# optlang 1.1.2

Formulate optimization problems using sympy expressions and solve them using interfaces to third-party optimization software (e.g. GLPK).

Sympy based mathematical programming language

Optlang is a Python package for solving mathematical optimization problems, i.e. maximizing or minimizing an objective function over a set of variables subject to a number of constraints. Optlang provides a common interface to a series of optimization tools, so different solver backends can be changed in a transparent way. Optlang’s object-oriented API takes advantage of the symbolic math library sympy to allow objective functions and constraints to be easily formulated from symbolic expressions of variables (see examples).

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Also, please use the GitHub issue tracker to let us know about bugs or feature requests, or if you have problems or questions regarding optlang.

## Installation

Install using pip

```pip install optlang
```

This will also install swiglpk, an interface to the open source (mixed integer) LP solver GLPK. Quadratic programming (and MIQP) is supported through additional optional solvers (see below).

## Dependencies

The following dependencies are needed.

The following are optional dependencies that allow other solvers to be used.

• cplex (LP, MILP, QP, MIQP)
• gurobipy (LP, MILP (QP and MIQP support will be added in the future))
• scipy (LP)

## Example

Formulating and solving the problem is straightforward (example taken from GLPK documentation):

```from __future__ import print_function
from optlang import Model, Variable, Constraint, Objective

# All the (symbolic) variables are declared, with a name and optionally a lower and/or upper bound.
x1 = Variable('x1', lb=0)
x2 = Variable('x2', lb=0)
x3 = Variable('x3', lb=0)

# A constraint is constructed from an expression of variables and a lower and/or upper bound (lb and ub).
c1 = Constraint(x1 + x2 + x3, ub=100)
c2 = Constraint(10 * x1 + 4 * x2 + 5 * x3, ub=600)
c3 = Constraint(2 * x1 + 2 * x2 + 6 * x3, ub=300)

# An objective can be formulated
obj = Objective(10 * x1 + 6 * x2 + 4 * x3, direction='max')

# Variables, constraints and objective are combined in a Model object, which can subsequently be optimized.
model = Model(name='Simple model')
model.objective = obj

status = model.optimize()

print("status:", model.status)
print("objective value:", model.objective.value)
print("----------")
for var_name, var in model.variables.iteritems():
print(var_name, "=", var.primal)
```

The example will produce the following output:

```status: optimal
objective value: 733.333333333
----------
x2 = 66.6666666667
x3 = 0.0
x1 = 33.3333333333
```

### Using a particular solver

If you have more than one solver installed, it’s also possible to specify which one to use, by importing directly from the respective solver interface, e.g. `from optlang.glpk_interface import Model, Variable, Constraint, Objective`

## Documentation

Documentation for optlang is provided at readthedocs.org.

## Citation

Please cite if you use optlang in a scientific publication. In case you would like to reference a specific version of of optlang you can also include the respective Zenodo DOI ( points to the latest version).

## Future outlook

• GAMS output (support non-linear problem formulation)
• DEAP (support for heuristic optimization)
• Interface to NEOS optimization server (for testing purposes and solver evaluation)
• Automatically handle fractional and absolute value problems when dealing with LP/MILP/QP solvers (like GLPK, CPLEX etc.)

The optlang trello board also provides a good overview of the project’s roadmap.

File Type Py Version Uploaded on Size
Python Wheel py2.py3 2017-03-14 106KB
Python Egg 3.5 2017-03-14 259KB
Source 2017-03-14 90KB
• Author: Nikolaus Sonnenschein