'TypeError' while using NSGA2 to solve Multi-objective prob. from pyopt-sparse in OpenMDAO 1.x
Question: I am trying to solve a multi-objective optimization problem using openMDAO's
pyopt-sparse driver with NSGA2 algorithm. Following is the code:

    
    
    from __future__ import print_function
    from openmdao.api import IndepVarComp, Component, Problem, Group, pyOptSparseDriver
    
    class Circ2(Component):
    
        def __init__(self):
            super(Circ2, self).__init__()
    
            self.add_param('x', val=10.0)
            self.add_param('y', val=10.0)
    
            self.add_output('f1', val=40.0)
            self.add_output('f2', val=40.0)
    
        def solve_nonlinear(self, params, unknowns, resids):
    
            x = params['x']
            y = params['y']
    
            unknowns['f1'] = (x - 0.0)**2 + (y - 0.0)**2
            unknowns['f2'] = (x - 1.0)**2 + (y - 1.0)**2
    
        def linearize(self, params, unknowns, resids):
    
            J = {}
            x = params['x']
            y = params['y']
    
            J['f1', 'x'] = 2*x
            J['f1', 'y'] = 2*y
            J['f2', 'x'] = 2*x-2
            J['f2', 'y'] = 2*y-2
            return J
    
    
    if __name__ == "__main__":
    
        # Defining Problem & Root
        top = Problem()
        root = top.root = Group()
    
        # Adding in-present variable values and model
        startVal = 50.0
        root.add('p1', IndepVarComp('x', startVal))
        root.add('p2', IndepVarComp('y', startVal))
    
        root.add('p', Circ2())
    
        # Making Connections
        root.connect('p1.x', 'p.x')
        root.connect('p2.y', 'p.y')
    
        # Configuring Driver
        top.driver = pyOptSparseDriver()
        top.driver.options['optimizer'] = 'NSGA2'
    
        # Setting bounds for the optimizer
        top.driver.add_desvar('p1.x', lower=-600, upper=600)
        top.driver.add_desvar('p2.y', lower=-600, upper=600)
    
        # Setting Objective Function(s)
        top.driver.add_objective('p.f1')
        top.driver.add_objective('p.f2')
    
        # # Setting up constraints
        # top.driver.add_constraint('con.c', lower=1.0)
    
        top.setup()
        top.run()
    

and I am getting the following error -

    
    
    Traceback (most recent call last):
      File "/home/prasad/DivyaManglam/Python Scripts/Pareto Testing/Basic_Sphere.py", line 89, in <module>
        top.run()
      File "/usr/local/lib/python2.7/dist-packages/openmdao/core/problem.py", line 1038, in run
        self.driver.run(self)
      File "/usr/local/lib/python2.7/dist-packages/openmdao/drivers/pyoptsparse_driver.py", line 280, in run
        sol = opt(opt_prob, sens=self._gradfunc, storeHistory=self.hist_file)
      File "/usr/local/lib/python2.7/dist-packages/pyoptsparse/pyNSGA2/pyNSGA2.py", line 193, in __call__
        self.optProb.comm.bcast(-1, root=0)
      File "MPI/Comm.pyx", line 1276, in mpi4py.MPI.Comm.bcast (src/mpi4py.MPI.c:108819)
      File "MPI/msgpickle.pxi", line 620, in mpi4py.MPI.PyMPI_bcast (src/mpi4py.MPI.c:47164)
      File "MPI/msgpickle.pxi", line 143, in mpi4py.MPI.Pickle.load (src/mpi4py.MPI.c:41248)
    TypeError: only length-1 arrays can be converted to Python scalars
    

Kindly tell if you can make anything of the above error and how to fix it.

Also, in what form would the output of the multi-objective problem's solution
be returned. I intend to generate a pareto-optimal front for this. Thank you
all.


Answer: It turns out this is not an OpenMDAO bug, but rather a bug in the Pyopt sparse
wrapper for NSGA2. The fix wasn't terrible, and I've submitted a [pull
request](https://bitbucket.org/mdolab/pyoptsparse/pull-requests/26/fixed-an-
mpi-related-bug-in-nsga2-wrapper/diff) to the pyoptsparse repo for it. In the
meantime it would be easy enough to patch your local copy of pyoptsparse.

You asked how the results will be reported. The current NSGA2 wrapper doesn't
do anything with the results. It just lets NSGA2 write them all out to a
series of text files such as `nsga2_best_pop.out` that look like this:

    
    
    # This file contains the data of final feasible population (if found)
    # of objectives = 1, # of constraints = 0, # of real_var = 2, # of bits of bin_var = 0, constr_violation, rank, crowding_distance
    -1.000000e+00   3.190310e+01    -2.413640e+02   0.000000e+00    1       1.000000e+14
    -1.000000e+00   -5.309160e+02   2.449727e+02    0.000000e+00    1       0.000000e+00
    -1.000000e+00   -3.995119e+02   -1.829071e+02   0.000000e+00    1       0.000000e+00
    

As a side note, in your example, you implemented a linearize method for the
component in your example. That method is used when you need to compute
gradients, but NSGA2 is a gradient free optimizer and won't use it at all. So
unless you're also planning to test out some gradient based methods you can
leave that method out of your components.

