Merge pull request #19 from matheusdiogenesandrade/master

Handling asymmetric TSP instances

src/solver.jl

@@ -1,6 +1,41 @@
+#=
+# Roy Jonker, Ton Volgenant. Transforming asymmetric into symmetric traveling salesman problems
+# (https://doi.org/10.1016/0167-6377(83)90048-2)
+=#
+function convert_atsp_to_tsp(dist_mtx::Matrix{Int})
+
+ n_nodes = size(dist_mtx, 1)
+
+ # infinity constant
+ U::Int = sum(filter(x::Int -> x > 0, dist_mtx)) + 1
+
+ # negative constant
+ M::Int = U
+
+ # symmetric matrix
+ sym_dist_mtx::Matrix{Int} = fill(U, (2 * n_nodes, 2 * n_nodes))
+
+ # fill
+ for i::Int in 1:n_nodes
+ for j::Int in 1:n_nodes
+ value::Int = i == j ? - M : dist_mtx[i, j]
+
+ sym_dist_mtx[j, n_nodes + i] = value
+ sym_dist_mtx[n_nodes + i, j] = value
+ end
+ end
+
+ return sym_dist_mtx, M
+end
+
 function solve_tsp(dist_mtx::Matrix{Int})
- if ! issymmetric(dist_mtx)
- error("Asymmetric TSP is not supported.")
+
+ is_sym_mtx = issymmetric(dist_mtx)
+
+ # asymmetric case
+ if ! is_sym_mtx
+# error("Asymmetric TSP is not supported.")
+ dist_mtx, M::Int = convert_atsp_to_tsp(dist_mtx)
  end
 
  n_nodes = size(dist_mtx, 1)
@@ -36,7 +71,15 @@ function solve_tsp(dist_mtx::Matrix{Int})
  write(io, "EOF\n")
  end
 
- return __solve_tsp__(filename)
+ opt_tour, opt_len = __solve_tsp__(filename)
+
+ # asymmetric case
+ if ! is_sym_mtx
+ opt_tour = opt_tour[isodd.(eachindex(opt_tour))]
+ opt_len = Int(opt_len + M * n_nodes / 2)
+ end
+
+ return opt_tour, opt_len
 end
 
 
@@ -96,4 +139,4 @@ function __solve_tsp__(tsp_file::String)
  cleanup(name)
 
  return opt_tour, opt_len 
-end
+end

test/runtests.jl

@@ -15,13 +15,29 @@ using Test
  end
 
  @testset "Asymmetric TSP" begin
+
+ # instance 1
  M = [
  0 1 7 14
  16 0 1 5
  7 5 0 1
  1 3 16 0 
  ]
- @test_throws ErrorException solve_tsp(M)
+ opt_tour, opt_len = solve_tsp(M)
+ @show opt_tour, opt_len
+ @test opt_tour == [1, 2, 3, 4]
+ @test opt_len == 4
+
+ # instance 2
+ M = [
+ 0 5 19
+ 12 0 15
+ 3 9 0
+ ]
+ opt_tour, opt_len = solve_tsp(M)
+ @show opt_tour, opt_len
+ @test opt_tour == [1, 2, 3]
+ @test opt_len == 23
  end
 
  @testset "Coordinates" begin