| insert_dummy {TSP} | R Documentation |
Inserts dummy cities into objects of class TSP or ATSP. A
dummy city has the same, constant distance (0) to all other cities and is
infinitely far from other dummy cities. A dummy city can be used to transform
a shortest Hamiltonian path problem (i.e., finding an optimal linear order)
into a shortest Hamiltonian cycle problem which can be solved by a TSP
solvers (Garfinkel 1985).
Several dummy cities can be used together with a TSP solvers to perform rearrangement clustering (Climer and Zhang 2006).
insert_dummy(x, n = 1, const = 0, inf = Inf, label = "dummy")
x |
an object of class TSP or ATSP. |
n |
number of dummy cities. |
const |
distance of the dummy cities to all other cities. |
inf |
distance between dummy cities. |
label |
labels for the dummy cities. If only one label is given, it is reused for all dummy cities. |
The dummy cities are inserted after the other cities in x.
A const of 0 is guaranteed to work if the TSP finds the optimal
solution. For heuristics returning suboptimal solutions, a higher
const (e.g., 2 * max{x}) might provide better results.
Sharlee Climer, Weixiong Zhang (2006): Rearrangement Clustering: Pitfalls, Remedies, and Applications, Journal of Machine Learning Research 7(Jun), pp. 919–943.
R.S. Garfinkel (1985): Motivation and modelling (chapter 2). In: E. L. Lawler, J. K. Lenstra, A.H.G. Rinnooy Kan, D. B. Shmoys (eds.) The traveling salesman problem - A guided tour of combinatorial optimization, Wiley & Sons.
## make runs comparable
set.seed(4444)
data("iris")
tsp <- TSP(dist(iris[-5]))
## insert 2 dummy cities
tsp_dummy <- insert_dummy(tsp, n = 2, label = "boundary")
## get a solution for the TSP
tour <- solve_TSP(tsp_dummy)
## plot the distance matrix
image(tsp_dummy, tour)
## draw lines where the dummy cities are located
abline(h = which(labels(tour)=="boundary"), col = "red")
abline(v = which(labels(tour)=="boundary"), col = "red")
## print the results (NAs are the dummy cities)
iris[tour, "Species"]