swap

 /* improvementSwap() //{ */

  std::vector<unsigned> tsp_solver::improvementSwap(std::vector<unsigned> solution){
    unsigned first_pos, second_pos;
    int delta_f, change_value = 0;
    for(unsigned i = 1; i < num_cities_ - 1; i++){
      for(unsigned j = i + 1; j < num_cities_; j++){
        /* delta_f = old edges cost - new edges cost */
        if(i + 1 == j){
          delta_f = ( dist_[ solution[i - 1] ][ solution[i] ] + dist_[ solution[i] ][ solution[j] ]
                        + dist_[ solution[j] ][ solution[j + 1] ])
                        -
                        ( dist_[ solution[i - 1] ][ solution[j] ] + dist_[ solution[j] ][ solution[i]]
                        + dist_[ solution[i] ][ solution[j + 1]]);
        }else{
          delta_f = ( dist_[ solution[i - 1] ][ solution[i] ] + dist_[ solution[i] ][ solution[i + 1] ]
                        + dist_[ solution[j - 1] ][ solution[j] ] + dist_[ solution[j] ][ solution[j + 1] ])
                        -
                        ( dist_[ solution[i - 1] ][ solution[j] ] + dist_[ solution[j] ][ solution[i + 1] ]
                        + dist_[ solution[j - 1] ][ solution[i] ] + dist_[ solution[i] ][ solution[j + 1] ]);
        }

        if(delta_f > change_value){
          change_value = delta_f;
          first_pos = i;
          second_pos = j;
        }
      }
    }

    /* change the solution if generates a cheaper route */
    if(change_value > 0){
      unsigned tmp = solution[first_pos];
      solution[first_pos] = solution[second_pos];
      solution[second_pos] = tmp;
    }

    return solution;
  }

  //}