def solve_problem(eigs, filename=None, use_stdout=False, use_tr=False):
# Get the A matrix
A = create_random_problem(eigs)
# Create the other problem data
b = np.random.uniform(size=len(eigs))
Acon = np.random.uniform(size=len(eigs))
bcon = np.random.uniform()
problem = Quadratic(A, b, Acon, bcon)
if use_tr:
# Create the trust region problem
max_lbfgs = 10
tr_init_size = 0.05
tr_min_size = 1e-6
tr_max_size = 10.0
tr_eta = 0.25
tr_penalty_gamma = 10.0
qn = ParOpt.LBFGS(problem, subspace=max_lbfgs)
tr = ParOpt.TrustRegion(problem, qn, tr_init_size, tr_min_size,
tr_max_size, tr_eta, tr_penalty_gamma)
tr.setMaxTrustRegionIterations(500)
# Set up the optimization problem
tr_opt = ParOpt.InteriorPoint(tr, 10, ParOpt.BFGS)
if filename is not None and use_stdout is False:
tr_opt.setOutputFile(filename)
# Set the tolerances
tr_opt.setAbsOptimalityTol(1e-8)
tr_opt.setStartingPointStrategy(ParOpt.AFFINE_STEP)
tr_opt.setStartAffineStepMultiplierMin(0.01)
# Set optimization parameters
tr_opt.setArmijoParam(1e-5)
tr_opt.setMaxMajorIterations(5000)
tr_opt.setBarrierPower(2.0)
tr_opt.setBarrierFraction(0.1)
# optimize
tr.setOutputFile(filename + '_tr')
tr.setPrintLevel(1)
tr.optimize(tr_opt)
else:
# Set up the optimization problem
max_lbfgs = 10
opt = ParOpt.InteriorPoint(problem, max_lbfgs, ParOpt.BFGS)
if filename is not None and use_stdout is False:
opt.setOutputFile(filename)
# Set optimization parameters
opt.setArmijoParam(1e-5)
opt.setMaxMajorIterations(5000)
opt.setBarrierPower(2.0)
opt.setBarrierFraction(0.1)
opt.optimize()
return
def paropt_truss(truss,
use_hessian=False,
max_qn_subspace=50,
qn_type=ParOpt.BFGS):
'''
Optimize the given truss structure using ParOpt
'''
# Create the optimizer
opt = ParOpt.InteriorPoint(truss, max_qn_subspace, qn_type)
# Set the optimality tolerance
opt.setAbsOptimalityTol(1e-5)
# Set the Hessian-vector product iterations
if use_hessian:
opt.setUseLineSearch(0)
opt.setUseHvecProduct(1)
opt.setGMRESSubspaceSize(100)
opt.setNKSwitchTolerance(1.0)
opt.setEisenstatWalkerParameters(0.5, 0.0)
opt.setGMRESTolerances(1.0, 1e-30)
else:
opt.setUseHvecProduct(0)
# Set optimization parameters
opt.setArmijioParam(1e-5)
opt.setMaxMajorIterations(2500)
# Perform a quick check of the gradient (and Hessian)
opt.checkGradients(1e-6)
return opt
def plot_it_all(problem):
'''
Plot a carpet plot with the search histories for steepest descent,
conjugate gradient and BFGS from the same starting point.
'''
# Set up the optimization problem
max_lbfgs = 20
opt = ParOpt.InteriorPoint(problem, max_lbfgs, ParOpt.BFGS)
# Create the data for the carpet plot
n = 150
xlow = -4.0
xhigh = 4.0
x1 = np.linspace(xlow, xhigh, n)
r = np.zeros((n, n))
for j in range(n):
for i in range(n):
fail, fobj, con = problem.evalObjCon([x1[i], x1[j]])
r[j, i] = fobj
# Assign the contour levels
levels = np.min(r) + np.linspace(0, 1.0, 75)**2*(np.max(r) - np.min(r))
# Create the plot
fig = plt.figure(facecolor='w')
plt.contour(x1, x1, r, levels)
colours = ['-bo', '-ko', '-co', '-mo', '-yo',
'-bx', '-kx', '-cx', '-mx', '-yx' ]
for k in range(len(colours)):
# Optimize the problem
problem.x_hist = []
opt.resetQuasiNewtonHessian()
opt.setInitBarrierParameter(0.1)
opt.setUseLineSearch(1)
opt.optimize()
# Copy out the steepest descent points
sd = np.zeros((2, len(problem.x_hist)))
for i in range(len(problem.x_hist)):
sd[0, i] = problem.x_hist[i][0]
sd[1, i] = problem.x_hist[i][1]
plt.plot(sd[0, :], sd[1, :], colours[k],
label='IP %d'%(sd.shape[1]))
plt.plot(sd[0, -1], sd[1, -1], '-ro')
plt.legend()
plt.axis([xlow, xhigh, xlow, xhigh])
plt.show()
def paropt_truss(truss, use_hessian=False,
prefix='results'):
'''
Optimize the given truss structure using ParOpt
'''
# Create the optimizer
max_qn_subspace = 10
opt = ParOpt.InteriorPoint(truss, max_qn_subspace, ParOpt.BFGS)
# Set the optimality tolerance
opt.setAbsOptimalityTol(1e-6)
opt.setBarrierStrategy(ParOpt.COMPLEMENTARITY_FRACTION)
# Set the Hessian-vector product iterations
if use_hessian:
# opt.setUseLineSearch(0)
opt.setUseHvecProduct(1)
opt.setGMRESSubspaceSize(25)
opt.setNKSwitchTolerance(1.0)
opt.setEisenstatWalkerParameters(0.01, 0.0)
opt.setGMRESTolerances(1.0, 1e-30)
else:
opt.setUseHvecProduct(0)
# Set the output level
opt.setOutputLevel(1)
# Set optimization parameters
opt.setArmijoParam(1e-5)
opt.setMaxMajorIterations(2500)
# Set the output file to use
fname = os.path.join(prefix, 'truss_paropt%dx%d.out'%(N, M))
opt.setOutputFile(fname)
# Optimize the truss
opt.optimize()
return opt
def solve_problem(eigs, filename=None, data_type='orthogonal', use_tr=False):
# Create a random orthogonal Q vector
if data_type == 'orthogonal':
B = np.random.uniform(size=(n, n))
Q, s, v = np.linalg.svd(B)
# Create a random Affine matrix
Affine = create_random_spd(eigs)
else:
Q = np.random.uniform(size=(n, n))
Affine = np.diag(1e-3 * np.ones(n))
# Create the random right-hand-side
b = np.random.uniform(size=n)
# Create the constraint data
Acon = np.random.uniform(size=n)
bcon = 0.25 * np.sum(Acon)
# Create the convex problem
problem = ConvexProblem(Q, Affine, b, Acon, bcon)
if use_tr:
# Create the trust region problem
max_lbfgs = 10
tr_init_size = 0.05
tr_min_size = 1e-6
tr_max_size = 10.0
tr_eta = 0.1
tr_penalty_gamma = 10.0
qn = ParOpt.LBFGS(problem, subspace=max_lbfgs)
subproblem = ParOpt.QuadraticSubproblem(problem, qn)
tr = ParOpt.TrustRegion(subproblem, tr_init_size, tr_min_size,
tr_max_size, tr_eta, tr_penalty_gamma)
tr.setMaxTrustRegionIterations(500)
infeas_tol = 1e-6
l1_tol = 1e-5
linfty_tol = 1e-5
tr.setTrustRegionTolerances(infeas_tol, l1_tol, linfty_tol)
# Set up the optimization problem
tr_opt = ParOpt.InteriorPoint(subproblem, 10, ParOpt.BFGS)
if filename is not None:
tr_opt.setOutputFile(filename)
tr.setOutputFile(os.path.splitext(filename)[0] + '.tr')
# Set the tolerances
tr_opt.setAbsOptimalityTol(1e-8)
tr_opt.setStartingPointStrategy(ParOpt.AFFINE_STEP)
tr_opt.setStartAffineStepMultiplierMin(0.01)
# Set optimization parameters
tr_opt.setArmijoParam(1e-5)
tr_opt.setMaxMajorIterations(5000)
tr_opt.setBarrierPower(2.0)
tr_opt.setBarrierFraction(0.1)
# optimize
tr.setPrintLevel(1)
tr.optimize(tr_opt)
# Get the optimized point from the trust-region subproblem
x = tr.getOptimizedPoint()
else:
# Set up the optimization problem
max_lbfgs = 50
opt = ParOpt.InteriorPoint(problem, max_lbfgs, ParOpt.BFGS)
if filename is not None:
opt.setOutputFile(filename)
# Set optimization parameters
opt.setArmijoParam(1e-5)
opt.setMaxMajorIterations(5000)
opt.setBarrierPower(2.0)
opt.setBarrierFraction(0.1)
opt.optimize()
# Get the optimized point
x, z, zw, zl, zu = opt.getOptimizedPoint()
return x
def __call__(self,
optProb,
sens=None,
sensStep=None,
sensMode=None,
storeHistory=None,
hotStart=None,
storeSens=True):
"""
This is the main routine used to solve the optimization
problem.
Parameters
----------
optProb : Optimization or Solution class instance
This is the complete description of the optimization problem
to be solved by the optimizer
sens : str or python Function.
Specifiy method to compute sensitivities. To
explictly use pyOptSparse gradient class to do the
derivatives with finite differenes use \'FD\'. \'sens\'
may also be \'CS\' which will cause pyOptSpare to compute
the derivatives using the complex step method. Finally,
\'sens\' may be a python function handle which is expected
to compute the sensitivities directly. For expensive
function evaluations and/or problems with large numbers of
design variables this is the preferred method.
sensStep : float
Set the step size to use for design variables. Defaults to
1e-6 when sens is \'FD\' and 1e-40j when sens is \'CS\'.
sensMode : str
Use \'pgc\' for parallel gradient computations. Only
available with mpi4py and each objective evaluation is
otherwise serial
storeHistory : str
File name of the history file into which the history of
this optimization will be stored
hotStart : str
File name of the history file to "replay" for the
optimziation. The optimization problem used to generate
the history file specified in \'hotStart\' must be
**IDENTICAL** to the currently supplied \'optProb\'. By
identical we mean, **EVERY SINGLE PARAMETER MUST BE
IDENTICAL**. As soon as he requested evaluation point
from ParOpt does not match the history, function and
gradient evaluations revert back to normal evaluations.
storeSens : bool
Flag sepcifying if sensitivities are to be stored in hist.
This is necessay for hot-starting only.
"""
self.callCounter = 0
self.storeSens = storeSens
if len(optProb.constraints) == 0:
# If the problem is unconstrained, add a dummy constraint.
self.unconstrained = True
optProb.dummyConstraint = True
# Save the optimization problem and finalize constraint
# jacobian, in general can only do on root proc
self.optProb = optProb
self.optProb.finalizeDesignVariables()
self.optProb.finalizeConstraints()
self._setInitialCacheValues()
self._setSens(sens, sensStep, sensMode)
blx, bux, xs = self._assembleContinuousVariables()
xs = np.maximum(xs, blx)
xs = np.minimum(xs, bux)
# The number of design variables
n = len(xs)
oneSided = True
if self.unconstrained:
m = 0
else:
indices, blc, buc, fact = self.optProb.getOrdering(
['ne', 'le', 'ni', 'li'], oneSided=oneSided)
m = len(indices)
self.optProb.jacIndices = indices
self.optProb.fact = fact
self.optProb.offset = buc
if self.optProb.comm.rank == 0:
# Set history/hotstart
self._setHistory(storeHistory, hotStart)
class Problem(_ParOpt.Problem):
def __init__(self, ptr, n, m, xs, blx, bux):
super(Problem, self).__init__(MPI.COMM_SELF, n, m)
self.ptr = ptr
self.n = n
self.m = m
self.xs = xs
self.blx = blx
self.bux = bux
self.fobj = 0.0
return
def getVarsAndBounds(self, x, lb, ub):
'''Get the variable values and bounds'''
lb[:] = self.blx
ub[:] = self.bux
x[:] = self.xs
return
def evalObjCon(self, x):
'''Evaluate the objective and constraint values'''
fobj, fcon, fail = self.ptr._masterFunc(
x[:], ['fobj', 'fcon'])
self.fobj = fobj
return fail, fobj, -fcon
def evalObjConGradient(self, x, g, A):
gobj, gcon, fail = self.ptr._masterFunc(
x[:], ['gobj', 'gcon'])
g[:] = gobj[:]
for i in range(self.m):
A[i][:] = -gcon[i][:]
return fail
# Create the ParOpt problem class
problem = Problem(self, n, m, xs, blx, bux)
# Get the algorithm/subspace size parameters
algorithm = self.getOption('algorithm').lower()
qn_subspace_size = self.getOption('qn_subspace_size')
filename = self.getOption('filename')
optTime = MPI.Wtime()
if algorithm == 'ip':
# Create the optimizer
opt = _ParOpt.InteriorPoint(problem, qn_subspace_size,
_ParOpt.BFGS)
# Set the ParOpt options
self._set_paropt_options(opt)
# Optimize!
opt.setOutputFile(filename)
opt.optimize()
else:
norm_type = self.getOption('norm_type').lower()
# Optimality tolerance
opt_tol = self.getOption('abs_optimality_tol')
# Trust region algorithm options
tr_init_size = self.getOption('tr_init_size')
tr_max_size = self.getOption('tr_max_size')
tr_min_size = self.getOption('tr_min_size')
tr_eta = self.getOption('tr_eta')
tr_penalty_gamma = self.getOption('tr_penalty_gamma')
tr_opt_abs_tol = self.getOption('tr_abs_optimality_tol')
tr_max_iterations = self.getOption('tr_max_iterations')
# Create the quasi-Newton Hessian approximation
qn = _ParOpt.LBFGS(problem, subspace=qn_subspace_size)
# Create the trust region problem
tr = _ParOpt.TrustRegion(problem, qn, tr_init_size,
tr_min_size, tr_max_size, tr_eta,
tr_penalty_gamma)
# Create the ParOpt problem
opt = _ParOpt.InteriorPoint(tr, qn_subspace_size,
_ParOpt.NO_HESSIAN_APPROX)
# Set the ParOpt options
self._set_paropt_options(opt)
# Set the output file name
opt.setOutputFile(filename)
# Set the penalty parameter internally in the
# code. These must be consistent between the trust
# region object and ParOpt.
opt.setPenaltyGamma(tr_penalty_gamma)
# Set parameters for ParOpt in the subproblem
opt.setMaxMajorIterations(tr_max_iterations)
opt.setAbsOptimalityTol(tr_opt_abs_tol)
# Don't update the quasi-Newton method
opt.setQuasiNewton(qn)
opt.setUseQuasiNewtonUpdates(0)
# Check the norm type
if norm_type == 'l1':
opt.setNormType(_ParOpt.L1_NORM)
elif norm_type == 'linfty':
opt.setNormType(_ParOpt.INFTY_NORM)
else:
opt.setNormType(_ParOpt.L2_NORM)
# Initialize the problem
tr.initialize()
# Iterate
max_iterations = self.getOption('max_iterations')
for i in range(max_iterations):
opt.setInitBarrierParameter(100.0)
opt.resetDesignAndBounds()
opt.optimize()
# Get the optimized point
x, z, zw, zl, zu = opt.getOptimizedPoint()
# Update the trust region method
infeas, l1, linfty = tr.update(x, z, zw)
if norm_type == 'l1':
opt_criteria = (l1 < opt_tol)
else:
opt_criteria = (linfty < opt_tol)
if ((infeas < opt_tol) and opt_criteria):
break
# Set the total opt time
optTime = MPI.Wtime() - optTime
# Get the obective function value
fobj = problem.fobj
# Get the optimized point
x, z, zw, zl, zu = opt.getOptimizedPoint()
# Create the optimization solution
sol_inform = {}
sol = self._createSolution(optTime, sol_inform, fobj, x[:])
# Indicate solution finished
self.optProb.comm.bcast(-1, root=0)
else: # We are not on the root process so go into waiting loop:
self._waitLoop()
sol = None
# Communication solution and return
sol = self._communicateSolution(sol)
return sol
tr_eta = 0.2
tr_penalty_gamma = 10.0
tr = ParOpt.TrustRegion(problem, qn, tr_init_size, tr_min_size,
tr_max_size, tr_eta, tr_penalty_gamma)
# Set the tolerances
infeas_tol = 1e-4
l1_tol = 1e-3
linfty_tol = 1e-3
tr.setTrustRegionTolerances(infeas_tol, l1_tol, linfty_tol)
# Set the maximum number of iterations
tr.setMaxTrustRegionIterations(100)
# Set up the optimization problem
tr_opt = ParOpt.InteriorPoint(tr, 2, ParOpt.BFGS)
# Set up the optimization problem
tr_opt.setOutputFile('topo_optimization_paropt.out')
# Set the tolerances
tr_opt.setAbsOptimalityTol(1e-8)
tr_opt.setStartingPointStrategy(ParOpt.AFFINE_STEP)
tr_opt.setStartAffineStepMultiplierMin(0.01)
# Set optimization parameters
tr_opt.setArmijoParam(1e-5)
tr_opt.setMaxMajorIterations(5000)
tr_opt.setBarrierPower(2.0)
tr_opt.setBarrierFraction(0.1)
'''Evaluate the objective and constraint'''
fail = 0
fobj = x[1] * x[1] + x[0] + x[2] + np.exp(-x[3])
cons = np.array([x[0] + x[1] - 1.0])
return fail, fobj, cons
def evalObjConGradient(self, x, g, A):
'''Evaluate the objective and constraint gradient'''
fail = 0
g[0] = 1.0
g[1] = 2.0 * x[1]
g[2] = 1.0
g[3] = -np.exp(-x[3])
A[0][0] = 1.0
A[0][1] = 1.0
return fail
# Allocate the optimization problem
problem = Sellar()
# Set up the optimization problem
max_lbfgs = 50
opt = ParOpt.InteriorPoint(problem, max_lbfgs, ParOpt.BFGS)
# Optimize
opt.optimize()
subproblem = ParOpt.QuadraticSubproblem(problem, qn)
tr = ParOpt.TrustRegion(subproblem, tr_init_size,
tr_min_size, tr_max_size,
tr_eta, tr_penalty_gamma)
# Set the tolerances
infeas_tol = 1e-4
l1_tol = 1e-3
linfty_tol = 1e-3
tr.setTrustRegionTolerances(infeas_tol, l1_tol, linfty_tol)
# Set the maximum number of iterations
tr.setMaxTrustRegionIterations(200)
# Set up the optimization problem
tr_opt = ParOpt.InteriorPoint(subproblem, 2, ParOpt.BFGS)
# Set up the optimization problem
tr_opt.setOutputFile('topo_optimization_paropt.out')
# Set the tolerances
tr_opt.setAbsOptimalityTol(1e-8)
tr_opt.setStartingPointStrategy(ParOpt.AFFINE_STEP)
tr_opt.setStartAffineStepMultiplierMin(0.01)
# Set optimization parameters
tr_opt.setArmijoParam(1e-5)
tr_opt.setMaxMajorIterations(5000)
tr_opt.setBarrierPower(2.0)
tr_opt.setBarrierFraction(0.1)
def plot_it_all(problem, use_tr=False):
'''
Plot a carpet plot with the search histories for steepest descent,
conjugate gradient and BFGS from the same starting point.
'''
# Set up the optimization problem
max_lbfgs = 20
opt = ParOpt.InteriorPoint(problem, max_lbfgs, ParOpt.BFGS)
opt.checkGradients(1e-6)
# Create the data for the carpet plot
n = 150
xlow = -4.0
xhigh = 4.0
x1 = np.linspace(xlow, xhigh, n)
ylow = -3.0
yhigh = 3.0
x2 = np.linspace(ylow, yhigh, n)
r = np.zeros((n, n))
for j in range(n):
for i in range(n):
fail, fobj, con = problem.evalObjCon([x1[i], x2[j]])
r[j, i] = fobj
# Assign the contour levels
levels = np.min(r) + np.linspace(0, 1.0, 75)**2 * (np.max(r) - np.min(r))
# Create the plot
fig = plt.figure(facecolor='w')
plt.contour(x1, x2, r, levels)
plt.plot([0.5 - yhigh, 0.5 - ylow], [yhigh, ylow], '-k')
colours = [
'-bo', '-ko', '-co', '-mo', '-yo', '-bx', '-kx', '-cx', '-mx', '-yx'
]
for k in range(len(colours)):
# Optimize the problem
problem.x_hist = []
if use_tr:
# Create the quasi-Newton Hessian approximation
qn = ParOpt.LBFGS(problem, subspace=2)
# Create the trust region problem
tr_init_size = 0.05
tr_min_size = 1e-6
tr_max_size = 10.0
tr_eta = 0.25
tr_penalty_gamma = 10.0
tr = ParOpt.TrustRegion(problem, qn, tr_init_size, tr_min_size,
tr_max_size, tr_eta, tr_penalty_gamma)
# Set up the optimization problem
tr_opt = ParOpt.InteriorPoint(tr, 2, ParOpt.BFGS)
# Optimize
tr.optimize(tr_opt)
# Get the optimized point
x, z, zw, zl, zu = tr_opt.getOptimizedPoint()
else:
opt.resetQuasiNewtonHessian()
opt.setInitBarrierParameter(0.1)
opt.setUseLineSearch(1)
opt.optimize()
# Get the optimized point and print out the data
x, z, zw, zl, zu = opt.getOptimizedPoint()
# Copy out the steepest descent points
popt = np.zeros((2, len(problem.x_hist)))
for i in range(len(problem.x_hist)):
popt[0, i] = problem.x_hist[i][0]
popt[1, i] = problem.x_hist[i][1]
plt.plot(popt[0, :],
popt[1, :],
colours[k],
label='ParOpt %d' % (popt.shape[1]))
plt.plot(popt[0, -1], popt[1, -1], '-ro')
# Print the data to the screen
g = np.zeros(2)
A = np.zeros((1, 2))
problem.evalObjConGradient(x, g, A)
print('The design variables: ', x[:])
print('The multipliers: ', z[:])
print('The objective gradient: ', g[:])
print('The constraint gradient: ', A[:])
ax = fig.axes[0]
ax.set_aspect('equal', 'box')
plt.legend()
plt.show()
def __call__(self,
optProb,
sens=None,
sensStep=None,
sensMode=None,
storeHistory=None,
hotStart=None,
storeSens=True):
"""
This is the main routine used to solve the optimization
problem.
Parameters
----------
optProb : Optimization or Solution class instance
This is the complete description of the optimization problem
to be solved by the optimizer
sens : str or python Function.
Specifiy method to compute sensitivities. To
explictly use pyOptSparse gradient class to do the
derivatives with finite differenes use \'FD\'. \'sens\'
may also be \'CS\' which will cause pyOptSpare to compute
the derivatives using the complex step method. Finally,
\'sens\' may be a python function handle which is expected
to compute the sensitivities directly. For expensive
function evaluations and/or problems with large numbers of
design variables this is the preferred method.
sensStep : float
Set the step size to use for design variables. Defaults to
1e-6 when sens is \'FD\' and 1e-40j when sens is \'CS\'.
sensMode : str
Use \'pgc\' for parallel gradient computations. Only
available with mpi4py and each objective evaluation is
otherwise serial
storeHistory : str
File name of the history file into which the history of
this optimization will be stored
hotStart : str
File name of the history file to "replay" for the
optimziation. The optimization problem used to generate
the history file specified in \'hotStart\' must be
**IDENTICAL** to the currently supplied \'optProb\'. By
identical we mean, **EVERY SINGLE PARAMETER MUST BE
IDENTICAL**. As soon as he requested evaluation point
from ParOpt does not match the history, function and
gradient evaluations revert back to normal evaluations.
storeSens : bool
Flag sepcifying if sensitivities are to be stored in hist.
This is necessay for hot-starting only.
"""
self.callCounter = 0
self.storeSens = storeSens
if len(optProb.constraints) == 0:
# If the problem is unconstrained, add a dummy constraint.
self.unconstrained = True
optProb.dummyConstraint = True
# Save the optimization problem and finalize constraint
# jacobian, in general can only do on root proc
self.optProb = optProb
self.optProb.finalizeDesignVariables()
self.optProb.finalizeConstraints()
self._setInitialCacheValues()
self._setSens(sens, sensStep, sensMode)
blx, bux, xs = self._assembleContinuousVariables()
xs = np.maximum(xs, blx)
xs = np.minimum(xs, bux)
# The number of design variables
n = len(xs)
oneSided = True
if self.unconstrained:
m = 0
else:
indices, blc, buc, fact = self.optProb.getOrdering(
["ne", "le", "ni", "li"], oneSided=oneSided)
m = len(indices)
self.optProb.jacIndices = indices
self.optProb.fact = fact
self.optProb.offset = buc
if self.optProb.comm.rank == 0:
# Set history/hotstart
self._setHistory(storeHistory, hotStart)
class Problem(_ParOpt.Problem):
def __init__(self, ptr, n, m, xs, blx, bux):
super(Problem, self).__init__(MPI.COMM_SELF, n, m)
self.ptr = ptr
self.n = n
self.m = m
self.xs = xs
self.blx = blx
self.bux = bux
self.fobj = 0.0
return
def getVarsAndBounds(self, x, lb, ub):
"""Get the variable values and bounds"""
# Find the average distance between lower and upper bound
bound_sum = 0.0
for i in range(len(x)):
if self.blx[i] <= -1e20 or self.bux[i] >= 1e20:
bound_sum += 1.0
else:
bound_sum += self.bux[i] - self.blx[i]
bound_sum = bound_sum / len(x)
for i in range(len(x)):
x[i] = self.xs[i]
lb[i] = self.blx[i]
ub[i] = self.bux[i]
if self.xs[i] <= self.blx[i]:
x[i] = self.blx[i] + 0.5 * np.min(
(bound_sum, self.bux[i] - self.blx[i]))
elif self.xs[i] >= self.bux[i]:
x[i] = self.bux[i] - 0.5 * np.min(
(bound_sum, self.bux[i] - self.blx[i]))
return
def evalObjCon(self, x):
"""Evaluate the objective and constraint values"""
fobj, fcon, fail = self.ptr._masterFunc(
x[:], ["fobj", "fcon"])
self.fobj = fobj
return fail, fobj, -fcon
def evalObjConGradient(self, x, g, A):
gobj, gcon, fail = self.ptr._masterFunc(
x[:], ["gobj", "gcon"])
g[:] = gobj[:]
for i in range(self.m):
A[i][:] = -gcon[i][:]
return fail
# Create the ParOpt problem class
problem = Problem(self, n, m, xs, blx, bux)
# Get the algorithm/subspace size parameters
algorithm = self.getOption("algorithm").lower()
qn_subspace_size = self.getOption("qn_subspace_size")
filename = self.getOption("filename")
optTime = MPI.Wtime()
if algorithm == "ip":
# Create the optimizer
opt = _ParOpt.InteriorPoint(problem, qn_subspace_size,
_ParOpt.BFGS)
# Set the ParOpt options
self._set_paropt_options(opt)
# Optimize!
opt.setOutputFile(filename)
opt.optimize()
else:
# Optimality tolerance
opt_tol = self.getOption("abs_optimality_tol")
# Trust region algorithm options
tr_init_size = self.getOption("tr_init_size")
tr_max_size = self.getOption("tr_max_size")
tr_min_size = self.getOption("tr_min_size")
tr_eta = self.getOption("tr_eta")
tr_penalty_gamma = self.getOption("tr_penalty_gamma")
tr_opt_abs_tol = self.getOption("tr_abs_optimality_tol")
tr_max_iterations = self.getOption("tr_max_iterations")
# Create the quasi-Newton Hessian approximation
qn = _ParOpt.LBFGS(problem, subspace=qn_subspace_size)
subproblem = _ParOpt.QuadraticSubproblem(problem, qn)
# Create the trust region problem
tr = _ParOpt.TrustRegion(subproblem, tr_init_size, tr_min_size,
tr_max_size, tr_eta, tr_penalty_gamma)
# Create the ParOpt problem
opt = _ParOpt.InteriorPoint(subproblem, qn_subspace_size,
_ParOpt.NO_HESSIAN_APPROX)
# Set the ParOpt options
self._set_paropt_options(opt)
# Set the output file name
opt.setOutputFile(filename)
tr.setOutputFile(os.path.splitext(filename)[0] + ".tr")
# Use the adaptive penalty update scheme by default
tr.setAdaptiveGammaUpdate(1)
tr.setPenaltyGammaMax(1e3)
# Set parameters for the trust-region algorithm
tr.setMaxTrustRegionIterations(tr_max_iterations)
# Set the tolerance
tr.setTrustRegionTolerances(opt_tol, opt_tol, opt_tol)
# Set optimality tolerance for the trust region problem
opt.setAbsOptimalityTol(tr_opt_abs_tol)
# Optimize the problem
tr.optimize(opt)
# Get the optimized point
x, z, zw, zl, zu = opt.getOptimizedPoint()
# Set the total opt time
optTime = MPI.Wtime() - optTime
# Get the obective function value
fobj = problem.fobj
# Get the optimized point
x, z, zw, zl, zu = opt.getOptimizedPoint()
if self.storeHistory:
self.metadata["endTime"] = datetime.datetime.now().strftime(
"%Y-%m-%d %H:%M:%S")
self.metadata["optTime"] = optTime
self.hist.writeData("metadata", self.metadata)
self.hist.close()
# Create the optimization solution. Note that the signs on the multipliers
# are switch since ParOpt uses a formulation with c(x) >= 0, while pyOpt
# uses g(x) = -c(x) <= 0. Therefore the multipliers are reversed.
sol_inform = {}
# If number of constraints is zero, ParOpt returns z as None.
# Thus if there is no constraints, should pass an empty list
# to multipliers instead of z.
if z is not None:
sol = self._createSolution(optTime,
sol_inform,
fobj,
x[:],
multipliers=-z)
else:
sol = self._createSolution(optTime,
sol_inform,
fobj,
x[:],
multipliers=[])
# Indicate solution finished
self.optProb.comm.bcast(-1, root=0)
else: # We are not on the root process so go into waiting loop:
self._waitLoop()
sol = None
# Communication solution and return
sol = self._communicateSolution(sol)
return sol
max_mma_iters = 10
problem = Toy(comm)
problem.setInequalityOptions(dense_ineq=True, sparse_ineq=False,
use_lower=True, use_upper=True)
# Set the ParOpt problem into MMA
mma = ParOpt.MMA(problem, use_mma=True)
mma.setInitAsymptoteOffset(0.5)
mma.setMinAsymptoteOffset(0.01)
mma.setBoundRelax(1e-4)
mma.setOutputFile(os.path.join(args.prefix,
'mma_output.out'))
# Create the ParOpt problem
opt = ParOpt.InteriorPoint(mma, args.max_lbfgs, ParOpt.BFGS)
# Set parameters
opt.setMaxMajorIterations(args.max_opt_iters)
opt.setHessianResetFreq(args.hessian_reset)
opt.setAbsOptimalityTol(args.opt_abs_tol)
opt.setBarrierFraction(args.opt_barrier_frac)
opt.setBarrierPower(args.opt_barrier_power)
opt.setOutputFrequency(args.output_freq)
opt.setAbsOptimalityTol(1e-7)
opt.setUseDiagHessian(1)
# Set the starting point using the mass fraction
x = mma.getOptimizedPoint()
print('Initial x = ', np.array(x))
def _setup_driver(self, problem):
"""
Prepare the driver for execution.
This is the final thing to run during setup.
Parameters
----------
paropt_problem : <Problem>
Pointer
"""
# TODO:
# - logic for different opt algorithms
# - treat equality constraints
super(ParOptDriver, self)._setup_driver(problem)
opt_type = self.options['optimizer']
# Raise error if multiple objectives are provided
if len(self._objs) > 1:
msg = 'ParOpt currently does not support multiple objectives.'
raise RuntimeError(msg.format(self.__class__.__name__))
# Set the limited-memory options
max_qn_subspace = self.options['max_qn_subspace']
if self.options['qn_type'] == 'BFGS':
qn_type = ParOpt.BFGS
elif self.options['qn_type'] == 'SR1':
qn_type = ParOpt.SR1
elif self.options['qn_type'] == 'No Hessian approx':
qn_type = ParOpt.NO_HESSIAN_APPROX
else:
qn_type = ParOpt.BFGS
# Create the ParOptProblem from the OpenMDAO problem
self.paropt_problem = ParOptProblem(problem)
# Create the problem
if opt_type == 'Trust Region':
# For the trust region method, you have to use a Hessian
# approximation
if qn_type == ParOpt.NO_HESSIAN_APPROX:
qn = ParOpt.BFGS
if max_qn_subspace < 1:
max_qn_subspace = 1
# Create the quasi-Newton method
qn = ParOpt.LBFGS(self.paropt_problem, subspace=max_qn_subspace)
# Retrieve the options for the trust region problem
tr_min_size = self.options['tr_min_size']
tr_max_size = self.options['tr_max_size']
tr_eta = self.options['tr_eta']
tr_penalty_gamma = self.options['tr_penalty_gamma']
tr_init_size = self.options['tr_init_size']
# Create the trust region sub-problem
tr_init_size = min(tr_max_size, max(tr_init_size, tr_min_size))
tr = ParOpt.TrustRegion(self.paropt_problem, qn, tr_init_size,
tr_min_size, tr_max_size, tr_eta,
tr_penalty_gamma)
# Set the penalty parameter
tr.setPenaltyGammaMax(self.options['tr_penalty_gamma_max'])
tr.setMaxTrustRegionIterations(self.options['tr_max_iterations'])
# Trust region convergence tolerances
infeas_tol = self.options['tr_infeas_tol']
l1_tol = self.options['tr_l1_tol']
linfty_tol = self.options['tr_linfty_tol']
tr.setTrustRegionTolerances(infeas_tol, l1_tol, linfty_tol)
# Trust region output file name
if self.options['tr_output_file'] is not None:
tr.setOutputFile(self.options['tr_output_file'])
tr.setOutputFrequency(self.options['tr_write_output_freq'])
# Create the interior-point optimizer for the trust region sub-problem
opt = ParOpt.InteriorPoint(tr, 0, ParOpt.NO_HESSIAN_APPROX)
self.tr = tr
else:
# Create the ParOpt object with the interior point method
opt = ParOpt.InteriorPoint(self.paropt_problem, max_qn_subspace,
qn_type)
# Apply the options to ParOpt
# Currently incomplete
opt.setAbsOptimalityTol(self.options['tol'])
opt.setMaxMajorIterations(self.options['maxiter'])
if self.options['dh']:
opt.checkGradients(self.options['dh'])
# Set barrier strategy
if self.options['barrier_strategy']:
if self.options['barrier_strategy'] == 'Monotone':
barrier_strategy = ParOpt.MONOTONE
elif self.options['barrier_strategy'] == 'Mehrotra':
barrier_strategy = ParOpt.MEHROTRA
elif self.options[
'barrier_strategy'] == 'Complementarity fraction':
barrier_strategy = ParOpt.COMPLEMENTARITY_FRACTION
opt.setBarrierStrategy(barrier_strategy)
# Set starting point strategy
if self.options['start_strategy']:
if self.options['barrier_strategy'] == 'None':
start_strategy = ParOpt.NO_START_STRATEGY
elif self.options[
'barrier_strategy'] == 'Least squares multipliers':
start_strategy = ParOpt.LEAST_SQUARES_MULTIPLIERS
elif self.options['barrier_strategy'] == 'Affine step':
start_strategy = ParOpt.AFFINE_STEP
opt.setStartingPointStrategy(start_strategy)
# Set norm type
if self.options['norm_type']:
if self.options['norm_type'] == 'Infinity':
norm_type = ParOpt.INFTY_NORM
elif self.options['norm_type'] == 'L1':
norm_type = ParOpt.L1_NORM
elif self.options['norm_type'] == 'L2':
norm_type = ParOpt.L2_NORM
opt.setBarrierStrategy(norm_type)
# Set BFGS update strategy
if self.options['bfgs_update_type']:
if self.options['bfgs_update_type'] == 'Skip negative':
bfgs_update_type = ParOpt.SKIP_NEGATIVE_CURVATURE
elif self.options['bfgs_update_type'] == 'Damped':
bfgs_update_type = ParOpt.DAMPED_UPDATE
opt.setBFGSUpdateType(bfgs_update_type)
if self.options['penalty_gamma']:
opt.setPenaltyGamma(self.options['penalty_gamma'])
if self.options['barrier_fraction']:
opt.setBarrierFraction(self.options['barrier_fraction'])
if self.options['barrier_power']:
opt.setBarrierPower(self.options['barrier_power'])
if self.options['hessian_reset_freq']:
opt.setHessianResetFrequency(self.options['hessian_reset_freq'])
if self.options['qn_diag_factor']:
opt.setQNDiagonalFactor(self.options['qn_diag_factor'])
if self.options['use_sequential_linear']:
opt.setSequentialLinearMethod(
self.options['use_sequential_linear'])
if self.options['affine_step_multiplier_min']:
opt.setStartAffineStepMultiplierMin(
self.options['affine_step_multiplier_min'])
if self.options['init_barrier_parameter']:
opt.setInitBarrierParameter(self.options['init_barrier_parameter'])
if self.options['relative_barrier']:
opt.setRelativeBarrier(self.options['relative_barrier'])
if self.options['set_qn']:
opt.setQuasiNewton(self.options['set_qn'])
if self.options['qn_updates']:
opt.setUseQuasiNewtonUpdates(self.options['qn_updates'])
if self.options['use_line_search']:
opt.setUseLineSearch(self.options['use_line_search'])
if self.options['max_ls_iters']:
opt.setMaxLineSearchIters(self.options['max_ls_iters'])
if self.options['backtrack_ls']:
opt.setBacktrackingLineSearch(self.options['backtrack_ls'])
if self.options['armijo_param']:
opt.setArmijoParam(self.options['armijo_param'])
if self.options['penalty_descent_frac']:
opt.setPenaltyDescentFraction(self.options['penalty_descent_frac'])
if self.options['min_penalty_param']:
opt.setMinPenaltyParameter(self.options['min_penalty_param'])
if self.options['use_hvec_prod']:
opt.setUseHvecProduct(self.options['use_hvec_prod'])
if self.options['use_diag_hessian']:
opt.setUseDiagHessian(self.options['use_diag_hessian'])
if self.options['use_qn_gmres_precon']:
opt.setUseQNGMRESPreCon(self.options['use_qn_gmres_precon'])
if self.options['set_nk_switch_tol']:
opt.setNKSwitchTolerance(self.options['set_nk_switch_tol'])
if self.options['eisenstat_walker_param']:
opt.setEisenstatWalkerParameters(
self.options['eisenstat_walker_param'][0],
self.options['eisenstat_walker_param'][1])
if self.options['gmres_tol']:
opt.setGMRESTolerances(self.options['gmres_tol'][0],
self.options['gmres_tol'][1])
if self.options['gmres_subspace_size']:
opt.setGMRESSubspaceSize(self.options['gmres_subspace_size'])
if self.options['output_freq']:
opt.setOutputFrequency(self.options['output_freq'])
if self.options['output_file']:
opt.setOutputFile(self.options['output_file'])
if self.options['major_iter_step_check']:
opt.setMajorIterStepCheck(self.options['major_iter_step_check'])
if self.options['output_level']:
opt.setOutputLevel(self.options['output_level'])
if self.options['grad_check_freq']:
opt.setGradCheckFrequency(self.options['grad_check_freq'])
# This opt object will be used again when 'run' is executed
self.opt = opt
return