# Complete TSP model

# Number of cities
param n := 6;

set V := { 1..n };

set E := { <i,j> in (V cross V) with i < j };

# Edge variables
var x[E] binary;

# Distances
param d[E] := 
  <1, 2>  10,
  <1, 3>  10,
  <1, 4>  55,
  <1, 5>  55,
  <1, 6>  55,
  <2, 3>  10,
  <2, 4>  55,
  <2, 5>  25,
  <2, 6>  55,
  <3, 4>  33,
  <3, 5>  44,
  <3, 6>  55,
  <4, 5>  10,
  <4, 6>  10,
  <5, 6>  10;

minimize tour_length:
  sum <i,j> in E : d[i,j] * x[i,j];

subto degree:
  forall <v> in V do
    sum <v,j> in E : x[v,j]  +  sum <i,v> in E : x[i,v] == 2;

# Subtour elimination:

set S[] := powerset(V);

set S_Indices := indexset(S);

subto no_subtour:

  forall <s_index> in S_Indices with
    card(S[s_index]) >= 3 and card(S[s_index]) <= n - 3 do

  sum <i,j> in E with <i> in S[s_index] and <j> in S[s_index] :
    x[i,j]
  <= card(S[s_index]) - 1;