Setting Up Problems for Automatic ArchitecturesΒΆ

In all the previous examples, first you defined an assembly and then added the Discipline 1 and Discipline 2 components to that assembly. You also added at least one driver (e.g., optimizer) to the assembly. This let you set up a specific version of the Sellar Problem that matched up with the structure for solving a problem using IDF, MDF, or CO. Each example had a different set of optimizers, parameters, constraints, and objectives.

In OpenMDAO you can automatically configure the Sellar Problem to be solved with IDF, MDF, or CO. Using this automatic formulation will result in a lot less effort on your part. But, before you can use the automatic architectures, you need to make a small change to how you define the Sellar Problem. You need to create a more general description of the Sellar Problem that is independent of how you would solve it with any given architecture.

In OpenMDAO you do this with a special kind of assembly called an ArchitectureAssembly. When you define your ArchitectureAssembly, in addition to adding the specific discipline analyses, you also specify the parameters, objectives, constraints, and coupling variables of the fundamental problem formulation. For example:

from openmdao.main.api import ArchitectureAssembly
from openmdao.lib.optproblems.sellar import Discipline1, Discipline2

class SellarProblem(ArchitectureAssembly):
    """ Sellar test problem definition.
    Creates a new Assembly with this problem

    Optimal Design at (1.9776, 0, 0)
    Optimal Objective = 3.18339"""

    def configure(self):
        #add the discipline components to the assembly
        self.add('dis1', Discipline1())
        self.add('dis2', Discipline2())

        #START OF MDAO Problem Definition
        #Global Des Vars
        self.add_parameter(("dis1.z1","dis2.z1"), name="z1", low=-10, high=10, start=5.0)
        self.add_parameter(("dis1.z2","dis2.z2"), name="z2", low=0, high=10, start=2.0)

        #Local Des Vars
        self.add_parameter("dis1.x1", low=0, high=10, start=1.0)

        #Coupling Vars
        self.add_coupling_var(("dis2.y1","dis1.y1"), name="y1", start=1.0)
        self.add_coupling_var(("dis1.y2","dis2.y2"), name="y2", start=1.0)

        self.add_objective('(dis1.x1)**2 + dis1.z2 + dis1.y1 + math.exp(-dis2.y2)', name="obj1")
        self.add_constraint('3.16 < dis1.y1')
        self.add_constraint('dis2.y2 < 24.0')


        #END OF Sellar Problem Definition

The first part of this file imports the same discipline analyses used for the IDF, MDF, and CO tutorials. Next you define the SellarProblem class, and add the discipline analyses to it.

from openmdao.main.api import ArchitectureAssembly
from openmdao.lib.optproblems.api import Discipline1, Discipline2

class SellarProblem(ArchitectureAssembly):
    """ Sellar test problem definition.
    Creates a new Assembly with this problem

    Optimal Design at (1.9776, 0, 0)
    Optimal Objective = 3.18339"""

    def configure(self):
        #add the discipline components to the assembly
        self.add('dis1', Discipline1())
        self.add('dis2', Discipline2())

Once you have the components added to the assembly, you can start specifying the problem formulation. Beside the analysis codes themselves, any problem definition will consist of the following five things:

  1. Global design values
  2. Local design values
  3. Objective(s)
  4. Coupling variable pairs
  5. Constraints

For the Sellar Problem, the problem formulation is specified as follows:

#START OF MDAO Problem Definition
#Global Des Vars
self.add_parameter(("dis1.z1","dis2.z1"), name="z1", low=-10, high=10, start=5.0)
self.add_parameter(("dis1.z2","dis2.z2"), name="z2", low=0, high=10, start=2.0)

#Local Des Vars
self.add_parameter("dis1.x1", low=0, high=10, start=1.0)

#Coupling Vars
#you can give simpler names to the global vars
self.add_coupling_var(("dis2.y1","dis1.y1"), name="y1", start=1.0)
self.add_coupling_var(("dis1.y2","dis2.y2"), name="y2", start=1.0)

#you can also give names to objectives
self.add_objective('(dis1.x1)**2 + dis1.z2 + dis1.y1 + math.exp(-dis2.y2)', name="obj1")
self.add_constraint('3.16 < dis1.y1')
self.add_constraint('dis2.y2 < 24.0')

Notice that nowhere in the problem formulation is there any information about optimizers, solvers, or any other drivers and their associated workflows. A good way to think about it is that the problem formulation contains all of the information that you actually care about to solve the problem. The specifics of what happens when you try to solve it with a given architecture are a secondary concern and don’t show up in your problem definition. Any problem that you want to solve using one of the automatic architectures has to be defined in the manner we showed you above.

In the OpenMDAO standard library, we have a number of optimization test problems defined for you to try out. These are located in the openmdao.lib.optproblems section of the library.

So once you have defined your problem, you can solve it using any of the architectures in the OpenMDAO standard library (or you can define your own architecture to test out). We currently have five architectures implemented:

  1. IDF
  2. MDF
  3. CO
  4. BLISS
  5. BLISS-2000

All instances of ArchitectureAssembly have a slot called architecture that lets you configure a specific MDAO architecture. This is how you configure a specific architecture. To test this out yourself, add the following code to the bottom of the file where you defined the SellarProblem class from above:

if __name__=="__main__":

    from openmdao.lib.architectures.api import IDF, MDF, CO, BLISS, BLISS2000

    def display_results():
        print "Minimum found at (%f, %f, %f)" % (problem.dis1.z1,
                                        problem.dis1.z2,
                                        problem.dis1.x1)
        print "Couping vars: %f, %f" % (problem.dis1.y1, problem.dis2.y2)
        print "Function calls dis1: %d, dis2: %d"%(problem.dis1.exec_count,problem.dis2.exec_count)
        print "\n"

    print "Running SellarProblem with IDF"
    problem = SellarProblem()
    problem.architecture = IDF()
    problem.run()

    display_results()

    print "Running SellarProblem with MDF"
    problem = SellarProblem()
    problem.architecture = MDF()
    problem.run()

    display_results()

    print "Running SellarProblem with CO"
    problem = SellarProblem()
    problem.architecture = CO()
    problem.run()

    display_results()

    print "Running SellarProblem with BLISS"
    problem = SellarProblem()
    problem.architecture = BLISS()
    problem.run()

    display_results()

    print "Running SellarProblem with BLISS2000"
    problem = SellarProblem()
    problem.architecture = BLISS2000()
    problem.run()

    display_results()

If you run that file, you should get results something like the following. The function counts for the results with BLISS2000 may not match exactly. BLISS2000 uses a stochastic process in part of its optimization process, so if you run the optimization a few times, you will see the function counts vary a bit.

Running SellarProblem with IDF
Minimum found at (1.977707, 0.000000, 0.000000)
Couping vars: 3.160000, 3.755627
Function calls dis1: 60, dis2: 54


Running SellarProblem with MDF
Minimum found at (1.977639, 0.000000, -0.000001)
Couping vars: 3.159999, 3.755278
Function calls dis1: 227, dis2: 222


Running SellarProblem with CO
Minimum found at (1.980130, 0.000000, 0.000707)
Couping vars: 3.160001, 3.790079
Function calls dis1: 8022, dis2: 9469


Running SellarProblem with BLISS
Minimum found at (1.981348, 0.000001, -0.000007)
Couping vars: 3.173192, 3.762692
Function calls dis1: 3808, dis2: 3649


Running SellarProblem with BLISS2000
Minimum found at (1.955188, 0.000000, 0.079449)
Couping vars: 3.160000, 3.730012
Function calls dis1: 1176, dis2: 165
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