Python optimization library for mathematical programming.
Introduction
Pytimize is a python library for
- Formulating and solving complex linear, integer, and nonlinear programs.
- Performing combinatorial optimization with directed/undirected graphs and flows.
- Visualizing polyhedrons and displaying computation process.
Install using pip install pytimize!
Documentation
Coming soon!
Example
The following shows a code snippet for constructing a linear program and solving
it with two phase simplex. For more detailed examples, please see pytimize/examples.
>>> from pytimize.formulations.linear import variables, minimize
>>> a, b, c, d, e = variables(5)
>>> p = minimize(4*c - 11*d - e + 17).subject_to(
a + 2*c + 7*d <= 2 + e,
b - 4*c - 5*d >= 1 - 3*e
).where(
a >= 0,
b >= 0,
c >= 0,
d <= 0,
e <= 0
)
>>> p
Min [0. 0. 4. -11. -1.]x + 17.
Subject To:
[1. 0. 2. 7. -1.] ≤ [2.]
[0. 1. -4. -5. 3.]x ≥ [1.]
x₄, x₅ ≤ 0
x₁, x₂, x₃ ≥ 0
>>> p.dual()
Max [2. 1.]x
Subject To:
[ 1. 0.] ≤ [ 0.]
[ 0. 1.] ≤ [ 0.]
[ 2. -4.]x ≤ [ 4.]
[ 7. -5.] ≥ [-11.]
[-1. 3.] ≥ [ -1.]
x₁ ≤ 0
x₂ ≥ 0
>>> p.to_sef(in_place=True)
Max [0. 0. -4. -11. -1. 0. 0.]x + 17.
Subject To:
[1. 0. 2. -7. 1. 1. 0.] = [2.]
[0. 1. -4. 5. -3. 0. -1.]x = [1.]
x ≥ 0
>>> solution, optimal_basis, certificate = p.two_phase_simplex()
>>> solution, optimal_basis, certificate
(array([2., 1., 0., 0., 0., 0., 0.]), [1, 2], array([0., 0.])
>>> p.verify_optimality(certificate)
True
>>> p.optimal_value()
17.0You can also formulate the exact same program by specifying the objective function and constraints in matrix form:
>>> from pytimize.programs import LinearProgram
>>> import numpy as np
>>> A = np.array([
[1, 0, 2, 7, -1],
[0, 1, -4, -5, 3]
])
>>> b = np.array([2, 1])
>>> c = np.array([0, 0, 4, -11, -1])
>>> z = 17
>>> p = LinearProgram(A, b, c, z, "min", ["<=", ">="], negative_variables=[4, 5])
>>> p
Min [0. 0. 4. -11. -1.]x + 17
Subject To:
[1. 0. 2. 7. -1.] ≤ [2.]
[0. 1. -4. -5. 3.]x ≥ [1.]
x₄, x₅ ≤ 0
x₁, x₂, x₃ ≥ 0Contributing
Pytimize is a work in progress project. Contributions are welcome on a pull request basis.
Credits
Pytimize is created and maintained by Terry Zheng, Jonathan Wang, and Colin He. Logo is designed by Kayla Estacio.