478 lines
20 KiB
Python
478 lines
20 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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from scipy.optimize import _differentialevolution
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from scipy.optimize._differentialevolution import DifferentialEvolutionSolver
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from scipy.optimize import differential_evolution
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import numpy as np
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from scipy.optimize import rosen
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from numpy.testing import (assert_equal, assert_allclose,
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assert_almost_equal,
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assert_string_equal, assert_)
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from pytest import raises as assert_raises
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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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def callback(param, convergence=0.):
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return True
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result = differential_evolution(rosen, bounds, callback=callback)
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assert_string_equal(result.message,
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'callback function requested stop early '
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'by returning True')
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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, None)]
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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)]
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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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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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def test_quadratic(self):
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# test the quadratic function from object
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solver = DifferentialEvolutionSolver(self.quadratic,
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[(-100, 100)],
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tol=0.02)
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solver.solve()
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assert_equal(np.argmin(solver.population_energies), 0)
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def test_quadratic_from_diff_ev(self):
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# test the quadratic function from differential_evolution function
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differential_evolution(self.quadratic,
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[(-100, 100)],
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tol=0.02)
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def test_seed_gives_repeatability(self):
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result = differential_evolution(self.quadratic,
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[(-100, 100)],
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polish=False,
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seed=1,
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tol=0.5)
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result2 = differential_evolution(self.quadratic,
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[(-100, 100)],
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polish=False,
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seed=1,
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tol=0.5)
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assert_equal(result.x, result2.x)
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def test_exp_runs(self):
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# test whether exponential mutation loop runs
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|
|
solver = DifferentialEvolutionSolver(rosen,
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||
|
|
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.
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||
|
|
bounds = [(-5, 5), (-5, 5)]
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||
|
|
result = differential_evolution(rosen, bounds, popsize=1815, maxiter=1)
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||
|
|
|
||
|
|
def test_calculate_population_energies(self):
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||
|
|
# if popsize is 3 then the overall generation has size (6,)
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||
|
|
solver = DifferentialEvolutionSolver(rosen, self.bounds, popsize=3)
|
||
|
|
solver._calculate_population_energies()
|
||
|
|
|
||
|
|
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)
|
||
|
|
for i, soln in enumerate(solver):
|
||
|
|
x_current, fun_current = soln
|
||
|
|
# need to have this otherwise the solver would never stop.
|
||
|
|
if i == 1000:
|
||
|
|
break
|
||
|
|
|
||
|
|
assert_almost_equal(fun_current, 0)
|
||
|
|
|
||
|
|
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 initialise 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 initialised 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 initialise 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})
|