Quickstart

The following shows how to get started with pyOptSparse by solving Schittkowski’s TP37 constrained problem. First, we show the complete program listing and then go through each statement line by line:

# First party modules
from pyoptsparse import SLSQP, Optimization


# rst begin objfunc
def objfunc(xdict):
    x = xdict["xvars"]
    funcs = {}
    funcs["obj"] = -x[0] * x[1] * x[2]
    conval = [0] * 2
    conval[0] = x[0] + 2.0 * x[1] + 2.0 * x[2] - 72.0
    conval[1] = -x[0] - 2.0 * x[1] - 2.0 * x[2]
    funcs["con"] = conval
    fail = False

    return funcs, fail


# rst begin optProb
# Optimization Object
optProb = Optimization("TP037 Constraint Problem", objfunc)

# rst begin addVar
# Design Variables
optProb.addVarGroup("xvars", 3, "c", lower=[0, 0, 0], upper=[42, 42, 42], value=10)

# rst begin addCon
# Constraints
optProb.addConGroup("con", 2, lower=None, upper=0.0)

# rst begin addObj
# Objective
optProb.addObj("obj")

# rst begin print
# Check optimization problem
print(optProb)

# rst begin OPT
# Optimizer
optOptions = {"IPRINT": -1}
opt = SLSQP(options=optOptions)

# rst begin solve
# Solve
sol = opt(optProb, sens="FD")

# rst begin check
# Check Solution
print(sol)

Start by importing the pyOptSparse package:

# First party modules
from pyoptsparse import SLSQP, Optimization


Next we define the objective function that takes in the design variable dictionary and returns a dictionary containing the constraints and objective, as well as a (boolean) flag indicating if the objective function evaluation was successful. For the TP37, the objective function is a simple analytic function:

def objfunc(xdict):
    x = xdict["xvars"]
    funcs = {}
    funcs["obj"] = -x[0] * x[1] * x[2]
    conval = [0] * 2
    conval[0] = x[0] + 2.0 * x[1] + 2.0 * x[2] - 72.0
    conval[1] = -x[0] - 2.0 * x[1] - 2.0 * x[2]
    funcs["con"] = conval
    fail = False

    return funcs, fail


Notes:

  • The xdict variable is a dictionary whose keys are the names from each addVar and addVarGroup call. The line:

    x = xdict['xvars']
    

    retrieves an array of length 3 which are all the variables for this optimization.

  • The line:

    conval = [0]*2
    

    creates a list of length 2, which stores the numerical values of the two constraints. The funcs dictionary return must contain keys that match the constraint names from addCon and addConGroup as well as the objectives from addObj calls. This is done in the following calls:

    funcs['obj'] = -x[0]*x[1]*x[2]
    funcs['con'] = conval
    

Now the optimization problem can be initialized:

# Optimization Object
optProb = Optimization("TP037 Constraint Problem", objfunc)

This creates an instance of the optimization class with a name and a reference to the objective function. To complete the setup of the optimization problem, the design variables and constraints need to be defined.

Design variables and constraints can be added either one-by-one or as a group. Adding variables by group is generally recommended for related variables:

# Design Variables
optProb.addVarGroup("xvars", 3, "c", lower=[0, 0, 0], upper=[42, 42, 42], value=10)

This calls adds a group of 3 variables with name xvars. The variable bounds (side constraints) are 0 for the lower bounds, and 42 for the upper bounds. The initial values for each variable is 10.0.

Now, we must add the constraints. Like design variables, these may be added individually or by group. It is recommended that related constraints are added by group where possible:

# Constraints
optProb.addConGroup("con", 2, lower=None, upper=0.0)

This call adds two variables with name con. There is no lower bound for the variables and the upper bound is 0.0.

We must also assign the the key value for the objective using the addObj call:

# Objective
optProb.addObj("obj")

The optimization problem can be printed to verify that it is set up correctly:

# Check optimization problem
print(optProb)

which produces the following table:

Optimization Problem -- TP037 Constraint Problem
================================================================================
   Objective Function: objfunc


   Objectives
      Index  Name            Value
         0  obj     0.000000E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name      Type      Lower Bound            Value      Upper Bound     Status
         0  xvars_0      c     0.000000E+00     1.000000E+01     4.200000E+01
         1  xvars_1      c     0.000000E+00     1.000000E+01     4.200000E+01
         2  xvars_2      c     0.000000E+00     1.000000E+01     4.200000E+01

   Constraints (i - inequality, e - equality)
      Index  Name Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
         0  con    i  -1.000000E+20    0.000000E+00    0.000000E+00         u    9.00000E+100
         1  con    i  -1.000000E+20    0.000000E+00    0.000000E+00         u    9.00000E+100

To solve an optimization problem with pyOptSparse an optimizer must be initialized. The initialization of one or more optimizers is independent of the initialization of the optimization problem. To initialize SLSQP, which is an open-source, sequential least squares programming algorithm that comes as part of the pyOptSparse package, use:

# Optimizer
optOptions = {"IPRINT": -1}
opt = SLSQP(options=optOptions)

This initializes an instance of SLSQP with the option IPRINT set to -1. All other options will be set to the default values, which can be found on the optimizer-specific pages. For example, the default options for SLSQP can be found in the page SLSQP.

Now TP37 can be solved using pyOptSparse’s automatic finite difference for the gradients:

# Solve
sol = opt(optProb, sens="FD")

We can print the solution objection to view the result of the optimization:

# Check Solution
print(sol)

which produces the following output:

Optimization Problem -- TP037 Constraint Problem
================================================================================
   Objective Function: objfunc

   Solution:
--------------------------------------------------------------------------------
   Total Time:                    0.0062
      User Objective Time :       0.0001
      User Sensitivity Time :     0.0011
      Interface Time :            0.0046
      Opt Solver Time:            0.0003
   Calls to Objective Function :      22
   Calls to Sens Function :            8


   Objectives
      Index  Name            Value
         0  obj    -3.456000E+03

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name      Type      Lower Bound            Value      Upper Bound     Status
         0  xvars_0      c     0.000000E+00     2.399997E+01     4.200000E+01
         1  xvars_1      c     0.000000E+00     1.200001E+01     4.200000E+01
         2  xvars_2      c     0.000000E+00     1.200000E+01     4.200000E+01

   Constraints (i - inequality, e - equality)
      Index  Name Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
         0  con    i  -1.000000E+20    7.564591E-07    0.000000E+00         u    9.00000E+100
         1  con    i  -1.000000E+20   -7.200000E+01    0.000000E+00              9.00000E+100