Skip to content
/ qap Public

Heuristics for the Quadratic Assignment Problem (QAP) - R package

License

Notifications You must be signed in to change notification settings

mhahsler/qap

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

56 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

R package qap - Heuristics for the Quadratic Assignment Problem (QAP)

r-universe status Package on CRAN CRAN RStudio mirror downloads

Introduction

This package implements heuristics for the Quadratic Assignment Problem (QAP). The QAP was introduced as a combinatorial optimization problem from the category of facilities location problems in operations research (Koopmans and Beckmann; 1957). It also has many applications in data analysis including cluster analysis and seriation (see Hubert and Schultz; 1976).

The problem is NP-hard and the package implements the very effective simulated annealing heuristic described in Burkard and Rendl (1984).

The following R packages use qap: seriation

To cite package ‘qap’ in publications use:

Hahsler M (2022). qap: Heuristics for the Quadratic Assignment Problem (QAP). R package version 0.1-2, https://CRAN.R-project.org/package=qap.

@Manual{,
  title = {qap: Heuristics for the Quadratic Assignment Problem (QAP)},
  author = {Michael Hahsler},
  year = {2022},
  note = {R package version 0.1-2},
  url = {https://CRAN.R-project.org/package=qap},
}

Installation

Stable CRAN version: Install from within R with

install.packages("qap")

Current development version: Install from r-universe.

install.packages("qap",
    repos = c("https://mhahsler.r-universe.dev",
              "https://cloud.r-project.org/"))

Usage

The package contains a copy of the problem instances and solutions from QAPLIB. We load the had20 QAPLIB problem. The problem contains the A and B matrices and the optimal solution and the optimal objective function value.

library(qap)
set.seed(1000)

p <- read_qaplib(system.file("qaplib", "had20.dat", package = "qap"))
p$solution
##  [1]  8 15 16 14 19  6  7 17  1 12 10 11  5 20  2  3  4  9 18 13
p$opt
## [1] 6922

We run the simulated annealing heuristic 10 times and use the best solution.

a <- qap(p$A, p$B, rep = 10)
a
##  [1]  8 15 16 14 19  6  7 12  1 11 10  5  3 20  2 17  4  9 18 13
## attr(,"obj")
## [1] 6926

Compare the solution with known optimum (% above optimum).

(attr(a, "obj") - p$opt)/p$opt * 100
## [1] 0.058

References