def test_constraint_wrapper(self):
lb = np.array([0, 20, 30])
ub = np.array([0.5, np.inf, 70])
x0 = np.array([1, 2, 3])
pc = _ConstraintWrapper(Bounds(lb, ub), x0)
assert (pc.violation(x0) > 0).any()
assert (pc.violation([0.25, 21, 31]) == 0).all()
x0 = np.array([1, 2, 3, 4])
A = np.array([[1, 2, 3, 4], [5, 0, 0, 6], [7, 0, 8, 0]])
pc = _ConstraintWrapper(LinearConstraint(A, -np.inf, 0), x0)
assert (pc.violation(x0) > 0).any()
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
pc = _ConstraintWrapper(LinearConstraint(csr_matrix(A), -np.inf, 0),
x0)
assert (pc.violation(x0) > 0).any()
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
def fun(x):
return A.dot(x)
nonlinear = NonlinearConstraint(fun, -np.inf, 0)
pc = _ConstraintWrapper(nonlinear, [-10, 2, -10, 4])
assert (pc.violation(x0) > 0).any()
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
def test_input_validation(self):
A = np.eye(4)
message = "`lb`, `ub`, and `keep_feasible` must be broadcastable"
with pytest.raises(ValueError, match=message):
LinearConstraint(A, [1, 2], [1, 2, 3])
A = np.empty((4, 3, 5))
message = "`A` must have exactly two dimensions."
with pytest.raises(ValueError, match=message):
LinearConstraint(A)
def test_prepare_constraint_infeasible_x0():
lb = np.array([0, 20, 30])
ub = np.array([0.5, np.inf, 70])
x0 = np.array([1, 2, 3])
enforce_feasibility = np.array([False, True, True], dtype=bool)
bounds = Bounds(lb, ub, enforce_feasibility)
pytest.raises(ValueError, PreparedConstraint, bounds, x0)
x0 = np.array([1, 2, 3, 4])
A = np.array([[1, 2, 3, 4], [5, 0, 0, 6], [7, 0, 8, 0]])
enforce_feasibility = np.array([True, True, True], dtype=bool)
linear = LinearConstraint(A, -np.inf, 0, enforce_feasibility)
pytest.raises(ValueError, PreparedConstraint, linear, x0)
def fun(x):
return A.dot(x)
def jac(x):
return A
def hess(x, v):
return sps.csr_matrix((4, 4))
nonlinear = NonlinearConstraint(fun, -np.inf, 0, jac, hess,
enforce_feasibility)
pytest.raises(ValueError, PreparedConstraint, nonlinear, x0)
def test_L4(self):
# Lampinen ([5]) test problem 4
def f(x):
return np.sum(x[:3])
A = np.zeros((4, 9))
A[1, [4, 6]] = 0.0025, 0.0025
A[2, [5, 7, 4]] = 0.0025, 0.0025, -0.0025
A[3, [8, 5]] = 0.01, -0.01
A = A[1:, 1:]
b = np.array([1, 1, 1])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
x[1] * x[6] - 833.33252 * x[4] - 100 * x[1] + 83333.333,
x[2] * x[7] - 1250 * x[5] - x[2] * x[4] + 1250 * x[4],
x[3] * x[8] - 1250000 - x[3] * x[5] + 2500 * x[5]
]
L = LinearConstraint(A, -np.inf, 1)
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(100, 10000)] + [(1000, 10000)] * 2 + [(10, 1000)] * 5
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f,
bounds,
strategy='rand1bin',
seed=1234,
constraints=constraints,
popsize=3)
f_opt = 7049.248
x_opt = [
579.306692, 1359.97063, 5109.9707, 182.0177, 295.601172, 217.9823,
286.416528, 395.601172
]
assert_allclose(f(x_opt), f_opt, atol=0.001)
assert_allclose(res.fun, f_opt, atol=0.001)
# selectively use higher tol here for 32-bit
# Windows based on gh-11693
if (platform.system() == 'Windows' and np.dtype(np.intp).itemsize < 8):
assert_allclose(res.x, x_opt, rtol=2.4e-6, atol=0.0035)
else:
assert_allclose(res.x, x_opt, atol=0.002)
assert res.success
assert_(np.all(A @ res.x <= b))
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_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_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_L1(self):
# Lampinen ([5]) test problem 1
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = np.sum(5 * x[1:5]) - 5 * x[1:5] @ x[1:5] - np.sum(x[5:])
return fun
A = np.zeros((10, 14)) # 1-indexed to match reference
A[1, [1, 2, 10, 11]] = 2, 2, 1, 1
A[2, [1, 10]] = -8, 1
A[3, [4, 5, 10]] = -2, -1, 1
A[4, [1, 3, 10, 11]] = 2, 2, 1, 1
A[5, [2, 11]] = -8, 1
A[6, [6, 7, 11]] = -2, -1, 1
A[7, [2, 3, 11, 12]] = 2, 2, 1, 1
A[8, [3, 12]] = -8, 1
A[9, [8, 9, 12]] = -2, -1, 1
A = A[1:, 1:]
b = np.array([10, 0, 0, 10, 0, 0, 10, 0, 0])
L = LinearConstraint(A, -np.inf, b)
bounds = [(0, 1)] * 9 + [(0, 100)] * 3 + [(0, 1)]
# using a lower popsize to speed the test up
res = differential_evolution(f,
bounds,
strategy='best1bin',
seed=1234,
constraints=(L),
popsize=2)
x_opt = (1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1)
f_opt = -15
assert_allclose(f(x_opt), f_opt)
assert res.success
assert_allclose(res.x, x_opt, atol=5e-4)
assert_allclose(res.fun, f_opt, atol=5e-3)
assert_(np.all(A @ res.x <= b))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
# now repeat the same solve, using the same overall constraints,
# but specify half the constraints in terms of LinearConstraint,
# and the other half by NonlinearConstraint
def c1(x):
x = np.hstack(([0], x))
return [2 * x[2] + 2 * x[3] + x[11] + x[12], -8 * x[3] + x[12]]
def c2(x):
x = np.hstack(([0], x))
return -2 * x[8] - x[9] + x[12]
L = LinearConstraint(A[:5, :], -np.inf, b[:5])
L2 = LinearConstraint(A[5:6, :], -np.inf, b[5:6])
N = NonlinearConstraint(c1, -np.inf, b[6:8])
N2 = NonlinearConstraint(c2, -np.inf, b[8:9])
constraints = (L, N, L2, N2)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f,
bounds,
strategy='rand1bin',
seed=1234,
constraints=constraints,
popsize=2)
assert_allclose(res.x, x_opt, atol=5e-4)
assert_allclose(res.fun, f_opt, atol=5e-3)
assert_(np.all(A @ res.x <= b))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_residual(self):
A = np.eye(2)
lc = LinearConstraint(A, -2, 4)
x0 = [-1, 2]
np.testing.assert_allclose(lc.residual(x0), ([1, 4], [5, 2]))
def test_defaults(self):
A = np.eye(4)
lc = LinearConstraint(A)
lc2 = LinearConstraint(A, -np.inf, np.inf)
assert_array_equal(lc.lb, lc2.lb)
assert_array_equal(lc.ub, lc2.ub)