pyOptSparseDriver#
pyOptSparseDriver wraps the optimizer package pyOptSparse, which provides a common interface for 11 optimizers, some of which are included in the package (e.g., SLSQP and NSGA2), and some of which are commercial products that must be obtained from their respective authors (e.g. SNOPT). The pyOptSparse package is based on pyOpt, but adds support for sparse specification of constraint Jacobians. Most of the sparsity features are only applicable when using the SNOPT optimizer.
Note
The pyOptSparse package does not come included with the OpenMDAO installation. It is a separate optional package that can be obtained from mdolab.
In this simple example, we use the SLSQP optimizer to minimize the objective of a Sellar MDA model.
We will use a SellarMDA class to encapsulate the Sellar model with it’s design variables, objective and constraints:
SellarDis1withDerivatives class definition
class SellarDis1withDerivatives(SellarDis1):
"""
Component containing Discipline 1 -- derivatives version.
"""
def setup_partials(self):
# Analytic Derivs
self.declare_partials(of='*', wrt='*')
def compute_partials(self, inputs, partials):
"""
Jacobian for Sellar discipline 1.
"""
partials['y1', 'y2'] = -0.2
partials['y1', 'z'] = np.array([[2.0 * inputs['z'][0], 1.0]])
partials['y1', 'x'] = 1.0
SellarDis2withDerivatives class definition
class SellarDis2withDerivatives(SellarDis2):
"""
Component containing Discipline 2 -- derivatives version.
"""
def setup_partials(self):
# Analytic Derivs
self.declare_partials(of='*', wrt='*')
def compute_partials(self, inputs, J):
"""
Jacobian for Sellar discipline 2.
"""
y1 = inputs['y1']
if y1.real < 0.0:
y1 *= -1
if y1.real < 1e-8:
y1 = 1e-8
J['y2', 'y1'] = .5*y1**-.5
J['y2', 'z'] = np.array([[1.0, 1.0]])
import numpy as np
import openmdao.api as om
from openmdao.test_suite.components.sellar import SellarDis1withDerivatives, SellarDis2withDerivatives
class SellarMDA(om.Group):
"""
Group containing the Sellar MDA model.
"""
def setup(self):
# add the two disciplines in an 'mda' subgroup
self.mda = mda = self.add_subsystem('mda', om.Group(), promotes=['x', 'z', 'y1', 'y2'])
mda.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2'])
mda.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2'])
# add components to calculate objectives and constraints
self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)',
z=np.array([0.0, 0.0]), x=0.0, y1=0.0, y2=0.0),
promotes=['obj', 'x', 'z', 'y1', 'y2'])
self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1'), promotes=['con1', 'y1'])
self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0'), promotes=['con2', 'y2'])
# set default values for the inputs
self.set_input_defaults('x', 1.0)
self.set_input_defaults('z', np.array([5.0, 2.0]))
# add design vars, objective and constraints
self.add_design_var('z', lower=np.array([-10.0, 0.0]), upper=np.array([10.0, 10.0]))
self.add_design_var('x', lower=0.0, upper=10.0)
self.add_objective('obj')
self.add_constraint('con1', upper=0.0)
self.add_constraint('con2', upper=0.0)
def configure(self):
# set the solvers for the model and cycle groups
self.nonlinear_solver = om.NonlinearBlockGS()
self.linear_solver = om.ScipyKrylov()
self.mda.nonlinear_solver = om.NonlinearBlockGS()
self.mda.linear_solver = om.ScipyKrylov()
# default to non-verbose
self.set_solver_print(0)
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SLSQP')
prob.run_driver()
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0327
User Objective Time : 0.0077
User Sensitivity Time : 0.0211
Interface Time : 0.0031
Opt Solver Time: 0.0008
Calls to Objective Function : 6
Calls to Sens Function : 6
Objectives
Index Name Value
0 obj 3.183394E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 z_0 c -1.000000E+01 1.977639E+00 1.000000E+01
1 z_1 c 0.000000E+00 -4.753534E-15 1.000000E+01 l
2 x_0 c 0.000000E+00 4.439131E-15 1.000000E+01 l
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 con1 i -1.000000E+30 -8.746648E-11 0.000000E+00 u 9.00000E+100
1 con2 i -1.000000E+30 -2.024472E+01 0.000000E+00 9.00000E+100
Exit Status
Inform Description
0 Optimization terminated successfully.
--------------------------------------------------------------------------------
Problem: problem
Driver: pyOptSparseDriver
success : True
iterations : 7
runtime : 3.6656E-02 s
model_evals : 7
model_time : 6.5407E-03 s
deriv_evals : 6
deriv_time : 2.0996E-02 s
exit_status : SUCCESS
print(prob.get_val('z', indices=0))
1.9776388834877525
pyOptSparseDriver Options#
| Option | Default | Acceptable Values | Acceptable Types | Description |
|---|---|---|---|---|
| debug_print | [] | ['desvars', 'nl_cons', 'ln_cons', 'objs', 'totals'] | ['list'] | List of what type of Driver variables to print at each iteration. |
| gradient_method | openmdao | ['openmdao', 'snopt_fd', 'pyopt_fd'] | N/A | Finite difference implementation to use |
| hist_file | N/A | N/A | ['str'] | File location for saving pyopt_sparse optimization history. Default is None for no output. |
| hotstart_file | N/A | N/A | ['str'] | File location of a pyopt_sparse optimization history to use to hot start the optimization. Default is None. |
| invalid_desvar_behavior | warn | ['warn', 'raise', 'ignore'] | N/A | Behavior of driver if the initial value of a design variable exceeds its bounds. The default value may beset using the `OPENMDAO_INVALID_DESVAR_BEHAVIOR` environment variable to one of the valid options. |
| optimizer | SLSQP | ['PSQP', 'NSGA2', 'ParOpt', 'ALPSO', 'NLPQLP', 'SLSQP', 'SNOPT', 'IPOPT', 'CONMIN'] | N/A | Name of optimizers to use |
| output_dir | DEFAULT_REPORTS_DIR | N/A | ['str', '_ReprClass'] | Directory location of pyopt_sparse output files.Default is {prob_name}_out/reports. |
| print_opt_prob | False | [True, False] | ['bool'] | Print the opt problem summary before running the optimization |
| print_results | True | N/A | ['bool', 'str'] | Print pyOpt results if True |
| singular_jac_behavior | warn | ['error', 'warn', 'ignore'] | N/A | Defines behavior of a zero row/col check after first call tocompute_totals:error - raise an error.warn - raise a warning.ignore - don't perform check. |
| singular_jac_tol | 1e-16 | N/A | N/A | Tolerance for zero row/column check. |
| title | Optimization using pyOpt_sparse | N/A | N/A | Title of this optimization run |
| user_terminate_signal | N/A | N/A | N/A | OS signal that triggers a clean user-termination. Only SNOPT supports this option. |
pyOptSparseDriver Constructor#
The call signature for the pyOptSparseDriver constructor is:
- pyOptSparseDriver.__init__(**kwargs)[source]
Initialize pyopt.
Using pyOptSparseDriver#
pyOptSparseDriver has a small number of unified options that can be specified as keyword arguments when it is instantiated or by using the “options” dictionary. We have already shown how to set the optimizer option. Next we see how the print_results option can be used to turn on or off the echoing of the results when the optimization finishes. The default is True, but here, we turn it off.
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SLSQP')
prob.driver.options['print_results'] = False
prob.run_driver()
Problem: problem2
Driver: pyOptSparseDriver
success : True
iterations : 7
runtime : 3.4209E-02 s
model_evals : 7
model_time : 5.9721E-03 s
deriv_evals : 6
deriv_time : 2.0419E-02 s
exit_status : SUCCESS
print(prob.get_val('z', indices=0))
1.9776388834877525
Every optimizer also has its own specialized settings that allow you to fine-tune the algorithm that it uses. You can access these within the opt_setting dictionary. These options are different for each optimizer, so to find out what they are, you need to read your optimizer’s documentation. We present a few common ones here.
SLSQP-Specific Settings#
Here, we set a convergence tolerance for SLSQP:
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SLSQP')
prob.driver.opt_settings['ACC'] = 1e-9
prob.setup(check=False, mode='rev')
prob.run_driver()
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0314
User Objective Time : 0.0072
User Sensitivity Time : 0.0206
Interface Time : 0.0028
Opt Solver Time: 0.0007
Calls to Objective Function : 6
Calls to Sens Function : 6
Objectives
Index Name Value
0 obj 3.183394E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 z_0 c -1.000000E+01 1.977639E+00 1.000000E+01
1 z_1 c 0.000000E+00 -4.753534E-15 1.000000E+01 l
2 x_0 c 0.000000E+00 4.439131E-15 1.000000E+01 l
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 con1 i -1.000000E+30 -8.746648E-11 0.000000E+00 u 9.00000E+100
1 con2 i -1.000000E+30 -2.024472E+01 0.000000E+00 9.00000E+100
Exit Status
Inform Description
0 Optimization terminated successfully.
--------------------------------------------------------------------------------
Problem: problem3
Driver: pyOptSparseDriver
success : True
iterations : 7
runtime : 3.4806E-02 s
model_evals : 7
model_time : 6.2417E-03 s
deriv_evals : 6
deriv_time : 2.0525E-02 s
exit_status : SUCCESS
print(prob.get_val('z', indices=0))
1.9776388834877525
Similarly, we can set an iteration limit. Here, we set it to just a few iterations, and don’t quite reach the optimum.
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SLSQP')
prob.driver.opt_settings['MAXIT'] = 3
prob.run_driver()
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0213
User Objective Time : 0.0051
User Sensitivity Time : 0.0137
Interface Time : 0.0019
Opt Solver Time: 0.0005
Calls to Objective Function : 4
Calls to Sens Function : 4
Objectives
Index Name Value
0 obj 3.203561E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 z_0 c -1.000000E+01 1.983377E+00 1.000000E+01
1 z_1 c 0.000000E+00 -5.325284E-13 1.000000E+01 l
2 x_0 c 0.000000E+00 -5.051337E-15 1.000000E+01 l
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 con1 i -1.000000E+30 -2.043382E-02 0.000000E+00 9.00000E+100
1 con2 i -1.000000E+30 -2.023325E+01 0.000000E+00 9.00000E+100
Exit Status
Inform Description
9 Iteration limit exceeded
--------------------------------------------------------------------------------
Problem: problem4
Driver: pyOptSparseDriver
success : False
iterations : 5
runtime : 2.4400E-02 s
model_evals : 5
model_time : 4.2098E-03 s
deriv_evals : 4
deriv_time : 1.3645E-02 s
exit_status : FAIL
print(prob.get_val('z', indices=0))
1.9833770833092614
SNOPT-Specific Settings#
SNOPT has many customizable settings. Here we show two common ones.
Setting the convergence tolerance:
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SNOPT')
prob.driver.opt_settings['Major feasibility tolerance'] = 1e-9
prob.run_driver()
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0382
User Objective Time : 0.0088
User Sensitivity Time : 0.0243
Interface Time : 0.0034
Opt Solver Time: 0.0017
Calls to Objective Function : 8
Calls to Sens Function : 7
Objectives
Index Name Value
0 obj 3.183394E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 z_0 c -1.000000E+01 1.977639E+00 1.000000E+01
1 z_1 c 0.000000E+00 0.000000E+00 1.000000E+01 l
2 x_0 c 0.000000E+00 0.000000E+00 1.000000E+01 l
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 con1 i -1.000000E+30 -5.966339E-12 0.000000E+00 u 9.00000E+100
1 con2 i -1.000000E+30 -2.024472E+01 0.000000E+00 9.00000E+100
Exit Status
Inform Description
1 optimality conditions satisfied
--------------------------------------------------------------------------------
Problem: problem5
Driver: pyOptSparseDriver
success : True
iterations : 9
runtime : 4.2213E-02 s
model_evals : 9
model_time : 7.4391E-03 s
deriv_evals : 7
deriv_time : 2.4214E-02 s
exit_status : SUCCESS
print(prob.get_val('z', indices=0))
1.9776388834648047
Setting a limit on the number of major iterations. Here, we set it to just a few iterations, and don’t quite reach the optimum.
import openmdao.api as om
prob = om.Problem(model=SellarMDA())
prob.setup(check=False, mode='rev')
prob.driver = om.pyOptSparseDriver(optimizer='SNOPT')
prob.driver.opt_settings['Major iterations limit'] = 5
prob.run_driver()
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0330
User Objective Time : 0.0079
User Sensitivity Time : 0.0208
Interface Time : 0.0030
Opt Solver Time: 0.0014
Calls to Objective Function : 7
Calls to Sens Function : 6
Objectives
Index Name Value
0 obj 3.183402E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 z_0 c -1.000000E+01 1.977641E+00 1.000000E+01
1 z_1 c 0.000000E+00 0.000000E+00 1.000000E+01 l
2 x_0 c 0.000000E+00 0.000000E+00 1.000000E+01 l
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 con1 i -1.000000E+30 -8.621022E-06 0.000000E+00 9.00000E+100
1 con2 i -1.000000E+30 -2.024472E+01 0.000000E+00 9.00000E+100
Exit Status
Inform Description
3 requested accuracy could not be achieved
--------------------------------------------------------------------------------
Problem: problem6
Driver: pyOptSparseDriver
success : False
iterations : 8
runtime : 3.6592E-02 s
model_evals : 8
model_time : 6.7164E-03 s
deriv_evals : 6
deriv_time : 2.0698E-02 s
exit_status : FAIL
print(prob.get_val('z', indices=0))
1.9776413083133966
If you have pyoptsparse 1.1 or greater, then you can send a signal such as SIGUSR1 to a running SNOPT optimization to tell it to terminate cleanly. This is useful if an optimization has gotten close enough to an optimum. How to do this is dependent on your operating system in all cases, on your mpi implementation if you are running mpi, and on your queuing software if you are on a supercomputing cluster. Here is a simple example for unix and mpi.
ktmoore1$ ps -ef |grep sig
502 17955 951 0 4:05PM ttys000 0:00.02 mpirun -n 2 python sig_demo.py
502 17956 17955 0 4:05PM ttys000 0:00.03 python sig_demo.py
502 17957 17955 0 4:05PM ttys000 0:00.03 python sig_demo.py
502 17959 17312 0 4:05PM ttys001 0:00.00 grep sig
ktmoore1$ kill -SIGUSR1 17955
You can enable this feature by setting the “user_terminate_signal” option and giving it a signal (imported from the signal library in Python). By default, user_terminate_signal is None, which disables the feature. Here, we set the signal to SIGUSR1:
import openmdao.api as om
import signal
prob = om.Problem()
prob.driver = om.pyOptSparseDriver()
prob.driver.options['optimizer'] = "SNOPT"
prob.driver.options['user_terminate_signal'] = signal.SIGUSR1
You can learn more about the available options in the SNOPT_Manual.