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},
}
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/"))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
- Hahsler M (2022). qap: Heuristics for the Quadratic Assignment Problem (QAP). R package version 0.1-2, https://CRAN.R-project.org/package=qap.
- R.E. Burkard and F. Rendl (1984). A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operations Research, 17(2):169-174. https://doi.org/10.1016/0377-2217(84)90231-5
- Koopmans TC, Beckmann M (1957). Assignment problems and the location of economic activities. Econometrica 25(1):53-76. https://doi.org/10.2307/1907742
- Hubert, L., and Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 29(2), 190–241. https://doi.org/10.1111/j.2044-8317.1976.tb00714.x