pulp2mat 0.1.3

convert pulp model into matrix formulation for scipy.optimize.milp

pulp2mat

Convert pulp model into matrix formulation.

It can be easily thrown to scipy.optimize.milp function.

How to install

$ pip install pulp2mat

Without poetry, please look at pyproject.toml and install all dependencies manually.

Quick Example

For example, the binpacking problem can be formulated with pulp as below;

import pulp as pl
import numpy as np

item_sizes = np.array([7, 3, 3, 1, 6, 8, 4, 9, 5, 2])
num_items = len(item_sizes)
num_bins = len(item_sizes)
bin_size = 10

# Variables * must be defined as dictionaries
x = {
    (i, j): pl.LpVariable("x_{}_{}".format(i, j), cat=pl.LpBinary)
    for i in range(num_items)
    for j in range(num_bins)
}
y = {
    j: pl.LpVariable("y_{}".format(j), cat=pl.LpBinary)
    for j in range(num_bins)
}

problem = pl.LpProblem()

# Bin size constraint for each bin
for j in range(num_bins):
    problem += (
        pl.lpSum(
            x[i, j] * item_sizes[i] for i in range(num_items)
        )
        <= bin_size * y[j]
    )
# One-hot constraint for each item
for i in range(num_items):
    problem += pl.lpSum(x[i, j] for j in range(num_bins)) == 1

# Objective: minimize number of bins used.
problem += pl.lpSum(y[j] for j in range(num_bins))

the pulp.LpProblem object and the list of variable dictionaries can be converted to the matrix format for scipy.optimize.milp.

import pulp2mat
from scipy.optimize import milp
c, integrality, constraints, bounds = pulp2mat.convert_all(problem)
result = milp(c, integrality=integrality, constraints=constraints, bounds=bounds)