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test__differential_evolution.py
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test__differential_evolution.py
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"""
Unit tests for the differential global minimization algorithm.
"""
import multiprocessing
import platform
from scipy.optimize._differentialevolution import (DifferentialEvolutionSolver,
_ConstraintWrapper)
from scipy.optimize import differential_evolution, OptimizeResult
from scipy.optimize._constraints import (Bounds, NonlinearConstraint,
LinearConstraint)
from scipy.optimize import rosen, minimize
from scipy.sparse import csr_matrix
from scipy import stats
import numpy as np
from numpy.testing import (assert_equal, assert_allclose, assert_almost_equal,
assert_string_equal, assert_, suppress_warnings)
from pytest import raises as assert_raises, warns
import pytest
class TestDifferentialEvolutionSolver:
def setup_method(self):
self.old_seterr = np.seterr(invalid='raise')
self.limits = np.array([[0., 0.],
[2., 2.]])
self.bounds = [(0., 2.), (0., 2.)]
self.dummy_solver = DifferentialEvolutionSolver(self.quadratic,
[(0, 100)])
# dummy_solver2 will be used to test mutation strategies
self.dummy_solver2 = DifferentialEvolutionSolver(self.quadratic,
[(0, 1)],
popsize=7,
mutation=0.5)
# create a population that's only 7 members long
# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
population = np.atleast_2d(np.arange(0.1, 0.8, 0.1)).T
self.dummy_solver2.population = population
def teardown_method(self):
np.seterr(**self.old_seterr)
def quadratic(self, x):
return x[0]**2
def test__strategy_resolves(self):
# test that the correct mutation function is resolved by
# different requested strategy arguments
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best1exp')
assert_equal(solver.strategy, 'best1exp')
assert_equal(solver.mutation_func.__name__, '_best1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best1bin')
assert_equal(solver.strategy, 'best1bin')
assert_equal(solver.mutation_func.__name__, '_best1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand1bin')
assert_equal(solver.strategy, 'rand1bin')
assert_equal(solver.mutation_func.__name__, '_rand1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand1exp')
assert_equal(solver.strategy, 'rand1exp')
assert_equal(solver.mutation_func.__name__, '_rand1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2exp')
assert_equal(solver.strategy, 'rand2exp')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best2bin')
assert_equal(solver.strategy, 'best2bin')
assert_equal(solver.mutation_func.__name__, '_best2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2bin')
assert_equal(solver.strategy, 'rand2bin')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2exp')
assert_equal(solver.strategy, 'rand2exp')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='randtobest1bin')
assert_equal(solver.strategy, 'randtobest1bin')
assert_equal(solver.mutation_func.__name__, '_randtobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='randtobest1exp')
assert_equal(solver.strategy, 'randtobest1exp')
assert_equal(solver.mutation_func.__name__, '_randtobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='currenttobest1bin')
assert_equal(solver.strategy, 'currenttobest1bin')
assert_equal(solver.mutation_func.__name__, '_currenttobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='currenttobest1exp')
assert_equal(solver.strategy, 'currenttobest1exp')
assert_equal(solver.mutation_func.__name__, '_currenttobest1')
def test__mutate1(self):
# strategies */1/*, i.e. rand/1/bin, best/1/exp, etc.
result = np.array([0.05])
trial = self.dummy_solver2._best1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
result = np.array([0.25])
trial = self.dummy_solver2._rand1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__mutate2(self):
# strategies */2/*, i.e. rand/2/bin, best/2/exp, etc.
# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
result = np.array([-0.1])
trial = self.dummy_solver2._best2((2, 3, 4, 5, 6))
assert_allclose(trial, result)
result = np.array([0.1])
trial = self.dummy_solver2._rand2((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__randtobest1(self):
# strategies randtobest/1/*
result = np.array([0.15])
trial = self.dummy_solver2._randtobest1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__currenttobest1(self):
# strategies currenttobest/1/*
result = np.array([0.1])
trial = self.dummy_solver2._currenttobest1(1, (2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test_can_init_with_dithering(self):
mutation = (0.5, 1)
solver = DifferentialEvolutionSolver(self.quadratic,
self.bounds,
mutation=mutation)
assert_equal(solver.dither, list(mutation))
def test_invalid_mutation_values_arent_accepted(self):
func = rosen
mutation = (0.5, 3)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = (-1, 1)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = (0.1, np.nan)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = 0.5
solver = DifferentialEvolutionSolver(func,
self.bounds,
mutation=mutation)
assert_equal(0.5, solver.scale)
assert_equal(None, solver.dither)
def test_invalid_functional(self):
def func(x):
return np.array([np.sum(x ** 2), np.sum(x)])
with assert_raises(
RuntimeError,
match=r"func\(x, \*args\) must return a scalar value"):
differential_evolution(func, [(-2, 2), (-2, 2)])
def test__scale_parameters(self):
trial = np.array([0.3])
assert_equal(30, self.dummy_solver._scale_parameters(trial))
# it should also work with the limits reversed
self.dummy_solver.limits = np.array([[100], [0.]])
assert_equal(30, self.dummy_solver._scale_parameters(trial))
def test__unscale_parameters(self):
trial = np.array([30])
assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
# it should also work with the limits reversed
self.dummy_solver.limits = np.array([[100], [0.]])
assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
def test_equal_bounds(self):
with np.errstate(invalid='raise'):
solver = DifferentialEvolutionSolver(
self.quadratic,
bounds=[(2.0, 2.0), (1.0, 3.0)]
)
v = solver._unscale_parameters([2.0, 2.0])
assert_allclose(v, 0.5)
res = differential_evolution(self.quadratic, [(2.0, 2.0), (3.0, 3.0)])
assert_equal(res.x, [2.0, 3.0])
def test__ensure_constraint(self):
trial = np.array([1.1, -100, 0.9, 2., 300., -0.00001])
self.dummy_solver._ensure_constraint(trial)
assert_equal(trial[2], 0.9)
assert_(np.logical_and(trial >= 0, trial <= 1).all())
def test_differential_evolution(self):
# test that the Jmin of DifferentialEvolutionSolver
# is the same as the function evaluation
solver = DifferentialEvolutionSolver(
self.quadratic, [(-2, 2)], maxiter=1, polish=False
)
result = solver.solve()
assert_equal(result.fun, self.quadratic(result.x))
solver = DifferentialEvolutionSolver(
self.quadratic, [(-2, 2)], maxiter=1, polish=True
)
result = solver.solve()
assert_equal(result.fun, self.quadratic(result.x))
def test_best_solution_retrieval(self):
# test that the getter property method for the best solution works.
solver = DifferentialEvolutionSolver(self.quadratic, [(-2, 2)])
result = solver.solve()
assert_equal(result.x, solver.x)
def test_intermediate_result(self):
# Check that intermediate result object passed into the callback
# function contains the expected information and that raising
# `StopIteration` causes the expected behavior.
maxiter = 10
def func(x):
val = rosen(x)
if val < func.val:
func.x = x
func.val = val
return val
func.x = None
func.val = np.inf
def callback(intermediate_result):
callback.nit += 1
callback.intermediate_result = intermediate_result
assert intermediate_result.population.ndim == 2
assert intermediate_result.population.shape[1] == 2
assert intermediate_result.nit == callback.nit
# Check that `x` and `fun` attributes are the best found so far
assert_equal(intermediate_result.x, callback.func.x)
assert_equal(intermediate_result.fun, callback.func.val)
# Check for consistency between `fun`, `population_energies`,
# `x`, and `population`
assert_equal(intermediate_result.fun, rosen(intermediate_result.x))
for i in range(len(intermediate_result.population_energies)):
res = intermediate_result.population_energies[i]
ref = rosen(intermediate_result.population[i])
assert_equal(res, ref)
assert_equal(intermediate_result.x,
intermediate_result.population[0])
assert_equal(intermediate_result.fun,
intermediate_result.population_energies[0])
assert intermediate_result.message == 'in progress'
assert intermediate_result.success is True
assert isinstance(intermediate_result, OptimizeResult)
if callback.nit == maxiter:
raise StopIteration
callback.nit = 0
callback.intermediate_result = None
callback.func = func
bounds = [(0, 2), (0, 2)]
kwargs = dict(func=func, bounds=bounds, seed=838245, polish=False)
res = differential_evolution(**kwargs, callback=callback)
ref = differential_evolution(**kwargs, maxiter=maxiter)
# Check that final `intermediate_result` is equivalent to returned
# result object and that terminating with callback `StopIteration`
# after `maxiter` iterations is equivalent to terminating with
# `maxiter` parameter.
assert res.success is ref.success is False
assert callback.nit == res.nit == maxiter
assert res.message == 'callback function requested stop early'
assert ref.message == 'Maximum number of iterations has been exceeded.'
for field, val in ref.items():
if field in {'message', 'success'}: # checked separately
continue
assert_equal(callback.intermediate_result[field], val)
assert_equal(res[field], val)
# Check that polish occurs after `StopIteration` as advertised
callback.nit = 0
func.val = np.inf
kwargs['polish'] = True
res = differential_evolution(**kwargs, callback=callback)
assert res.fun < ref.fun
def test_callback_terminates(self):
# test that if the callback returns true, then the minimization halts
bounds = [(0, 2), (0, 2)]
expected_msg = 'callback function requested stop early'
def callback_python_true(param, convergence=0.):
return True
result = differential_evolution(
rosen, bounds, callback=callback_python_true
)
assert_string_equal(result.message, expected_msg)
# if callback raises StopIteration then solve should be interrupted
def callback_stop(intermediate_result):
raise StopIteration
result = differential_evolution(rosen, bounds, callback=callback_stop)
assert not result.success
def callback_evaluates_true(param, convergence=0.):
# DE should stop if bool(self.callback) is True
return [10]
result = differential_evolution(rosen, bounds, callback=callback_evaluates_true)
assert_string_equal(result.message, expected_msg)
assert not result.success
def callback_evaluates_false(param, convergence=0.):
return []
result = differential_evolution(rosen, bounds,
callback=callback_evaluates_false)
assert result.success
def test_args_tuple_is_passed(self):
# test that the args tuple is passed to the cost function properly.
bounds = [(-10, 10)]
args = (1., 2., 3.)
def quadratic(x, *args):
if type(args) != tuple:
raise ValueError('args should be a tuple')
return args[0] + args[1] * x + args[2] * x**2.
result = differential_evolution(quadratic,
bounds,
args=args,
polish=True)
assert_almost_equal(result.fun, 2 / 3.)
def test_init_with_invalid_strategy(self):
# test that passing an invalid strategy raises ValueError
func = rosen
bounds = [(-3, 3)]
assert_raises(ValueError,
differential_evolution,
func,
bounds,
strategy='abc')
def test_bounds_checking(self):
# test that the bounds checking works
func = rosen
bounds = [(-3)]
assert_raises(ValueError,
differential_evolution,
func,
bounds)
bounds = [(-3, 3), (3, 4, 5)]
assert_raises(ValueError,
differential_evolution,
func,
bounds)
# test that we can use a new-type Bounds object
result = differential_evolution(rosen, Bounds([0, 0], [2, 2]))
assert_almost_equal(result.x, (1., 1.))
def test_select_samples(self):
# select_samples should return 5 separate random numbers.
limits = np.arange(12., dtype='float64').reshape(2, 6)
bounds = list(zip(limits[0, :], limits[1, :]))
solver = DifferentialEvolutionSolver(None, bounds, popsize=1)
candidate = 0
r1, r2, r3, r4, r5 = solver._select_samples(candidate, 5)
assert_equal(
len(np.unique(np.array([candidate, r1, r2, r3, r4, r5]))), 6)
def test_maxiter_stops_solve(self):
# test that if the maximum number of iterations is exceeded
# the solver stops.
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxiter=1)
result = solver.solve()
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of iterations has been exceeded.')
def test_maxfun_stops_solve(self):
# test that if the maximum number of function evaluations is exceeded
# during initialisation the solver stops
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxfun=1,
polish=False)
result = solver.solve()
assert_equal(result.nfev, 2)
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of function evaluations has '
'been exceeded.')
# test that if the maximum number of function evaluations is exceeded
# during the actual minimisation, then the solver stops.
# Have to turn polishing off, as this will still occur even if maxfun
# is reached. For popsize=5 and len(bounds)=2, then there are only 10
# function evaluations during initialisation.
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
popsize=5,
polish=False,
maxfun=40)
result = solver.solve()
assert_equal(result.nfev, 41)
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of function evaluations has '
'been exceeded.')
# now repeat for updating='deferred version
# 47 function evaluations is not a multiple of the population size,
# so maxfun is reached partway through a population evaluation.
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
popsize=5,
polish=False,
maxfun=47,
updating='deferred')
result = solver.solve()
assert_equal(result.nfev, 47)
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)
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', 'sobol', 'halton']
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)))
solver.init_population_qmc(qmc_engine='halton')
assert_equal(solver._nfev, 0)
assert_(np.all(np.isinf(solver.population_energies)))
solver = DifferentialEvolutionSolver(rosen, self.bounds, init='sobol')
solver.init_population_qmc(qmc_engine='sobol')
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})
# provide an initial solution
# bounds are [(0, 2), (0, 2)]
x0 = np.random.uniform(low=0.0, high=2.0, size=2)
solver = DifferentialEvolutionSolver(
rosen, self.bounds, x0=x0
)
# parameters are scaled to unit interval
assert_allclose(solver.population[0], x0 / 2.0)
def test_x0(self):
# smoke test that checks that x0 is usable.
res = differential_evolution(rosen, self.bounds, x0=[0.2, 0.8])
assert res.success
# check what happens if some of the x0 lay outside the bounds
with assert_raises(ValueError):
differential_evolution(rosen, self.bounds, x0=[0.2, 2.1])
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')
# Safely forking from a multithreaded process is
# problematic, and deprecated in Python 3.12, so
# we use a slower but portable alternative
# see gh-19848
ctx = multiprocessing.get_context("spawn")
with ctx.Pool(2) as p:
# should raise a UserWarning because the updating='immediate'
# is being overridden by the workers keyword
with warns(UserWarning):
with DifferentialEvolutionSolver(rosen, bounds, workers=p.map) as s:
pass
assert s._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 np.array([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(np.array([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.
xs = [(1.2, 1), (2.0, 2.0), (0.5, 0.5)]
vs = [(0.3, 0.64, 0.0), (2.1, 4.2, 0.0), (0, 0, 0)]
for x, v in zip(xs, vs):
cv = solver._constraint_violation_fn(np.array(x))
assert_allclose(cv, np.atleast_2d(v))
# vectorized calculation of a series of solutions
assert_allclose(
solver._constraint_violation_fn(np.array(xs)), np.array(vs)
)
# the following line is used in _calculate_population_feasibilities.
# _constraint_violation_fn returns an (1, M) array when
# x.shape == (N,), i.e. a single solution. Therefore this list
# comprehension should generate (S, 1, M) array.
constraint_violation = np.array([solver._constraint_violation_fn(x)
for x in np.array(xs)])
assert constraint_violation.shape == (3, 1, 3)
# we need reasonable error messages if the constraint function doesn't
# return the right thing
def constr_f3(x):
# returns (S, M), rather than (M, S)
return constr_f2(x).T
nlc2 = NonlinearConstraint(constr_f3, -np.inf, 1.8)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc, nlc2),
vectorized=False)
solver.vectorized = True
with pytest.raises(
RuntimeError, match="An array returned from a Constraint"
):
solver._constraint_violation_fn(np.array(xs))
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)
for vectorize in [False, True]:
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc, nlc2),
vectorized=vectorize,
updating='deferred')
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]), 0.1, True, np.array([0.0])) is 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 not (fn(1.0, False, np.array([0.5, 0.5]),
1.0, False, np.array([1.0, 0.4])))
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()
# check vectorized Bounds constraint
xs = np.arange(1, 16).reshape(5, 3)
violations = []
for x in xs:
violations.append(pc.violation(x))
np.testing.assert_allclose(pc.violation(xs.T), np.array(violations).T)
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()
# check vectorized LinearConstraint, for 7 lots of parameter vectors
# with each parameter vector being 4 long, with 3 constraints
# xs is the same shape as stored in the differential evolution
# population, but it's sent to the violation function as (len(x), M)
xs = np.arange(1, 29).reshape(7, 4)
violations = []
for x in xs:
violations.append(pc.violation(x))
np.testing.assert_allclose(pc.violation(xs.T), np.array(violations).T)
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):
# written in vectorised form to accept an array of (N, S)
# returning (M, S)
# where N is the number of parameters,
# S is the number of solution vectors to be examined,
# and M is the number of constraint components
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
xs = [(0.5, 1), (0.5, 1.2), (1.2, 1.2), (0.1, -1.2), (0.1, 2.0)]
vs = [(0, 0), (0, 0.1), (0.64, 0), (0.19, 0), (0.01, 1.14)]
for x, v in zip(xs, vs):
assert_allclose(pc.violation(x), v)
# now check that we can vectorize the constraint wrapper
assert_allclose(pc.violation(np.array(xs).T),
np.array(vs).T)
assert pc.fun(np.array(xs).T).shape == (2, len(xs))
assert pc.violation(np.array(xs).T).shape == (2, len(xs))
assert pc.num_constr == 2
assert pc.parameter_count == 2
def test_matrix_linear_constraint(self):
# gh20041 supplying an np.matrix to construct a LinearConstraint caused
# _ConstraintWrapper to start returning constraint violations of the
# wrong shape.
with suppress_warnings() as sup:
sup.filter(PendingDeprecationWarning)
matrix = np.matrix([[1, 1, 1, 1.],
[2, 2, 2, 2.]])
lc = LinearConstraint(matrix, 0, 1)
x0 = np.ones(4)
cw = _ConstraintWrapper(lc, x0)
# the shape of the constraint violation should be the same as the number