Solving your first model in Python¶

Writing the model¶

Below is the Python program which models this nonlinear problem (see examples/optimal_bucket).

import hexaly.optimizer
import sys

with hexaly.optimizer.HexalyOptimizer() as optimizer:
    PI = 3.14159265359

    #
    # Declare the optimization model
    #
    m = optimizer.model

    # Numerical decisions
    R = m.float(0, 1)
    r = m.float(0, 1)
    h = m.float(0, 1)

    # Surface must not exceed the surface of the plain disc
    surface = PI * r ** 2 + PI * (R + r) * m.sqrt((R - r) ** 2 + h ** 2)
    m.constraint(surface <= PI)

    # Maximize the volume
    volume = PI * h / 3 * (R ** 2 + R * r + r ** 2)
    m.maximize(volume)

    m.close()

    #
    # Parametrize the optimizer
    #
    if len(sys.argv) >= 3:
        optimizer.param.time_limit = int(sys.argv[2])
    else:
        optimizer.param.time_limit = 2

    optimizer.solve()

    #
    # Write the solution in a file with the following format:
    #  - surface and volume of the bucket
    #  - values of R, r and h
    #
    if len(sys.argv) >= 2:
        with open(sys.argv[1], 'w') as f:
            f.write("%f %f\n" % (surface.value, volume.value))
            f.write("%f %f %f\n" % (R.value, r.value, h.value))

After creating the Hexaly Optimizer environment with HexalyOptimizer(), all the decision variables of the model are declared with the float() function (or also bool(), int(), set(), list(), interval()). Intermediate expressions can be built upon these decision variables by using other operators or functions. For example, in the model above: power (pow), square root (sqrt), less than or equal to (<=). Many other mathematical operators are available, allowing you to model and solve highly nonlinear combinatorial optimization problems. The methods constraint or maximize are used for tagging expressions as constrained or maximized.

Running the Python program¶

A Python distribution must be installed on your computer. Hexaly Optimizer is compatible with Python 2.7 and Python >= 3.4.

On any system, if you applied the recommended pip install procedure described above, your Python program is directly launched with:

python optimal_bucket.py

Then, the following trace will appear in your console:

Model:  expressions = 26, decisions = 3, constraints = 1, objectives = 1
Param:  time limit = 2 sec, no iteration limit

[objective direction ]:     maximize

[  0 sec,       0 itr]:            0
[ optimality gap     ]:         100%
[  0 sec,   42898 itr]:      0.68709
[ optimality gap     ]:      < 0.01%

42898 iterations performed in 0 seconds

Optimal solution:
    obj    =      0.68709
    gap    =      < 0.01%
    bounds =     0.687189

If no time limit is set, the search will continue until optimality is proven (Optimal solution message) or until you force the stop of the program by pressing Ctrl+C. The trace in console starts with the key figures of the model: number of expressions, decisions, constraints, and objectives.

Once the search is finished, the total number of iterations and the elapsed time are displayed, as well as the status and the value of the best solution found. The solution status can be Inconsistent, Infeasible, Feasible, or Optimal.

If you have trouble compiling or launching the program, please have a look at the Installation & licensing instructions. We invite users willing to go further with APIs to consult the Python API Reference.

Running Hexaly Optimizer without pip¶

If you don’t have pip or if you don’t want to use pip, executing your program will require setting the PYTHONPATH environment variable beforehand, and the launching lines will depend on your system. If you are using a Python development environment, its settings page allows configuring the PYTHONPATH environment variable. Otherwise you can proceed as follows:

• In a Windows command prompt you will type

  set PYTHONPATH=%HX_HOME%\bin\python

• In a Windows PowerShell console you will type

  $env:PYTHONPATH=”$env:HX_HOME\bin\python”

• On Linux of MacOS, the command is

  export PYTHONPATH=/opt/hexaly_13_5/bin/python