This package implements heuristics for the Quadratic Assignment Problem (QAP) first introduced by Koopmans and Beckmann (1957). Although, the QAP was introduced as a combinatorial optimization problem for the facility location problem in operations research, it also has many applications in data analysis (see Hubert and Schultz; 1976).
The problem is NP-hard and the package implements the simulated annealing heuristic described in Burkard and Rendl (1984).
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$solution## [1] 8 15 16 14 19 6 7 17 1 12 10 11 5 20 2 3 4 9 18 13p$opt## [1] 6922We 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] 6926Compare the solution with known optimum (% above optimum).
(attr(a, "obj") - p$opt)/p$opt * 100## [1] 0.058