Note
This feature requires MPI, and may not be able to be run on Colab.
Adding Constraints#
To add a constraint to an optimization, use the add_constraint method on System.
- System.add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, units=None, indices=None, linear=False, parallel_deriv_color=None, cache_linear_solution=False, flat_indices=False, alias=None)[source]
Add a constraint variable to this system.
- Parameters:
- namestr
Name of the response variable in the system.
- lowerfloat or ndarray, optional
Lower boundary for the variable.
- upperfloat or ndarray, optional
Upper boundary for the variable.
- equalsfloat or ndarray, optional
Equality constraint value for the variable.
- reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
- ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
- adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
- scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
- unitsstr, optional
Units to convert to before applying scaling.
- indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.
- linearbool
Set to True if constraint is linear. Default is False.
- parallel_deriv_colorstr
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
- cache_linear_solutionbool
If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.
- flat_indicesbool
If True, interpret specified indices as being indices into a flat source array.
- aliasstr
Alias for this response. Necessary when adding multiple constraints on different indices or slices of a single variable.
Notes
The response can be scaled using ref and ref0. The argument
ref0represents the physical value when the scaled value is 0. The argumentrefrepresents the physical value when the scaled value is 1. The arguments (lower,upper,equals) can not be strings or variable names.
Specifying units#
You can specify units when adding a constraint. When this is done, the constraint value is converted from the target output’s units to the desired unit before giving it to the optimizer. If you also specify scaling, that scaling is applied after the unit conversion. Moreover, the upper and lower limits in the constraint definition should be specified using these units.
import openmdao.api as om
prob = om.Problem()
model = prob.model
model.add_subsystem('comp1', om.ExecComp('y1 = 2.0*x',
x={'val': 2.0, 'units': 'degF'},
y1={'val': 2.0, 'units': 'degF'}),
promotes=['x', 'y1'])
model.add_subsystem('comp2', om.ExecComp('y2 = 3.0*x',
x={'val': 2.0, 'units': 'degF'},
y2={'val': 2.0, 'units': 'degF'}),
promotes=['x', 'y2'])
model.set_input_defaults('x', 35.0, units='degF')
model.add_design_var('x', units='degC', lower=0.0, upper=100.0)
model.add_constraint('y1', units='degC', lower=0.0, upper=100.0)
model.add_objective('y2', units='degC')
prob.setup()
prob.run_driver()
print('Model variables')
print(prob.get_val('x', indices=[0]))
Model variables
[35.]
print(prob.get_val('comp2.y2', indices=[0]))
[105.]
print(prob.get_val('comp1.y1', indices=[0]))
[70.]
print('Driver variables')
dv = prob.driver.get_design_var_values()
print(dv['x'][0])
Driver variables
1.6666666666666983
obj = prob.driver.get_objective_values(driver_scaling=True)
print(obj['comp2.y2'][0])
40.555555555555586
con = prob.driver.get_constraint_values(driver_scaling=True)
print(con['comp1.y1'][0])
21.111111111111143
Using the output of a distributed component as a constraint#
You can use an output of a distributed component as a constraint or an objective. OpenMDAO automatically collects the values from all processors and provides them to the driver.
Here is an example where we perform optimization on a model that contains a DistParabFeature component that is distributed. The output is declared as a inequality constraint.
Show code cell outputs
[output:0]
class DistParabFeature(om.ExplicitComponent):
def initialize(self):
self.options.declare('arr_size', types=int, default=10,
desc="Size of input and output vectors.")
def setup(self):
arr_size = self.options['arr_size']
self.add_input('x', val=1., distributed=False,
shape=arr_size)
self.add_input('y', val=1., distributed=False,
shape=arr_size)
sizes, offsets = evenly_distrib_idxs(self.comm.size, arr_size)
self.start = offsets[self.comm.rank]
self.end = self.start + sizes[self.comm.rank]
self.a = -3.0 + 0.6 * np.arange(self.start,self.end)
self.add_output('f_xy', shape=len(self.a), distributed=True)
self.add_output('f_sum', shape=1, distributed=False)
self.declare_coloring(wrt='*', method='fd')
def compute(self, inputs, outputs):
x = inputs['x'][self.start:self.end]
y = inputs['y'][self.start:self.end]
outputs['f_xy'] = (x + self.a)**2 + x * y + (y + 4.0)**2 - 3.0
local_sum = np.sum(outputs['f_xy'])
global_sum = np.zeros(1)
self.comm.Allreduce(local_sum, global_sum, op=MPI.SUM)
outputs['f_sum'] = global_sum
[output:1]
class DistParabFeature(om.ExplicitComponent):
def initialize(self):
self.options.declare('arr_size', types=int, default=10,
desc="Size of input and output vectors.")
def setup(self):
arr_size = self.options['arr_size']
self.add_input('x', val=1., distributed=False,
shape=arr_size)
self.add_input('y', val=1., distributed=False,
shape=arr_size)
sizes, offsets = evenly_distrib_idxs(self.comm.size, arr_size)
self.start = offsets[self.comm.rank]
self.end = self.start + sizes[self.comm.rank]
self.a = -3.0 + 0.6 * np.arange(self.start,self.end)
self.add_output('f_xy', shape=len(self.a), distributed=True)
self.add_output('f_sum', shape=1, distributed=False)
self.declare_coloring(wrt='*', method='fd')
def compute(self, inputs, outputs):
x = inputs['x'][self.start:self.end]
y = inputs['y'][self.start:self.end]
outputs['f_xy'] = (x + self.a)**2 + x * y + (y + 4.0)**2 - 3.0
local_sum = np.sum(outputs['f_xy'])
global_sum = np.zeros(1)
self.comm.Allreduce(local_sum, global_sum, op=MPI.SUM)
outputs['f_sum'] = global_sum
[output:3]
class DistParabFeature(om.ExplicitComponent):
def initialize(self):
self.options.declare('arr_size', types=int, default=10,
desc="Size of input and output vectors.")
def setup(self):
arr_size = self.options['arr_size']
self.add_input('x', val=1., distributed=False,
shape=arr_size)
self.add_input('y', val=1., distributed=False,
shape=arr_size)
sizes, offsets = evenly_distrib_idxs(self.comm.size, arr_size)
self.start = offsets[self.comm.rank]
self.end = self.start + sizes[self.comm.rank]
self.a = -3.0 + 0.6 * np.arange(self.start,self.end)
self.add_output('f_xy', shape=len(self.a), distributed=True)
self.add_output('f_sum', shape=1, distributed=False)
self.declare_coloring(wrt='*', method='fd')
def compute(self, inputs, outputs):
x = inputs['x'][self.start:self.end]
y = inputs['y'][self.start:self.end]
outputs['f_xy'] = (x + self.a)**2 + x * y + (y + 4.0)**2 - 3.0
local_sum = np.sum(outputs['f_xy'])
global_sum = np.zeros(1)
self.comm.Allreduce(local_sum, global_sum, op=MPI.SUM)
outputs['f_sum'] = global_sum
[output:2]
class DistParabFeature(om.ExplicitComponent):
def initialize(self):
self.options.declare('arr_size', types=int, default=10,
desc="Size of input and output vectors.")
def setup(self):
arr_size = self.options['arr_size']
self.add_input('x', val=1., distributed=False,
shape=arr_size)
self.add_input('y', val=1., distributed=False,
shape=arr_size)
sizes, offsets = evenly_distrib_idxs(self.comm.size, arr_size)
self.start = offsets[self.comm.rank]
self.end = self.start + sizes[self.comm.rank]
self.a = -3.0 + 0.6 * np.arange(self.start,self.end)
self.add_output('f_xy', shape=len(self.a), distributed=True)
self.add_output('f_sum', shape=1, distributed=False)
self.declare_coloring(wrt='*', method='fd')
def compute(self, inputs, outputs):
x = inputs['x'][self.start:self.end]
y = inputs['y'][self.start:self.end]
outputs['f_xy'] = (x + self.a)**2 + x * y + (y + 4.0)**2 - 3.0
local_sum = np.sum(outputs['f_xy'])
global_sum = np.zeros(1)
self.comm.Allreduce(local_sum, global_sum, op=MPI.SUM)
outputs['f_sum'] = global_sum
%%px
import numpy as np
import openmdao.api as om
from openmdao.test_suite.components.paraboloid_distributed import DistParabFeature
size = 7
prob = om.Problem()
model = prob.model
ivc = om.IndepVarComp()
ivc.add_output('x', np.ones(size))
ivc.add_output('y', -1.42 * np.ones(size))
model.add_subsystem('p', ivc, promotes=['*'])
model.add_subsystem("parab", DistParabFeature(arr_size=size), promotes=['*'])
model.add_design_var('x', lower=-50.0, upper=50.0)
model.add_constraint('f_xy', lower=0.0)
model.add_objective('f_sum', index=-1)
prob.driver = om.pyOptSparseDriver(optimizer='SLSQP')
prob.setup()
prob.run_driver()
[stdout:0]
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.1141
User Objective Time : 0.0113
User Sensitivity Time : 0.0922
Interface Time : 0.0079
Opt Solver Time: 0.0028
Calls to Objective Function : 7
Calls to Sens Function : 7
Objectives
Index Name Value
0 parab.f_sum 1.150150E+01
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 p.x_0 c -5.000000E+01 2.657527E+00 5.000000E+01
1 p.x_1 c -5.000000E+01 2.604332E+00 5.000000E+01
2 p.x_2 c -5.000000E+01 2.510059E+00 5.000000E+01
3 p.x_3 c -5.000000E+01 1.910212E+00 5.000000E+01
4 p.x_4 c -5.000000E+01 1.310076E+00 5.000000E+01
5 p.x_5 c -5.000000E+01 7.099281E-01 5.000000E+01
6 p.x_6 c -5.000000E+01 1.097805E-01 5.000000E+01
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 parab.f_xy i 0.000000E+00 -3.108624E-15 1.000000E+30 l 9.00000E+100
1 parab.f_xy i 0.000000E+00 -1.394440E-13 1.000000E+30 l 9.00000E+100
2 parab.f_xy i 0.000000E+00 5.963000E-01 1.000000E+30 9.00000E+100
3 parab.f_xy i 0.000000E+00 1.448300E+00 1.000000E+30 9.00000E+100
4 parab.f_xy i 0.000000E+00 2.300300E+00 1.000000E+30 9.00000E+100
5 parab.f_xy i 0.000000E+00 3.152300E+00 1.000000E+30 9.00000E+100
6 parab.f_xy i 0.000000E+00 4.004300E+00 1.000000E+30 9.00000E+100
--------------------------------------------------------------------------------
[stderr:1] /usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/system.py:1739: DerivativesWarning:'parab' <class DistParabFeature>: Coloring was deactivated. Improvement of 0.0% was less than min allowed (5.0%).
Out[1:14]: False
[stderr:3] /usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/system.py:1739: DerivativesWarning:'parab' <class DistParabFeature>: Coloring was deactivated. Improvement of 0.0% was less than min allowed (5.0%).
[stderr:2] /usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/system.py:1739: DerivativesWarning:'parab' <class DistParabFeature>: Coloring was deactivated. Improvement of 0.0% was less than min allowed (5.0%).
Out[3:14]: False
Out[2:14]: False
[stderr:0] /usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/system.py:1739: DerivativesWarning:'parab' <class DistParabFeature>: Coloring was deactivated. Improvement of 0.0% was less than min allowed (5.0%).
Out[0:14]: False
%%px
desvar = prob.get_val('p.x', get_remote=True)
obj = prob.get_val('f_sum', get_remote=True)
print(desvar)
[stdout:0] [2.65752672 2.60433212 2.51005939 1.91021206 1.31007579 0.70992813
0.10978047]
[stdout:1] [2.65752672 2.60433212 2.51005939 1.91021206 1.31007579 0.70992813
0.10978047]
[stdout:2] [2.65752672 2.60433212 2.51005939 1.91021206 1.31007579 0.70992813
0.10978047]
[stdout:3] [2.65752672 2.60433212 2.51005939 1.91021206 1.31007579 0.70992813
0.10978047]
%%px
print(obj)
[stdout:0] [11.50150011]
[stdout:1] [11.50150011]
[stdout:2] [11.50150011]
[stdout:3] [11.50150011]
Adding multiple constraints on an array variable.#
Sometimes you have a variable and you would like to constrain difference parts of it in different ways. OpenMDAO maintains the constraint data in a dictionary that keys on the variable pathname, so we need to specify an additional “alias” argument when we declare any additional constraints.
In the following example, the variable “exec.z” has an equality constraint on the first point and a lower bound on the end point. We constrain them by giving the second one an alias to differentiate it from the first one.
p = om.Problem()
exec = om.ExecComp(['y = x**2',
'z = a + x**2'],
a={'shape': (1,)},
y={'shape': (101,)},
x={'shape': (101,)},
z={'shape': (101,)})
p.model.add_subsystem('exec', exec)
p.model.add_design_var('exec.a', lower=-1000, upper=1000)
p.model.add_objective('exec.y', index=50)
p.model.add_constraint('exec.z', indices=[0], equals=25)
p.model.add_constraint('exec.z', indices=[-1], lower=20, alias="End_Constraint")
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.setup()
p.set_val('exec.x', np.linspace(-10, 10, 101))
p.run_driver()
print(p.get_val('exec.z')[0], 25)
print(p.get_val('exec.z')[50], -75)
Coloring for 'exec' (class ExecComp)
Jacobian shape: (202, 102) ( 1.47% nonzero)
FWD solves: 2 REV solves: 0
Total colors vs. total size: 2 vs 102 (98.0% improvement)
Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.007517 sec.
Time to compute coloring: 0.024551 sec.
Memory to compute coloring: 0.000000 MB.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 0.0406
User Objective Time : 0.0013
User Sensitivity Time : 0.0367
Interface Time : 0.0022
Opt Solver Time: 0.0005
Calls to Objective Function : 2
Calls to Sens Function : 1
Objectives
Index Name Value
0 exec.y 0.000000E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 exec.a_0 c -1.000000E+03 -7.500000E+01 1.000000E+03
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 exec.z e 2.500000E+01 2.500000E+01 2.500000E+01 9.00000E+100
1 End_Constraint i 2.000000E+01 2.500000E+01 1.000000E+30 9.00000E+100
--------------------------------------------------------------------------------
25.0 25
-75.0 -75
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1636: DerivativesWarning:Constraints or objectives [('exec.y', inds=[50])] cannot be impacted by the design variables of the problem.