def test_get_size_P_matrix(self):
"""Verify that the size is always between 0 and n+1."""
settings = RbfoptSettings()
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
for n in range(20):
size = ru.get_size_P_matrix(settings, n)
self.assertTrue(0 <= size <= n + 1)
def maximize_one_over_mu(settings, n, k, var_lower, var_upper, node_pos,
mat, integer_vars):
"""Compute the maximum of :math: `1/\mu`.
Construct a PyOmo model to maximize :math: `1/\mu`
See paper by Costa and Nannicini, equation (7) pag 4, and the
references therein.
Parameters
----------
settings : rbfopt_settings.RbfSettings
Global and algorithmic settings.
n : int
The dimension of the problem, i.e. size of the space.
k : int
Number of nodes, i.e. interpolation points.
var_lower : List[float]
Vector of variable lower bounds.
var_upper : List[float]
Vector of variable upper bounds.
node_pos : List[List[float]]
List of coordinates of the nodes
mat : numpy.matrix
The matrix necessary for the computation. This is the inverse
of the matrix [Phi P; P^T 0], see paper as cited above. Must
be a square numpy.matrix of appropriate dimension.
integer_vars : List[int] or None
A list containing the indices of the integrality constrained
variables. If None or empty list, all variables are assumed to
be continuous.
Returns
-------
float
A maximizer. It is difficult to do global optimization so
typically this method returns a local maximum.
Raises
------
ValueError
If the type of radial basis function is not supported.
RuntimeError
If the solver cannot be found.
"""
assert(len(var_lower)==n)
assert(len(var_upper)==n)
assert(len(node_pos)==k)
assert(isinstance(mat, np.matrix))
assert(isinstance(settings, RbfSettings))
# Determine the size of the P matrix
p = ru.get_size_P_matrix(settings, n)
assert(mat.shape==(k + p, k + p))
# Instantiate model
if (ru.get_degree_polynomial(settings) == 1):
model = rbfopt_degree1_models
elif (ru.get_degree_polynomial(settings) == 0):
model = rbfopt_degree0_models
else:
raise ValueError('RBF type ' + settings.rbf + ' not supported')
instance = model.create_max_one_over_mu_model(settings, n, k, var_lower,
var_upper, node_pos, mat,
integer_vars)
# Initialize variables for local search
initialize_instance_variables(settings, instance)
# Instantiate optimizer
opt = pyomo.opt.SolverFactory(config.MINLP_SOLVER_EXEC, solver_io='nl')
if opt is None:
raise RuntimeError('Solver ' + config.MINLP_SOLVER_EXEC + ' not found')
set_minlp_solver_options(opt)
# Solve and load results
try:
results = opt.solve(instance, keepfiles = False,
tee = settings.print_solver_output)
if ((results.solver.status == pyomo.opt.SolverStatus.ok) and
(results.solver.termination_condition ==
TerminationCondition.optimal)):
# this is feasible and optimal
instance.solutions.load_from(results)
point = [instance.x[i].value for i in instance.N]
ru.round_integer_vars(point, integer_vars)
else:
point = None
except:
point = None
return point
def minimize_rbf(settings, n, k, var_lower, var_upper, node_pos,
rbf_lambda, rbf_h, integer_vars):
"""Compute the minimum of the RBF interpolant.
Compute the minimum of the RBF interpolant with a PyOmo model.
Parameters
----------
settings : rbfopt_settings.RbfSettings
Global and algorithmic settings.
n : int
The dimension of the problem, i.e. size of the space.
k : int
Number of nodes, i.e. interpolation points.
var_lower : List[float]
Vector of variable lower bounds.
var_upper : List[float]
Vector of variable upper bounds.
node_pos : List[List[float]]
List of coordinates of the nodes.
rbf_lambda : List[float]
The lambda coefficients of the RBF interpolant, corresponding
to the radial basis functions. List of dimension k.
rbf_h : List[float]
The h coefficients of the RBF interpolant, corresponding to
the polynomial. List of dimension n+1.
integer_vars: List[int] or None
A list containing the indices of the integrality constrained
variables. If None or empty list, all variables are assumed to
be continuous.
Returns
-------
float
A minimizer. It is difficult to do global optimization so
typically this method returns a local minimum.
Raises
------
ValueError
If the type of radial basis function is not supported.
RuntimeError
If the solver cannot be found.
"""
assert(len(var_lower)==n)
assert(len(var_upper)==n)
assert(len(rbf_lambda)==k)
assert(len(node_pos)==k)
assert(isinstance(settings, RbfSettings))
# Determine the size of the P matrix
p = ru.get_size_P_matrix(settings, n)
assert(len(rbf_h)==(p))
# Instantiate model
if (ru.get_degree_polynomial(settings) == 1):
model = rbfopt_degree1_models
elif (ru.get_degree_polynomial(settings) == 0):
model = rbfopt_degree0_models
else:
raise ValueError('RBF type ' + settings.rbf + ' not supported')
instance = model.create_min_rbf_model(settings, n, k, var_lower,
var_upper, node_pos, rbf_lambda,
rbf_h, integer_vars)
# Initialize variables for local search
initialize_instance_variables(settings, instance)
# Instantiate optimizer
opt = pyomo.opt.SolverFactory(config.MINLP_SOLVER_EXEC, solver_io='nl')
if opt is None:
raise RuntimeError('Solver ' + config.MINLP_SOLVER_EXEC + ' not found')
set_minlp_solver_options(opt)
# Solve and load results
try:
results = opt.solve(instance, keepfiles = False,
tee = settings.print_solver_output)
if ((results.solver.status == pyomo.opt.SolverStatus.ok) and
(results.solver.termination_condition ==
TerminationCondition.optimal)):
# this is feasible and optimal
instance.solutions.load_from(results)
point = [instance.x[i].value for i in instance.N]
ru.round_integer_vars(point, integer_vars)
else:
point = None
except:
point = None
return point
