def test_multistarted_gradient_descent_optimizer_crippled_start(self):
"""Check that multistarted GD is finding the best result from GD."""
# Only allow 1 GD iteration.
max_num_steps = 1
max_num_restarts = 1
param_dict = self.gd_parameters._asdict()
param_dict['max_num_steps'] = max_num_steps
param_dict['max_num_restarts'] = max_num_restarts
gd_parameters_crippled = GradientDescentParameters(**param_dict)
gradient_descent_optimizer_crippled = GradientDescentOptimizer(
self.domain, self.polynomial, gd_parameters_crippled)
num_points = 15
points = self.domain.generate_uniform_random_points_in_domain(
num_points)
multistart_optimizer = MultistartOptimizer(
gradient_descent_optimizer_crippled, num_points)
test_best_point, _ = multistart_optimizer.optimize(
random_starts=points)
# This point set won't include the optimum so multistart GD won't find it.
for value in (test_best_point - self.polynomial.optimum_point):
assert value != 0.0
points_with_opt = numpy.append(points,
self.polynomial.optimum_point.reshape(
(1, self.polynomial.dim)),
axis=0)
test_best_point, _ = multistart_optimizer.optimize(
random_starts=points_with_opt)
# This point set will include the optimum so multistart GD will find it.
for value in (test_best_point - self.polynomial.optimum_point):
assert value == 0.0
def test_multistarted_gradient_descent_optimizer_crippled_start(self):
"""Check that multistarted GD is finding the best result from GD."""
# Only allow 1 GD iteration.
gd_parameters_crippled = GradientDescentParameters(
1,
1,
self.gd_parameters.num_steps_averaged,
self.gd_parameters.gamma,
self.gd_parameters.pre_mult,
self.gd_parameters.max_relative_change,
self.gd_parameters.tolerance,
)
gradient_descent_optimizer_crippled = GradientDescentOptimizer(self.domain, self.polynomial, gd_parameters_crippled)
num_points = 15
points = self.domain.generate_uniform_random_points_in_domain(num_points)
multistart_optimizer = MultistartOptimizer(gradient_descent_optimizer_crippled, num_points)
test_best_point, _ = multistart_optimizer.optimize(random_starts=points)
# This point set won't include the optimum so multistart GD won't find it.
for value in (test_best_point - self.polynomial.optimum_point):
T.assert_not_equal(value, 0.0)
points_with_opt = numpy.append(points, self.polynomial.optimum_point.reshape((1, self.polynomial.dim)), axis=0)
test_best_point, _ = multistart_optimizer.optimize(random_starts=points_with_opt)
# This point set will include the optimum so multistart GD will find it.
for value in (test_best_point - self.polynomial.optimum_point):
T.assert_equal(value, 0.0)
def test_multistarted_gradient_descent_optimizer_crippled_start(self):
"""Check that multistarted GD is finding the best result from GD."""
# Only allow 1 GD iteration.
max_num_steps = 1
max_num_restarts = 1
param_dict = self.gd_parameters._asdict()
param_dict['max_num_steps'] = max_num_steps
param_dict['max_num_restarts'] = max_num_restarts
gd_parameters_crippled = GradientDescentParameters(**param_dict)
gradient_descent_optimizer_crippled = GradientDescentOptimizer(self.domain, self.polynomial, gd_parameters_crippled)
num_points = 15
points = self.domain.generate_uniform_random_points_in_domain(num_points)
multistart_optimizer = MultistartOptimizer(gradient_descent_optimizer_crippled, num_points)
test_best_point, _ = multistart_optimizer.optimize(random_starts=points)
# This point set won't include the optimum so multistart GD won't find it.
for value in (test_best_point - self.polynomial.optimum_point):
assert value != 0.0
points_with_opt = numpy.append(points, self.polynomial.optimum_point.reshape((1, self.polynomial.dim)), axis=0)
test_best_point, _ = multistart_optimizer.optimize(random_starts=points_with_opt)
# This point set will include the optimum so multistart GD will find it.
for value in (test_best_point - self.polynomial.optimum_point):
assert value == 0.0
def test_multistarted_bfgs_optimizer(self):
"""Check that multistarted GD can find the optimum in a 'very' large domain."""
# Set a large domain: a single GD run is unlikely to reach the optimum
domain_bounds = [ClosedInterval(-10.0, 10.0)] * self.dim
domain = TensorProductDomain(domain_bounds)
tolerance = 2.0e-10
num_points = 10
bfgs_optimizer = LBFGSBOptimizer(domain, self.polynomial,
self.BFGS_parameters)
multistart_optimizer = MultistartOptimizer(bfgs_optimizer, num_points)
output, _ = multistart_optimizer.optimize()
# Verify coordinates
self.assert_vector_within_relative(output,
self.polynomial.optimum_point,
tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value,
self.polynomial.optimum_value,
tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
tolerance)
def test_multistarted_gradient_descent_optimizer_crippled_start(self):
"""Check that multistarted GD is finding the best result from GD."""
# Only allow 1 GD iteration.
gd_parameters_crippled = GradientDescentParameters(
1,
1,
self.gd_parameters.num_steps_averaged,
self.gd_parameters.gamma,
self.gd_parameters.pre_mult,
self.gd_parameters.max_relative_change,
self.gd_parameters.tolerance,
)
gradient_descent_optimizer_crippled = GradientDescentOptimizer(
self.domain, self.polynomial, gd_parameters_crippled)
num_points = 15
points = self.domain.generate_uniform_random_points_in_domain(
num_points)
multistart_optimizer = MultistartOptimizer(
gradient_descent_optimizer_crippled, num_points)
test_best_point, _ = multistart_optimizer.optimize(
random_starts=points)
# This point set won't include the optimum so multistart GD won't find it.
for value in (test_best_point - self.polynomial.optimum_point):
T.assert_not_equal(value, 0.0)
points_with_opt = numpy.append(points,
self.polynomial.optimum_point.reshape(
(1, self.polynomial.dim)),
axis=0)
test_best_point, _ = multistart_optimizer.optimize(
random_starts=points_with_opt)
# This point set will include the optimum so multistart GD will find it.
for value in (test_best_point - self.polynomial.optimum_point):
T.assert_equal(value, 0.0)
def multistarted_optimizer_test(self, optimizer):
"""Check that the multistarted optimizer can find the optimum in a 'very' large domain."""
tolerance = 2.0e-10
num_points = 10
multistart_optimizer = MultistartOptimizer(optimizer, num_points)
output, _ = multistart_optimizer.optimize()
# Verify coordinates
self.assert_vector_within_relative(output, self.polynomial.optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value, self.polynomial.optimum_value, tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), tolerance)
def test_multistarted_bfgs_optimizer(self):
"""Check that multistarted GD can find the optimum in a 'very' large domain."""
# Set a large domain: a single GD run is unlikely to reach the optimum
domain_bounds = [ClosedInterval(-10.0, 10.0)] * self.dim
domain = TensorProductDomain(domain_bounds)
tolerance = 2.0e-10
num_points = 10
bfgs_optimizer = LBFGSBOptimizer(domain, self.polynomial, self.BFGS_parameters)
multistart_optimizer = MultistartOptimizer(bfgs_optimizer, num_points)
output, _ = multistart_optimizer.optimize()
# Verify coordinates
self.assert_vector_within_relative(output, self.polynomial.optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value, self.polynomial.optimum_value, tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), tolerance)
def multistarted_optimizer_test(self, optimizer):
"""Check that the multistarted optimizer can find the optimum in a 'very' large domain."""
tolerance = 2.0e-10
num_points = 10
multistart_optimizer = MultistartOptimizer(optimizer, num_points)
output, _ = multistart_optimizer.optimize()
# Verify coordinates
self.assert_vector_within_relative(output,
self.polynomial.optimum_point,
tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value,
self.polynomial.optimum_value,
tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
tolerance)