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 |
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.
Michael Hahsler
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")