This repository provides a Python implementation of solving a classical instance of the maximum coverage location problem described in Church 1974.

The problem is defined as: given N points, find K circles with radius of r to cover as many points as possible.

• Example 1: Select 20 circles with radius of 0.1 to cover 300 points (uniform distribution)

(M is the number of candidate sites and C is the number of points covered)

• Example 2: Select 20 circles with radius of 0.2 to cover 300 points (moon distribution)

The method randomly generates a set of candidate sites within the region of the input points. The problem is then solved by integer programming.

The mathematical formulation is given below:

from mclp import *
import numpy as np
Npoints = 300
from sklearn.datasets import make_moons
points,_ = make_moons(Npoints,noise=0.15)
# Number of sites to select
K = 20
# Service radius of each site
radius = 0.2
# Candidate site size (random sites generated)
M = 100
# Run mclp 
# opt_sites is the location of optimal sites 
# f is the number of points covered
opt_sites,f = mclp(points,K,radius,M)
# Plot the result 
plot_result(points,opt_sites,radius)

Check the jupyter-notebook demo.ipynb.

To run the example interactively, inside the project directory type the command

jupyter-notebook

• Python 2.7
• Scipy, Numpy (available as part of Anaconda)
• Shapely
• Gurobi, commercial software (free for academic usage)

It is recommended to use Anaconda directly, where the packages can be installed with pip or conda.

pip install shapely
conda config --add channels https://conda.anaconda.org/gurobi
conda install gurobi

Can Yang, Ph.D. student at KTH, Royal Institute of Technology in Sweden

Email: cyang(at)kth.se

Homepage: https://people.kth.se/~cyang/

• Church R, ReVelle C. The maximal covering location problem. Papers in regional science, 1974, 32(1): 101-118.
• https://examples.gurobi.com/facility-location/