Setting up an Optimization Problem

The final step is to create a top level Assembly that defines the problem using DrivingSim and the vehicle assembly.

The first problem we would like to solve is a single-objective optimization problem where we adjust some of the design variables to minimize the 0-60 acceleration time. The chosen design variables are the bore and spark angle. The optimal value of the first variable should be quite intuitive (i.e., larger bore means faster acceleration), but the second variable cannot be optimized by mere inspection.

The optimization will be handled by the gradient optimizer CONMIN.

To tackle this problem, let’s take a look at the iteration hierarchy.

Iteration Hierarchy for Vehicle Design Optimization

This time, our top level driver is the CONMIN optimizer. Its workflow contains the three simulations. Note that there is very little difference between this iteration hierarchy and the one we just built, so it should be pretty easy to change the code.

In engine_optimization.py, we define the class EngineOptimization and create an instance of CONMINdriver and DrivingSim, which are added to the driver’s workflow. We also create a Vehicle instance and insert it into the socket in DrivingSim:

from openmdao.main.api import Assembly
from openmdao.lib.drivers.api import CONMINdriver

from openmdao.examples.enginedesign.driving_sim import SimAcceleration, SimEconomy
from openmdao.examples.enginedesign.vehicle import Vehicle

class EngineOptimization(Assembly):
    """Optimization of a Vehicle."""

    def configure(self):
        """ Creates a new Assembly for vehicle performance optimization."""

        # pylint: disable-msg=E1101

        # Create CONMIN Optimizer instance
        self.add('driver', CONMINdriver())

        # Create Vehicle instance
        self.add('vehicle', Vehicle())

        # Create Driving Simulation instances
        self.add('sim_acc', SimAcceleration())
        self.add('sim_EPA_city', SimEconomy())
        self.add('sim_EPA_highway', SimEconomy())

        # add Sims to optimizer workflow
        self.driver.workflow.add(['sim_acc', 'sim_EPA_city', 'sim_EPA_highway'])

        # Add vehicle to sim workflows.
        self.sim_acc.workflow.add('vehicle')
        self.sim_EPA_city.workflow.add('vehicle')
        self.sim_EPA_highway.workflow.add('vehicle')

        # CONMIN Flags
        self.driver.iprint = 0
        self.driver.itmax = 30

        # CONMIN Objective
        self.driver.add_objective('sim_acc.accel_time')

        # CONMIN Design Variables
        self.driver.add_parameter('vehicle.spark_angle', -50., 10.)
        self.driver.add_parameter('vehicle.bore', 65., 100.)

        # Acceleration Sim setup
        self.sim_acc.add_parameter('vehicle.velocity', name='velocity',
                                   low=0.0, high=150.0)
        self.sim_acc.add_parameter('vehicle.throttle', name='throttle',
                                   low=0.01, high=1.0)
        self.sim_acc.add_parameter('vehicle.current_gear', name='gear',
                                   low=0, high=5)
        self.sim_acc.add_objective('vehicle.acceleration', name='acceleration')
        self.sim_acc.add_objective('vehicle.overspeed', name='overspeed')

        # EPA City MPG Sim Setup
        self.sim_EPA_city.add_parameter('vehicle.velocity', name='velocity',
                                        low=0.0, high=150.0)
        self.sim_EPA_city.add_parameter('vehicle.throttle', name='throttle',
                                        low=0.01, high=1.0)
        self.sim_EPA_city.add_parameter('vehicle.current_gear', name='gear',
                                        low=0, high=5)
        self.sim_EPA_city.add_objective('vehicle.acceleration', name='acceleration')
        self.sim_EPA_city.add_objective('vehicle.fuel_burn', name='fuel_burn')
        self.sim_EPA_city.add_objective('vehicle.overspeed', name='overspeed')
        self.sim_EPA_city.add_objective('vehicle.underspeed', name='underspeed')
        self.sim_EPA_city.profilename = 'EPA-city.csv'

        # EPA Highway MPG Sim Setup
        self.sim_EPA_highway.add_parameter('vehicle.velocity', name='velocity',
                                           low=0.0, high=150)
        self.sim_EPA_highway.add_parameter('vehicle.throttle', name='throttle',
                                           low=0.01, high=1.0)
        self.sim_EPA_highway.add_parameter('vehicle.current_gear', name='gear',
                                           low=0, high=5)
        self.sim_EPA_highway.add_objective('vehicle.acceleration', name='acceleration')
        self.sim_EPA_highway.add_objective('vehicle.fuel_burn', name='fuel_burn')
        self.sim_EPA_highway.add_objective('vehicle.overspeed', name='overspeed')
        self.sim_EPA_highway.add_objective('vehicle.underspeed', name='underspeed')
        self.sim_EPA_highway.profilename = 'EPA-highway.csv'

if __name__ == "__main__":

    def prz(title):
        """ Print before and after"""

        print '---------------------------------'
        print title
        print '---------------------------------'
        print 'Engine: Bore = ', opt_problem.vehicle.bore
        print 'Engine: Spark Angle = ', opt_problem.vehicle.spark_angle
        print '---------------------------------'
        print '0-60 Accel Time = ', opt_problem.sim_acc.accel_time
        print 'EPA City MPG = ', opt_problem.sim_EPA_city.fuel_economy
        print 'EPA Highway MPG = ', opt_problem.sim_EPA_highway.fuel_economy
        print '\n'

    import time

    opt_problem = EngineOptimization()

    opt_problem.sim_acc.run()
    opt_problem.sim_EPA_city.run()
    opt_problem.sim_EPA_highway.run()
    prz('Old Design')

    tt = time.time()
    opt_problem.run()
    prz('New Design')
    print "CONMIN Iterations: ", opt_problem.driver.iter_count
    print ""
    print "Elapsed time: ", time.time()-tt

Recall that the iprint flag enables or disables the printing of diagnostics internal to CONMIN, while the itmax parameter specifies the maximum number of iterations for the optimization loop.

The optimization objective is to minimize the 0-60 mph acceleration time by adjusting the design variables bore and spark angle. In the previous examples, we learned to use strings to build mathematical expressions with variables that point to locations in the data hierarchy, so here we do it once again with our objectives and design variables. The information we need for each variable is the expression that points to it (e.g., vehicle.spark_angle), and the minimum and maximum value of the search range for that variable (e.g., -.50, 10). Once again, if the min and max aren’t specified, the low and high attributes from the OpenMDAO variable will be used if they have been specified.

We are now ready to solve an optimization problem.