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Let's suppose I have the following cost matrix, and I would like the path (and total cost) starting from node 20 from the perspective of Traveling salesman problem via nearest insertion method.

ds.ex <- structure(c(0, Inf, Inf, 1.9, 1.7, Inf, 0, 7.3, 7.4, 7.2, Inf, 
7.3, 0, 7.7, 7.8, 1.9, 7.4, 7.7, 0, 9.2, 1.7, 7.2, 7.8, 9.2, 
0), .Dim = c(5L, 5L), .Dimnames = list(c("2", "13", "14", "17", 
"20"), c("2", "13", "14", "17", "20")))

ds.ex
     2  13  14  17  20
2  0.0 Inf Inf 1.9 1.7
13 Inf 0.0 7.3 7.4 7.2
14 Inf 7.3 0.0 7.7 7.8
17 1.9 7.4 7.7 0.0 9.2
20 1.7 7.2 7.8 9.2 0.0

I am using TSP package to solve:

ds.ex.tsp <- as.TSP(ds.ex)
(a <- solve_TSP(ds.ex.tsp, method = "nearest_insertion", start=5))
object of class ‘TOUR’ 
result of method ‘nearest_insertion’ for 5 cities
tour length: 25.8

Can I get the path from:

`attr(a, "names")
[1] "20" "2"  "17" "14" "13"

?

If that is really the path, why isn't the path 20-2-17-13-14 the result? Once after having nodes 20, 2 and 17 visited, the one with smaller cost is the 13 and not 14.

Thanks in advance!

Guilherme Parreira
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1 Answers1

3

We can use labels.TSP, i.e.

library(TSP)
ds.ex.tsp <- as.TSP(ds.ex)
a <- solve_TSP(ds.ex.tsp, method = "nearest_insertion", start = 5)

labels(a)
#[1] "20" "13" "14" "17" "2"

Note that in the nearest insertion heuristic you add cities to a route based on its minimal distance to all the cities that are already in the route. A city is chosen at random if there are two cities that have the same distance. So solve_TSP may return different optimal paths upon replication. This seems to be the case in the example you give.

Sample data

ds.ex <- structure(c(0, Inf, Inf, 1.9, 1.7, Inf, 0, 7.3, 7.4, 7.2, Inf, 
7.3, 0, 7.7, 7.8, 1.9, 7.4, 7.7, 0, 9.2, 1.7, 7.2, 7.8, 9.2, 
0), .Dim = c(5L, 5L), .Dimnames = list(c("2", "13", "14", "17", 
"20"), c("2", "13", "14", "17", "20")))
Maurits Evers
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  • Thanks for the answer! But I just copied your code and run it, and it gave me a different answer as your did. Could you check it for me, please? – Guilherme Parreira Sep 09 '19 at 01:31
  • @GuilhermeParreira You're right. In fact if you keep repeating that block of code you'll get different answers from `solve_TSP`. I've made an edit, please take a look. – Maurits Evers Sep 09 '19 at 01:45