3RNN/Lib/site-packages/scipy/optimize/tests/test__differential_evolution.py
2024-05-26 19:49:15 +02:00

1678 lines
67 KiB
Python

"""
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
# of constraints applied.
assert cw.violation(x0).shape == (2,)
# let's try a vectorised violation call.
xtrial = np.arange(4 * 5).reshape(4, 5)
assert cw.violation(xtrial).shape == (2, 5)
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, atol=6e-4)
assert res.success
assert_allclose(res.x, x_opt, atol=6e-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=6e-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)
# use higher tol here for 32-bit Windows, see 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:
# tolerance determined from macOS + MKL failure, see gh-12701
assert_allclose(res.x, x_opt, rtol=5e-6, atol=0.0024)
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
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]))
def test_integrality(self):
# test fitting discrete distribution to data
rng = np.random.default_rng(6519843218105)
dist = stats.nbinom
shapes = (5, 0.5)
x = dist.rvs(*shapes, size=10000, random_state=rng)
def func(p, *args):
dist, x = args
# negative log-likelihood function
ll = -np.log(dist.pmf(x, *p)).sum(axis=-1)
if np.isnan(ll): # occurs when x is outside of support
ll = np.inf # we don't want that
return ll
integrality = [True, False]
bounds = [(1, 18), (0, 0.95)]
res = differential_evolution(func, bounds, args=(dist, x),
integrality=integrality, polish=False,
seed=rng)
# tolerance has to be fairly relaxed for the second parameter
# because we're fitting a distribution to random variates.
assert res.x[0] == 5
assert_allclose(res.x, shapes, rtol=0.025)
# check that we can still use integrality constraints with polishing
res2 = differential_evolution(func, bounds, args=(dist, x),
integrality=integrality, polish=True,
seed=rng)
def func2(p, *args):
n, dist, x = args
return func(np.array([n, p[0]]), dist, x)
# compare the DE derived solution to an LBFGSB solution (that doesn't
# have to find the integral values). Note we're setting x0 to be the
# output from the first DE result, thereby making the polishing step
# and this minimisation pretty much equivalent.
LBFGSB = minimize(func2, res2.x[1], args=(5, dist, x),
bounds=[(0, 0.95)])
assert_allclose(res2.x[1], LBFGSB.x)
assert res2.fun <= res.fun
def test_integrality_limits(self):
def f(x):
return x
integrality = [True, False, True]
bounds = [(0.2, 1.1), (0.9, 2.2), (3.3, 4.9)]
# no integrality constraints
solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
integrality=False)
assert_allclose(solver.limits[0], [0.2, 0.9, 3.3])
assert_allclose(solver.limits[1], [1.1, 2.2, 4.9])
# with integrality constraints
solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
integrality=integrality)
assert_allclose(solver.limits[0], [0.5, 0.9, 3.5])
assert_allclose(solver.limits[1], [1.5, 2.2, 4.5])
assert_equal(solver.integrality, [True, False, True])
assert solver.polish is False
bounds = [(-1.2, -0.9), (0.9, 2.2), (-10.3, 4.1)]
solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
integrality=integrality)
assert_allclose(solver.limits[0], [-1.5, 0.9, -10.5])
assert_allclose(solver.limits[1], [-0.5, 2.2, 4.5])
# A lower bound of -1.2 is converted to
# np.nextafter(np.ceil(-1.2) - 0.5, np.inf)
# with a similar process to the upper bound. Check that the
# conversions work
assert_allclose(np.round(solver.limits[0]), [-1.0, 1.0, -10.0])
assert_allclose(np.round(solver.limits[1]), [-1.0, 2.0, 4.0])
bounds = [(-10.2, -8.1), (0.9, 2.2), (-10.9, -9.9999)]
solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
integrality=integrality)
assert_allclose(solver.limits[0], [-10.5, 0.9, -10.5])
assert_allclose(solver.limits[1], [-8.5, 2.2, -9.5])
bounds = [(-10.2, -10.1), (0.9, 2.2), (-10.9, -9.9999)]
with pytest.raises(ValueError, match='One of the integrality'):
DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
integrality=integrality)
def test_vectorized(self):
def quadratic(x):
return np.sum(x**2)
def quadratic_vec(x):
return np.sum(x**2, axis=0)
# A vectorized function needs to accept (len(x), S) and return (S,)
with pytest.raises(RuntimeError, match='The vectorized function'):
differential_evolution(quadratic, self.bounds,
vectorized=True, updating='deferred')
# vectorized overrides the updating keyword, check for warning
with warns(UserWarning, match="differential_evolution: the 'vector"):
differential_evolution(quadratic_vec, self.bounds,
vectorized=True)
# vectorized defers to the workers keyword, check for warning
with warns(UserWarning, match="differential_evolution: the 'workers"):
differential_evolution(quadratic_vec, self.bounds,
vectorized=True, workers=map,
updating='deferred')
ncalls = [0]
def rosen_vec(x):
ncalls[0] += 1
return rosen(x)
bounds = [(0, 10), (0, 10)]
res1 = differential_evolution(rosen, bounds, updating='deferred',
seed=1)
res2 = differential_evolution(rosen_vec, bounds, vectorized=True,
updating='deferred', seed=1)
# the two minimisation runs should be functionally equivalent
assert_allclose(res1.x, res2.x)
assert ncalls[0] == res2.nfev
assert res1.nit == res2.nit
def test_vectorized_constraints(self):
def constr_f(x):
return np.array([x[0] + x[1]])
def constr_f2(x):
return np.array([x[0]**2 + x[1], x[0] - x[1]])
nlc1 = NonlinearConstraint(constr_f, -np.inf, 1.9)
nlc2 = NonlinearConstraint(constr_f2, (0.9, 0.5), (2.0, 2.0))
def rosen_vec(x):
# accept an (len(x0), S) array, returning a (S,) array
v = 100 * (x[1:] - x[:-1]**2.0)**2.0
v += (1 - x[:-1])**2.0
return np.squeeze(v)
bounds = [(0, 10), (0, 10)]
res1 = differential_evolution(rosen, bounds, updating='deferred',
seed=1, constraints=[nlc1, nlc2],
polish=False)
res2 = differential_evolution(rosen_vec, bounds, vectorized=True,
updating='deferred', seed=1,
constraints=[nlc1, nlc2],
polish=False)
# the two minimisation runs should be functionally equivalent
assert_allclose(res1.x, res2.x)
def test_constraint_violation_error_message(self):
def func(x):
return np.cos(x[0]) + np.sin(x[1])
# Intentionally infeasible constraints.
c0 = NonlinearConstraint(lambda x: x[1] - (x[0]-1)**2, 0, np.inf)
c1 = NonlinearConstraint(lambda x: x[1] + x[0]**2, -np.inf, 0)
result = differential_evolution(func,
bounds=[(-1, 2), (-1, 1)],
constraints=[c0, c1],
maxiter=10,
polish=False,
seed=864197532)
assert result.success is False
# The numerical value in the error message might be sensitive to
# changes in the implementation. It can be updated if the code is
# changed. The essential part of the test is that there is a number
# after the '=', so if necessary, the text could be reduced to, say,
# "MAXCV = 0.".
assert "MAXCV = 0.414" in result.message
def test_strategy_fn(self):
# examines ability to customize strategy by mimicking one of the
# in-built strategies and comparing to the actual in-built strategy.
parameter_count = 4
popsize = 10
bounds = [(0, 10.)] * parameter_count
total_popsize = parameter_count * popsize
mutation = 0.8
recombination = 0.7
def custom_strategy_fn(candidate, population, rng=None):
trial = np.copy(population[candidate])
fill_point = rng.choice(parameter_count)
pool = np.arange(total_popsize)
rng.shuffle(pool)
idxs = []
while len(idxs) < 2 and len(pool) > 0:
idx = pool[0]
pool = pool[1:]
if idx != candidate:
idxs.append(idx)
r0, r1 = idxs[:2]
bprime = (population[0] + mutation *
(population[r0] - population[r1]))
crossovers = rng.uniform(size=parameter_count)
crossovers = crossovers < recombination
crossovers[fill_point] = True
trial = np.where(crossovers, bprime, trial)
return trial
solver = DifferentialEvolutionSolver(
rosen,
bounds,
popsize=popsize,
recombination=recombination,
mutation=mutation,
maxiter=2,
strategy=custom_strategy_fn,
seed=10,
polish=False
)
assert solver.strategy is custom_strategy_fn
res = solver.solve()
res2 = differential_evolution(
rosen,
bounds,
mutation=mutation,
popsize=popsize,
recombination=recombination,
maxiter=2,
strategy='best1bin',
polish=False,
seed=10
)
assert_allclose(res.population, res2.population)
assert_allclose(res.x, res2.x)
def custom_strategy_fn(candidate, population, rng=None):
return np.array([1.0, 2.0])
with pytest.raises(RuntimeError, match="strategy*"):
differential_evolution(
rosen,
bounds,
strategy=custom_strategy_fn
)