cflg: an algorithmic toolkit for continuous set covering on networks

Facility location is an important application in operations research. Continuous set covering on networks generalizes the classical dicrete set covering problems in graphs, which allows both the demands and facilities continuously locating in edges. cflg contains several algorithms for solving continuous set covering on networks. cflg is written in Julia based on JuMP.

Installation

cflg has been developped and tested under Linux System.

To use cflg, it requires:

Julia,
JuMP,

and one of the following MILP solvers:

CPLEX,
GLPK,
Gurobi.

Benchmarks

There are six benchmarks city, Kgroup_A, Kgroup_B, random_A, random_B and test. Each benchmark contains instances in .txt file format.

Each instance file contains data of a graph. Its first line contains the number of nodes and edges of the graph; Edges are represented as a list from the second line: each line indicates an edge's end nodes and weight.

Usage

You can run cflg.jl via the following command:

julia ./cflg.jl solver time_limit instance algorithm raidus

The settings of the above arguments are as follows.

solver: one of the solvers in CPLEX, GLPK and Gurobi.
time_limit: time limit in seconds.
instance: the instance path.
algorithm: one of the algorithms in EF, F0, F, SF, RF, SFD and None.
raidus: the coverage raidus.

To reproduce the computational results in the accompanied paper, clear the results directory, go to the test directory, and execute the following command in the terminal (in Linux)

/bin/bash run.sh

Note that you should change the solver option solver and the GNU parallel test option gnuparalleltest according to their availability in your system.

Algorithm Option

The algorithm option is summarized in the following table.

	Continuous demand	Continuous facility	Set delimitation	Strengthenning	Long edge	Model size	Input graph	Comment
`EF`	Yes	Yes	No	No	No	Very large	Subdivided graph	From Covering edges in networks
`F0`	Yes	Yes	No	No	No	Large	Subdivided graph	Naive model
`F`	Yes	Yes	Yes	No	No	Medium	Subdivided graph	Complete model
`SF`	Yes	Yes	Yes	Yes	No	Meidum	Subdivided graph	Strenghtenned model
`RF`	Yes	Yes	Yes	Yes	Yes	Small	Degree-2-free graph	Reduced model
`SFD`	No	Yes	Yes	Yes	No	Very small	Subdivided graph	Discrete model

The None option is used for computing the parameters of subdivided and degree-2-free graphs.

References

If you find cflg useful in your work, we kindly request that you cite the following paper draft (arXiv preprint), which is recommended reading for advanced users:

@misc{pelegrín2022continuous,
    title={Continuous Covering on Networks: Strong Mixed Integer Programming Formulations}, 
    author={Mercedes Pelegrín and Liding Xu},
    year={2022},
    eprint={2203.00284},
    archivePrefix={arXiv},
    primaryClass={math.OC}
}

lidingxu / CFLG