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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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)
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
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 readthedocs.org.
Please cite
Please read CONTRIBUTING.md.
The development of optlang was partly support by the Novo Nordisk Foundation.
- 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.)