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

Project description

Sympy based mathematical programming language

Current PyPI Version Supported Python Versions Apache Software License Version 2.0 Code of Conduct GitHub Actions Codecov Documentation Status Join the chat at Publication Zenodo Source Code

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 our gitter channel if you have problems or questions regarding optlang.


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).


The following dependencies are needed.

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


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
model.add([c1, c2, c3])

status = model.optimize()

print("status:", model.status)
print("objective value:", model.objective.value)
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 for optlang is provided at


Please cite Publication 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 (Zenodo Source Code points to the latest version).


Please read


The development of optlang was partly support by the Novo Nordisk Foundation.

Future outlook

  • Mosek interface (provides academic licenses)

  • 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.)

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