multi level - How to use nested problems in OpenMDAO 1.x?

Question

I am trying to implement Collaborative Optimization & other multi-level architectures on OpenMDAO. I read here that this can be done by defining a separate solve_nonlinear method in the Subclass of Problem.

The issue is that while running the problem instance the defined solve_linear is not being called. Here is the code -

from __future__ import print_function, division
import numpy as np
import time

from openmdao.api import Component,Group, IndepVarComp, ExecComp,
    Problem, ScipyOptimizer, NLGaussSeidel, ScipyGMRES


class SellarDis1(Component):
    """Component containing Discipline 1."""

    def __init__(self):
        super(SellarDis1, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('x', val=0.0)
        self.add_param('y2', val=1.0)

        self.add_output('y1', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):
        y1 = z1**2 + z2 + x1 - 0.2*y2"""

        z1 = params['z'][0]
        z2 = params['z'][1]
        x1 = params['x']
        y2 = params['y2']

        unknowns['y1'] = z1**2 + z2 + x1 - 0.2*y2

    def linearize(self, params, unknowns, resids):
        J = {}

        J['y1','y2'] = -0.2
        J['y1','z'] = np.array([[2*params['z'][0], 1.0]])
        J['y1','x'] = 1.0

        return J

class SellarDis2(Component):

    def __init__(self):
        super(SellarDis2, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('y1', val=1.0)

        self.add_output('y2', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):

        z1 = params['z'][0]
        z2 = params['z'][1]
        y1 = params['y1']
        y1 = abs(y1)

        unknowns['y2'] = y1**.5 + z1 + z2

    def linearize(self, params, unknowns, resids):
        J = {}

        J['y2', 'y1'] = 0.5*params['y1']**-0.5
        J['y2', 'z'] = np.array([[1.0, 1.0]])

        return J

class Sellar(Group):

    def __init__(self):
        super(Sellar, self).__init__()

        self.add('px', IndepVarComp('x', 1.0), promotes=['*'])
        self.add('pz', IndepVarComp('z', np.array([5.0,2.0])), promotes=['*'])

        self.add('d1', SellarDis1(), promotes=['*'])
        self.add('d2', SellarDis2(), promotes=['*'])

        self.add('obj_cmp', 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=['*'])

        self.add('con_cmp1', ExecComp('con1 = 3.16 - y1'), promotes=['*'])
        self.add('con_cmp2', ExecComp('con2 = y2 - 24.0'), promotes=['*'])

        self.nl_solver = NLGaussSeidel()
        self.nl_solver.options['atol'] = 1.0e-12

        self.ln_solver = ScipyGMRES()

    def solve_nonlinear(self, params=None, unknowns=None, resids=None, metadata=None):

        print("Group's solve_nonlinear was called!!")
        # Discipline Optimizer would be called here?
        super(Sellar, self).solve_nonlinear(params, unknowns, resids)


class ModifiedProblem(Problem):

    def solve_nonlinear(self, params, unknowns, resids):

        print("Problem's solve_nonlinear was called!!")
        # or here ?
        super(ModifiedProblem, self).solve_nonlinear()


top = ModifiedProblem()
top.root = Sellar()

top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'

top.driver.add_desvar('z', lower=np.array([-10.0, 0.0]),
                     upper=np.array([10.0, 10.0]))
top.driver.add_desvar('x', lower=0., upper=10.0)
top.driver.add_objective('obj')
top.driver.add_constraint('con1', upper=0.0)
top.driver.add_constraint('con2', upper=0.0)


top.setup(check=False)
top.run()

The output of above code is -

Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Group's solve_nonlinear was called!!
Optimization terminated successfully.    (Exit mode 0)
            Current function value: [ 3.18339395]
            Iterations: 6
            Function evaluations: 6
            Gradient evaluations: 6
Optimization Complete
-----------------------------------

which means that the solve_nonlinear defined in subclass of Problem isn't called at any time. So, should I call the discipline optimizers in Group's Subclass?

Also, how do I pass the target variables between the two optimization problems (System & Disciplines), specially returning the optimized global variables from individual disciplines back to the system optimizer.

Thanks to all.

Answer 1

You are right that solve_nonlinear on Problem is never called, because Problem is not an OpenMDAO component and doesn't have a solve_nonlinear method. What you want to do in order to run a submodel problem inside another problem is to encapsulate it in a Component instance. It would look something like this:

class SubOptimization(Component)

    def __init__(self):
        super(SubOptimization, self).__init__()

        # Inputs to this subprob
        self.add_param('z', val=np.zeros(2))
        self.add_param('x', val=0.0)
        self.add_param('y2', val=1.0)

        # Unknowns for this sub prob
        self.add_output('y1', val=1.0)

        self.problem = prob = Problem()
        prob.root = Group()
        prob.add('px', IndepVarComp('x', 1.0), promotes=['*'])
        prob.add('d1', SellarDis1(), promotes=['*'])

        # TODO - add cons/objs for sub prob

        prob.driver = ScipyOptimizer()
        prob.driver.options['optimizer'] = 'SLSQP'

        prob.driver.add_desvar('x', lower=0., upper=10.0)
        prob.driver.add_objective('obj')
        prob.driver.add_constraint('con1', upper=0.0)
        prob.driver.add_constraint('con2', upper=0.0)

        prob.setup()

        # Must finite difference across optimizer
        self.fd_options['force_fd'] = True

    def solve_nonlinear(self, params, unknowns, resids):

        prob = self.problem

        # Pass values into our problem
        prob['x'] = params['x']
        prob['z'] = params['z']
        prob['y2'] = params['y2']

        # Run problem
        prob.run()

        # Pull values from problem
        unknowns['y1'] = prob['y1']

You can place this component into your main Problem (along with one for discipline 2, though 2 doesn't really need a sub-optimization since it has no local design variabes) and optimize the global design variable around it.

One caveat: this isn't something I have tried (nor have I tested the incomplete code snippet above), but it should get you on the right track. It's possible you may encounter a bug since this isn't really tested much. When I get some time, I will put together a CO test like this for the OpenMDAO tests so that we are safe.