In mhahsler/qap: Heuristics for the Quadratic Assignment Problem (QAP)

pkg <- 'qap'

source("https://raw.githubusercontent.com/mhahsler/pkg_helpers/main/pkg_helpers.R")
pkg_title(pkg)

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).

pkg_usage(pkg)
pkg_citation(pkg)
pkg_install(pkg)

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$solution
p$opt

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

a <- qap(p$A, p$B, rep = 10)
a

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

(attr(a, "obj") - p$opt)/p$opt * 100

References

  print(citation("qap"), style = "text")

• 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

mhahsler/qap documentation built on April 24, 2024, 10:07 p.m.