = np.array([0.5, np.inf, 70])
|
||
|
|
x0 = np.array([1, 2, 3])
|
||
|
|
pc = _ConstraintWrapper(Bounds(lb, ub), x0)
|
||
|
|
assert (pc.violation(x0) > 0).any()
|
||
|
|
assert (pc.violation([0.25, 21, 31]) == 0).all()
|
||
|
|
|
||
|
|
x0 = np.array([1, 2, 3, 4])
|
||
|
|
A = np.array([[1, 2, 3, 4], [5, 0, 0, 6], [7, 0, 8, 0]])
|
||
|
|
pc = _ConstraintWrapper(LinearConstraint(A, -np.inf, 0), x0)
|
||
|
|
assert (pc.violation(x0) > 0).any()
|
||
|
|
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
|
||
|
|
|
||
|
|
pc = _ConstraintWrapper(LinearConstraint(csr_matrix(A), -np.inf, 0),
|
||
|
|
x0)
|
||
|
|
assert (pc.violation(x0) > 0).any()
|
||
|
|
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
|
||
|
|
|
||
|
|
def fun(x):
|
||
|
|
return A.dot(x)
|
||
|
|
|
||
|
|
nonlinear = NonlinearConstraint(fun, -np.inf, 0)
|
||
|
|
pc = _ConstraintWrapper(nonlinear, [-10, 2, -10, 4])
|
||
|
|
assert (pc.violation(x0) > 0).any()
|
||
|
|
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
|
||
|
|
|
||
|
|
def test_constraint_wrapper_violation(self):
|
||
|
|
def cons_f(x):
|
||
|
|
return np.array([x[0] ** 2 + x[1], x[0] ** 2 - x[1]])
|
||
|
|
|
||
|
|
nlc = NonlinearConstraint(cons_f, [-1, -0.8500], [2, 2])
|
||
|
|
pc = _ConstraintWrapper(nlc, [0.5, 1])
|
||
|
|
assert np.size(pc.bounds[0]) == 2
|
||
|
|
|
||
|
|
assert_array_equal(pc.violation([0.5, 1]), [0., 0.])
|
||
|
|
assert_almost_equal(pc.violation([0.5, 1.2]), [0., 0.1])
|
||
|
|
assert_almost_equal(pc.violation([1.2, 1.2]), [0.64, 0])
|
||
|
|
assert_almost_equal(pc.violation([0.1, -1.2]), [0.19, 0])
|
||
|
|
assert_almost_equal(pc.violation([0.1, 2]), [0.01, 1.14])
|
||
|
|
|
||
|
|
def test_L1(self):
|
||
|
|
# Lampinen ([5]) test problem 1
|
||
|
|
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = np.sum(5*x[1:5]) - 5*x[1:5]@x[1:5] - np.sum(x[5:])
|
||
|
|
return fun
|
||
|
|
|
||
|
|
A = np.zeros((10, 14)) # 1-indexed to match reference
|
||
|
|
A[1, [1, 2, 10, 11]] = 2, 2, 1, 1
|
||
|
|
A[2, [1, 10]] = -8, 1
|
||
|
|
A[3, [4, 5, 10]] = -2, -1, 1
|
||
|
|
A[4, [1, 3, 10, 11]] = 2, 2, 1, 1
|
||
|
|
A[5, [2, 11]] = -8, 1
|
||
|
|
A[6, [6, 7, 11]] = -2, -1, 1
|
||
|
|
A[7, [2, 3, 11, 12]] = 2, 2, 1, 1
|
||
|
|
A[8, [3, 12]] = -8, 1
|
||
|
|
A[9, [8, 9, 12]] = -2, -1, 1
|
||
|
|
A = A[1:, 1:]
|
||
|
|
|
||
|
|
b = np.array([10, 0, 0, 10, 0, 0, 10, 0, 0])
|
||
|
|
|
||
|
|
L = LinearConstraint(A, -np.inf, b)
|
||
|
|
|
||
|
|
bounds = [(0, 1)]*9 + [(0, 100)]*3 + [(0, 1)]
|
||
|
|
|
||
|
|
# using a lower popsize to speed the test up
|
||
|
|
res = differential_evolution(f, bounds, strategy='best1bin', seed=1234,
|
||
|
|
constraints=(L), popsize=2)
|
||
|
|
|
||
|
|
x_opt = (1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1)
|
||
|
|
f_opt = -15
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt)
|
||
|
|
assert res.success
|
||
|
|
assert_allclose(res.x, x_opt, atol=5e-4)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=5e-3)
|
||
|
|
assert_(np.all(A@res.x <= b))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
# now repeat the same solve, using the same overall constraints,
|
||
|
|
# but using a sparse matrix for the LinearConstraint instead of an
|
||
|
|
# array
|
||
|
|
|
||
|
|
L = LinearConstraint(csr_matrix(A), -np.inf, b)
|
||
|
|
|
||
|
|
# using a lower popsize to speed the test up
|
||
|
|
res = differential_evolution(f, bounds, strategy='best1bin', seed=1234,
|
||
|
|
constraints=(L), popsize=2)
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt)
|
||
|
|
assert res.success
|
||
|
|
assert_allclose(res.x, x_opt, atol=5e-4)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=5e-3)
|
||
|
|
assert_(np.all(A@res.x <= b))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
# now repeat the same solve, using the same overall constraints,
|
||
|
|
# but specify half the constraints in terms of LinearConstraint,
|
||
|
|
# and the other half by NonlinearConstraint
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x))
|
||
|
|
return [2*x[2] + 2*x[3] + x[11] + x[12],
|
||
|
|
-8*x[3] + x[12]]
|
||
|
|
|
||
|
|
def c2(x):
|
||
|
|
x = np.hstack(([0], x))
|
||
|
|
return -2*x[8] - x[9] + x[12]
|
||
|
|
|
||
|
|
L = LinearConstraint(A[:5, :], -np.inf, b[:5])
|
||
|
|
L2 = LinearConstraint(A[5:6, :], -np.inf, b[5:6])
|
||
|
|
N = NonlinearConstraint(c1, -np.inf, b[6:8])
|
||
|
|
N2 = NonlinearConstraint(c2, -np.inf, b[8:9])
|
||
|
|
constraints = (L, N, L2, N2)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning)
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin',
|
||
|
|
seed=1234, constraints=constraints,
|
||
|
|
popsize=2)
|
||
|
|
|
||
|
|
assert_allclose(res.x, x_opt, atol=5e-4)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=5e-3)
|
||
|
|
assert_(np.all(A@res.x <= b))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L2(self):
|
||
|
|
# Lampinen ([5]) test problem 2
|
||
|
|
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = ((x[1]-10)**2 + 5*(x[2]-12)**2 + x[3]**4 + 3*(x[4]-11)**2 +
|
||
|
|
10*x[5]**6 + 7*x[6]**2 + x[7]**4 - 4*x[6]*x[7] - 10*x[6] -
|
||
|
|
8*x[7])
|
||
|
|
return fun
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [127 - 2*x[1]**2 - 3*x[2]**4 - x[3] - 4*x[4]**2 - 5*x[5],
|
||
|
|
196 - 23*x[1] - x[2]**2 - 6*x[6]**2 + 8*x[7],
|
||
|
|
282 - 7*x[1] - 3*x[2] - 10*x[3]**2 - x[4] + x[5],
|
||
|
|
-4*x[1]**2 - x[2]**2 + 3*x[1]*x[2] - 2*x[3]**2 -
|
||
|
|
5*x[6] + 11*x[7]]
|
||
|
|
|
||
|
|
N = NonlinearConstraint(c1, 0, np.inf)
|
||
|
|
bounds = [(-10, 10)]*7
|
||
|
|
constraints = (N)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning)
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin',
|
||
|
|
seed=1234, constraints=constraints)
|
||
|
|
|
||
|
|
f_opt = 680.6300599487869
|
||
|
|
x_opt = (2.330499, 1.951372, -0.4775414, 4.365726,
|
||
|
|
-0.6244870, 1.038131, 1.594227)
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt)
|
||
|
|
assert_allclose(res.fun, f_opt)
|
||
|
|
assert_allclose(res.x, x_opt, atol=1e-5)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= 0))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L3(self):
|
||
|
|
# Lampinen ([5]) test problem 3
|
||
|
|
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = (x[1]**2 + x[2]**2 + x[1]*x[2] - 14*x[1] - 16*x[2] +
|
||
|
|
(x[3]-10)**2 + 4*(x[4]-5)**2 + (x[5]-3)**2 + 2*(x[6]-1)**2 +
|
||
|
|
5*x[7]**2 + 7*(x[8]-11)**2 + 2*(x[9]-10)**2 +
|
||
|
|
(x[10] - 7)**2 + 45
|
||
|
|
)
|
||
|
|
return fun # maximize
|
||
|
|
|
||
|
|
A = np.zeros((4, 11))
|
||
|
|
A[1, [1, 2, 7, 8]] = -4, -5, 3, -9
|
||
|
|
A[2, [1, 2, 7, 8]] = -10, 8, 17, -2
|
||
|
|
A[3, [1, 2, 9, 10]] = 8, -2, -5, 2
|
||
|
|
A = A[1:, 1:]
|
||
|
|
b = np.array([-105, 0, -12])
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [3*x[1] - 6*x[2] - 12*(x[9]-8)**2 + 7*x[10],
|
||
|
|
-3*(x[1]-2)**2 - 4*(x[2]-3)**2 - 2*x[3]**2 + 7*x[4] + 120,
|
||
|
|
-x[1]**2 - 2*(x[2]-2)**2 + 2*x[1]*x[2] - 14*x[5] + 6*x[6],
|
||
|
|
-5*x[1]**2 - 8*x[2] - (x[3]-6)**2 + 2*x[4] + 40,
|
||
|
|
-0.5*(x[1]-8)**2 - 2*(x[2]-4)**2 - 3*x[5]**2 + x[6] + 30]
|
||
|
|
|
||
|
|
L = LinearConstraint(A, b, np.inf)
|
||
|
|
N = NonlinearConstraint(c1, 0, np.inf)
|
||
|
|
bounds = [(-10, 10)]*10
|
||
|
|
constraints = (L, N)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning)
|
||
|
|
res = differential_evolution(f, bounds, seed=1234,
|
||
|
|
constraints=constraints, popsize=3)
|
||
|
|
|
||
|
|
x_opt = (2.171996, 2.363683, 8.773926, 5.095984, 0.9906548,
|
||
|
|
1.430574, 1.321644, 9.828726, 8.280092, 8.375927)
|
||
|
|
f_opt = 24.3062091
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt, atol=1e-5)
|
||
|
|
assert_allclose(res.x, x_opt, atol=1e-6)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=1e-5)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(A @ res.x >= b))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= 0))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L4(self):
|
||
|
|
# Lampinen ([5]) test problem 4
|
||
|
|
def f(x):
|
||
|
|
return np.sum(x[:3])
|
||
|
|
|
||
|
|
A = np.zeros((4, 9))
|
||
|
|
A[1, [4, 6]] = 0.0025, 0.0025
|
||
|
|
A[2, [5, 7, 4]] = 0.0025, 0.0025, -0.0025
|
||
|
|
A[3, [8, 5]] = 0.01, -0.01
|
||
|
|
A = A[1:, 1:]
|
||
|
|
b = np.array([1, 1, 1])
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [x[1]*x[6] - 833.33252*x[4] - 100*x[1] + 83333.333,
|
||
|
|
x[2]*x[7] - 1250*x[5] - x[2]*x[4] + 1250*x[4],
|
||
|
|
x[3]*x[8] - 1250000 - x[3]*x[5] + 2500*x[5]]
|
||
|
|
|
||
|
|
L = LinearConstraint(A, -np.inf, 1)
|
||
|
|
N = NonlinearConstraint(c1, 0, np.inf)
|
||
|
|
|
||
|
|
bounds = [(100, 10000)] + [(1000, 10000)]*2 + [(10, 1000)]*5
|
||
|
|
constraints = (L, N)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning)
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin',
|
||
|
|
seed=1234, constraints=constraints,
|
||
|
|
popsize=3)
|
||
|
|
|
||
|
|
f_opt = 7049.248
|
||
|
|
|
||
|
|
x_opt = [579.306692, 1359.97063, 5109.9707, 182.0177, 295.601172,
|
||
|
|
217.9823, 286.416528, 395.601172]
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt, atol=0.001)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=0.001)
|
||
|
|
|
||
|
|
# selectively use higher tol here for 32-bit
|
||
|
|
# Windows based on gh-11693
|
||
|
|
if (platform.system() == 'Windows' and np.dtype(np.intp).itemsize < 8):
|
||
|
|
assert_allclose(res.x, x_opt, rtol=2.4e-6, atol=0.0035)
|
||
|
|
else:
|
||
|
|
assert_allclose(res.x, x_opt, atol=0.002)
|
||
|
|
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(A @ res.x <= b))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= 0))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L5(self):
|
||
|
|
# Lampinen ([5]) test problem 5
|
||
|
|
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = (np.sin(2*np.pi*x[1])**3*np.sin(2*np.pi*x[2]) /
|
||
|
|
(x[1]**3*(x[1]+x[2])))
|
||
|
|
return -fun # maximize
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [x[1]**2 - x[2] + 1,
|
||
|
|
1 - x[1] + (x[2]-4)**2]
|
||
|
|
|
||
|
|
N = NonlinearConstraint(c1, -np.inf, 0)
|
||
|
|
bounds = [(0, 10)]*2
|
||
|
|
constraints = (N)
|
||
|
|
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
|
||
|
|
constraints=constraints)
|
||
|
|
|
||
|
|
x_opt = (1.22797135, 4.24537337)
|
||
|
|
f_opt = -0.095825
|
||
|
|
print(res)
|
||
|
|
assert_allclose(f(x_opt), f_opt, atol=2e-5)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=1e-4)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(np.array(c1(res.x)) <= 0))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L6(self):
|
||
|
|
# Lampinen ([5]) test problem 6
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = (x[1]-10)**3 + (x[2] - 20)**3
|
||
|
|
return fun
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [(x[1]-5)**2 + (x[2] - 5)**2 - 100,
|
||
|
|
-(x[1]-6)**2 - (x[2] - 5)**2 + 82.81]
|
||
|
|
|
||
|
|
N = NonlinearConstraint(c1, 0, np.inf)
|
||
|
|
bounds = [(13, 100), (0, 100)]
|
||
|
|
constraints = (N)
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
|
||
|
|
constraints=constraints, tol=1e-7)
|
||
|
|
x_opt = (14.095, 0.84296)
|
||
|
|
f_opt = -6961.814744
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt, atol=1e-6)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=0.001)
|
||
|
|
assert_allclose(res.x, x_opt, atol=1e-4)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= 0))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L7(self):
|
||
|
|
# Lampinen ([5]) test problem 7
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = (5.3578547*x[3]**2 + 0.8356891*x[1]*x[5] +
|
||
|
|
37.293239*x[1] - 40792.141)
|
||
|
|
return fun
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [
|
||
|
|
85.334407 + 0.0056858*x[2]*x[5] + 0.0006262*x[1]*x[4] -
|
||
|
|
0.0022053*x[3]*x[5],
|
||
|
|
|
||
|
|
80.51249 + 0.0071317*x[2]*x[5] + 0.0029955*x[1]*x[2] +
|
||
|
|
0.0021813*x[3]**2,
|
||
|
|
|
||
|
|
9.300961 + 0.0047026*x[3]*x[5] + 0.0012547*x[1]*x[3] +
|
||
|
|
0.0019085*x[3]*x[4]
|
||
|
|
]
|
||
|
|
|
||
|
|
N = NonlinearConstraint(c1, [0, 90, 20], [92, 110, 25])
|
||
|
|
|
||
|
|
bounds = [(78, 102), (33, 45)] + [(27, 45)]*3
|
||
|
|
constraints = (N)
|
||
|
|
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
|
||
|
|
constraints=constraints)
|
||
|
|
|
||
|
|
# using our best solution, rather than Lampinen/Koziel. Koziel solution
|
||
|
|
# doesn't satisfy constraints, Lampinen f_opt just plain wrong.
|
||
|
|
x_opt = [78.00000686, 33.00000362, 29.99526064, 44.99999971,
|
||
|
|
36.77579979]
|
||
|
|
|
||
|
|
f_opt = -30665.537578
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt)
|
||
|
|
assert_allclose(res.x, x_opt, atol=1e-3)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=1e-3)
|
||
|
|
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= np.array([0, 90, 20])))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) <= np.array([92, 110, 25])))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
@pytest.mark.xfail(platform.machine() == 'ppc64le',
|
||
|
|
reason="fails on ppc64le")
|
||
|
|
def test_L8(self):
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
fun = 3*x[1] + 0.000001*x[1]**3 + 2*x[2] + 0.000002/3*x[2]**3
|
||
|
|
return fun
|
||
|
|
|
||
|
|
A = np.zeros((3, 5))
|
||
|
|
A[1, [4, 3]] = 1, -1
|
||
|
|
A[2, [3, 4]] = 1, -1
|
||
|
|
A = A[1:, 1:]
|
||
|
|
b = np.array([-.55, -.55])
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [
|
||
|
|
1000*np.sin(-x[3]-0.25) + 1000*np.sin(-x[4]-0.25) +
|
||
|
|
894.8 - x[1],
|
||
|
|
1000*np.sin(x[3]-0.25) + 1000*np.sin(x[3]-x[4]-0.25) +
|
||
|
|
894.8 - x[2],
|
||
|
|
1000*np.sin(x[4]-0.25) + 1000*np.sin(x[4]-x[3]-0.25) +
|
||
|
|
1294.8
|
||
|
|
]
|
||
|
|
L = LinearConstraint(A, b, np.inf)
|
||
|
|
N = NonlinearConstraint(c1, np.full(3, -0.001), np.full(3, 0.001))
|
||
|
|
|
||
|
|
bounds = [(0, 1200)]*2+[(-.55, .55)]*2
|
||
|
|
constraints = (L, N)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning)
|
||
|
|
# original Lampinen test was with rand1bin, but that takes a
|
||
|
|
# huge amount of CPU time. Changing strategy to best1bin speeds
|
||
|
|
# things up a lot
|
||
|
|
res = differential_evolution(f, bounds, strategy='best1bin',
|
||
|
|
seed=1234, constraints=constraints,
|
||
|
|
maxiter=5000)
|
||
|
|
|
||
|
|
x_opt = (679.9453, 1026.067, 0.1188764, -0.3962336)
|
||
|
|
f_opt = 5126.4981
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt, atol=1e-3)
|
||
|
|
assert_allclose(res.x[:2], x_opt[:2], atol=2e-3)
|
||
|
|
assert_allclose(res.x[2:], x_opt[2:], atol=2e-3)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=2e-2)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(A@res.x >= b))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= -0.001))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) <= 0.001))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|
||
|
|
|
||
|
|
def test_L9(self):
|
||
|
|
# Lampinen ([5]) test problem 9
|
||
|
|
|
||
|
|
def f(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return x[1]**2 + (x[2]-1)**2
|
||
|
|
|
||
|
|
def c1(x):
|
||
|
|
x = np.hstack(([0], x)) # 1-indexed to match reference
|
||
|
|
return [x[2] - x[1]**2]
|
||
|
|
|
||
|
|
N = NonlinearConstraint(c1, [-.001], [0.001])
|
||
|
|
|
||
|
|
bounds = [(-1, 1)]*2
|
||
|
|
constraints = (N)
|
||
|
|
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
|
||
|
|
constraints=constraints)
|
||
|
|
|
||
|
|
x_opt = [np.sqrt(2)/2, 0.5]
|
||
|
|
f_opt = 0.75
|
||
|
|
|
||
|
|
assert_allclose(f(x_opt), f_opt)
|
||
|
|
assert_allclose(np.abs(res.x), x_opt, atol=1e-3)
|
||
|
|
assert_allclose(res.fun, f_opt, atol=1e-3)
|
||
|
|
assert res.success
|
||
|
|
assert_(np.all(np.array(c1(res.x)) >= -0.001))
|
||
|
|
assert_(np.all(np.array(c1(res.x)) <= 0.001))
|
||
|
|
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
|
||
|
|
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
|