Try our new documentation site (beta).


tsp_c++.cpp


/* Copyright 2022, Gurobi Optimization, LLC */

/* Solve a traveling salesman problem on a randomly generated set of
   points using lazy constraints.   The base MIP model only includes
   'degree-2' constraints, requiring each node to have exactly
   two incident edges.  Solutions to this model may contain subtours -
   tours that don't visit every node.  The lazy constraint callback
   adds new constraints to cut them off. */

#include "gurobi_c++.h"
#include <cassert>
#include <cstdlib>
#include <cmath>
#include <sstream>
using namespace std;

string itos(int i) {stringstream s; s << i; return s.str(); }
double distance(double* x, double* y, int i, int j);
void findsubtour(int n, double** sol, int* tourlenP, int* tour);

// Subtour elimination callback.  Whenever a feasible solution is found,
// find the smallest subtour, and add a subtour elimination constraint
// if the tour doesn't visit every node.

class subtourelim: public GRBCallback
{
  public:
    GRBVar** vars;
    int n;
    subtourelim(GRBVar** xvars, int xn) {
      vars = xvars;
      n    = xn;
    }
  protected:
    void callback() {
      try {
        if (where == GRB_CB_MIPSOL) {
          // Found an integer feasible solution - does it visit every node?
          double **x = new double*[n];
          int *tour = new int[n];
          int i, j, len;
          for (i = 0; i < n; i++)
            x[i] = getSolution(vars[i], n);

          findsubtour(n, x, &len, tour);

          if (len < n) {
            // Add subtour elimination constraint
            GRBLinExpr expr = 0;
            for (i = 0; i < len; i++)
              for (j = i+1; j < len; j++)
                expr += vars[tour[i]][tour[j]];
            addLazy(expr <= len-1);
          }

          for (i = 0; i < n; i++)
            delete[] x[i];
          delete[] x;
          delete[] tour;
        }
      } catch (GRBException e) {
        cout << "Error number: " << e.getErrorCode() << endl;
        cout << e.getMessage() << endl;
      } catch (...) {
        cout << "Error during callback" << endl;
      }
    }
};

// Given an integer-feasible solution 'sol', find the smallest
// sub-tour.  Result is returned in 'tour', and length is
// returned in 'tourlenP'.

void
findsubtour(int      n,
            double** sol,
            int*     tourlenP,
            int*     tour)
{
  bool* seen = new bool[n];
  int bestind, bestlen;
  int i, node, len, start;

  for (i = 0; i < n; i++)
    seen[i] = false;

  start = 0;
  bestlen = n+1;
  bestind = -1;
  node = 0;
  while (start < n) {
    for (node = 0; node < n; node++)
      if (!seen[node])
        break;
    if (node == n)
      break;
    for (len = 0; len < n; len++) {
      tour[start+len] = node;
      seen[node] = true;
      for (i = 0; i < n; i++) {
        if (sol[node][i] > 0.5 && !seen[i]) {
          node = i;
          break;
        }
      }
      if (i == n) {
        len++;
        if (len < bestlen) {
          bestlen = len;
          bestind = start;
        }
        start += len;
        break;
      }
    }
  }

  for (i = 0; i < bestlen; i++)
    tour[i] = tour[bestind+i];
  *tourlenP = bestlen;

  delete[] seen;
}

// Euclidean distance between points 'i' and 'j'.

double
distance(double* x,
         double* y,
         int     i,
         int     j)
{
  double dx = x[i]-x[j];
  double dy = y[i]-y[j];

  return sqrt(dx*dx+dy*dy);
}

int
main(int   argc,
     char *argv[])
{
  if (argc < 2) {
    cout << "Usage: tsp_c++ size" << endl;
    return 1;
  }

  int n = atoi(argv[1]);
  double* x = new double[n];
  double* y = new double[n];

  int i;
  for (i = 0; i < n; i++) {
    x[i] = ((double) rand())/RAND_MAX;
    y[i] = ((double) rand())/RAND_MAX;
  }

  GRBEnv *env = NULL;
  GRBVar **vars = NULL;

  vars = new GRBVar*[n];
  for (i = 0; i < n; i++)
    vars[i] = new GRBVar[n];

  try {
    int j;

    env = new GRBEnv();
    GRBModel model = GRBModel(*env);

    // Must set LazyConstraints parameter when using lazy constraints

    model.set(GRB_IntParam_LazyConstraints, 1);

    // Create binary decision variables

    for (i = 0; i < n; i++) {
      for (j = 0; j <= i; j++) {
        vars[i][j] = model.addVar(0.0, 1.0, distance(x, y, i, j),
                                  GRB_BINARY, "x_"+itos(i)+"_"+itos(j));
        vars[j][i] = vars[i][j];
      }
    }

    // Degree-2 constraints

    for (i = 0; i < n; i++) {
      GRBLinExpr expr = 0;
      for (j = 0; j < n; j++)
        expr += vars[i][j];
      model.addConstr(expr == 2, "deg2_"+itos(i));
    }

    // Forbid edge from node back to itself

    for (i = 0; i < n; i++)
      vars[i][i].set(GRB_DoubleAttr_UB, 0);

    // Set callback function

    subtourelim cb = subtourelim(vars, n);
    model.setCallback(&cb);

    // Optimize model

    model.optimize();

    // Extract solution

    if (model.get(GRB_IntAttr_SolCount) > 0) {
      double **sol = new double*[n];
      for (i = 0; i < n; i++)
        sol[i] = model.get(GRB_DoubleAttr_X, vars[i], n);

      int* tour = new int[n];
      int len;

      findsubtour(n, sol, &len, tour);
      assert(len == n);

      cout << "Tour: ";
      for (i = 0; i < len; i++)
        cout << tour[i] << " ";
      cout << endl;

      for (i = 0; i < n; i++)
        delete[] sol[i];
      delete[] sol;
      delete[] tour;
    }

  } catch (GRBException e) {
    cout << "Error number: " << e.getErrorCode() << endl;
    cout << e.getMessage() << endl;
  } catch (...) {
    cout << "Error during optimization" << endl;
  }

  for (i = 0; i < n; i++)
    delete[] vars[i];
  delete[] vars;
  delete[] x;
  delete[] y;
  delete env;
  return 0;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization