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://github.com/mhahsler/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://github.com/mhahsler/qap},
}
Stable CRAN version: Install from within R with
install.packages("qap")
Current development version: Install from r-universe.
install.packages("qap", repos = "https://mhahsler.r-universe.dev")
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
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