Tutorial

The following shows how to get started with pyOpt by solving Schittkowski’s TP37 constrained problem.

Start by importing the pyOpt package:

>>> import pyOpt

Setting up an Optimization Problem

The optimization class in pyOpt requires an objective function that takes in the design variable list or array and returns the objective function value, a list/array of constraints and a flag indicating if the objective function evaluation was successful. For the TP37, the objective function is a simple analytic function:

def objfunc(x):

  f = -x[0]*x[1]*x[2]
  g = [0.0]*2
  g[0] = x[0] + 2.*x[1] + 2.*x[2] - 72.0
  g[1] = -x[0] - 2.*x[1] - 2.*x[2]

  fail = 0
  return f,g, fail

Now the optimization problem can be initialized:

>>> opt_prob = pyOpt.Optimization('TP37 Constrained Problem',objfunc)

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

>>> opt_prob.addObj('f')

Design variables and constraints can be added either one-by-one or as a group:

>>> opt_prob.addVar('x1','c',lower=0.0,upper=42.0,value=10.0)
>>> opt_prob.addVar('x2','c',lower=0.0,upper=42.0,value=10.0)
>>> opt_prob.addVar('x3','c',lower=0.0,upper=42.0,value=10.0)
>>> opt_prob.addConGroup('g',2,'i')

In the case of constraints, all equality constraints must be added before adding inequality constraints.

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

>>> print opt_prob

Optimization Problem -- TP37 Constrained Problem
================================================================================

Objective Function: objfunc

Objectives:
    Name        Value        Optimum
    f            0             0

Variables (c - continuous, i - integer, d - discrete):
    Name    Type       Value       Lower Bound  Upper Bound
    x1       c       10.000000      0.00e+00     4.20e+01
    x2       c       10.000000      0.00e+00     4.20e+01
    x3       c       10.000000      0.00e+00     4.20e+01

Constraints (i - inequality, e - equality):
    Name    Type                    Bounds
    g1       i        -1.00e+21 <= 0.000000 <= 0.00e+00
    g2       i        -1.00e+21 <= 0.000000 <= 0.00e+00

Solving an Optimization Problem

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

>>> slsqp = pyOpt.SLSQP()

This initializes an instance of SLSQP with the default options. The setOption method can be used to change any optimizer specific option, for example the internal output flag of SLSQP:

>>> slsqp.setOption('IPRINT', -1)

The different optimizers and their specific options can be seen in Optimizers .

Now TP37 can be solved using SLSQP and for example, pyOpt’s automatic finite difference for the gradients:

>>> [fstr, xstr, inform] = slsqp(opt_prob,sens_type='FD')

By default, the solution information of an optimizer is also stored in the specific optimization problem. To output solution to the screen one can use:

>>> print opt_prob.solution(0)

SLSQP Solution to TP37 Constrained Problem
================================================================================

        Objective Function: objfunc

    Solution:
--------------------------------------------------------------------------------
    Total Time:                    0.0000
    Total Function Evaluations:
    Sensitivities:        FD

   Objectives:
     Name        Value        Optimum
      f          -3456         0

  Variables (c - continuous, i - integer, d - discrete):
    Name    Type       Value       Lower Bound  Upper Bound
    x1       c       24.000000       0.00e+00     4.20e+01
    x2       c       12.000000       0.00e+00     4.20e+01
    x3       c       12.000000       0.00e+00     4.20e+01

  Constraints (i - inequality, e - equality):
    Name    Type                    Bounds
    g1       i       -1.00e+21 <=   0.000000 <= 0.00e+00
    g2       i       -1.00e+21 <= -72.000000 <= 0.00e+00

--------------------------------------------------------------------------------

Where to go next

For more information on how to use the features of pyOpt see the Quickguide and the Examples .