Tsp.java


/* Copyright 2023, 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.

import com.gurobi.gurobi.*;

public class Tsp extends GRBCallback {
  private GRBVar[][] vars;

  public Tsp(GRBVar[][] xvars) {
    vars = xvars;
  }

  // Subtour elimination callback.  Whenever a feasible solution is found,
  // find the subtour that contains node 0, and add a subtour elimination
  // constraint if the tour doesn't visit every node.

  protected void callback() {
    try {
      if (where == GRB.CB_MIPSOL) {
        // Found an integer feasible solution - does it visit every node?
        int n = vars.length;
        int[] tour = findsubtour(getSolution(vars));

        if (tour.length < n) {
          // Add subtour elimination constraint
          GRBLinExpr expr = new GRBLinExpr();
          for (int i = 0; i < tour.length; i++)
            for (int j = i+1; j < tour.length; j++)
              expr.addTerm(1.0, vars[tour[i]][tour[j]]);
          addLazy(expr, GRB.LESS_EQUAL, tour.length-1);
        }
      }
    } catch (GRBException e) {
      System.out.println("Error code: " + e.getErrorCode() + ". " +
          e.getMessage());
      e.printStackTrace();
    }
  }

  // Given an integer-feasible solution 'sol', return the smallest
  // sub-tour (as a list of node indices).

  protected static int[] findsubtour(double[][] sol)
  {
    int n = sol.length;
    boolean[] seen = new boolean[n];
    int[] tour = new int[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;
        }
      }
    }

    int result[] = new int[bestlen];
    for (i = 0; i < bestlen; i++)
      result[i] = tour[bestind+i];
    return result;
  }

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

  protected static double distance(double[] x,
                                   double[] y,
                                   int      i,
                                   int      j) {
    double dx = x[i]-x[j];
    double dy = y[i]-y[j];
    return Math.sqrt(dx*dx+dy*dy);
  }

  public static void main(String[] args) {

    if (args.length < 1) {
      System.out.println("Usage: java Tsp ncities");
      System.exit(1);
    }

    int n = Integer.parseInt(args[0]);

    try {
      GRBEnv   env   = new GRBEnv();
      GRBModel model = new GRBModel(env);

      // Must set LazyConstraints parameter when using lazy constraints

      model.set(GRB.IntParam.LazyConstraints, 1);

      double[] x = new double[n];
      double[] y = new double[n];

      for (int i = 0; i < n; i++) {
        x[i] = Math.random();
        y[i] = Math.random();
      }

      // Create variables

      GRBVar[][] vars = new GRBVar[n][n];

      for (int i = 0; i < n; i++)
        for (int j = 0; j <= i; j++) {
          vars[i][j] = model.addVar(0.0, 1.0, distance(x, y, i, j),
                                    GRB.BINARY,
                                  "x"+String.valueOf(i)+"_"+String.valueOf(j));
          vars[j][i] = vars[i][j];
        }

      // Degree-2 constraints

      for (int i = 0; i < n; i++) {
        GRBLinExpr expr = new GRBLinExpr();
        for (int j = 0; j < n; j++)
          expr.addTerm(1.0, vars[i][j]);
        model.addConstr(expr, GRB.EQUAL, 2.0, "deg2_"+String.valueOf(i));
      }

      // Forbid edge from node back to itself

      for (int i = 0; i < n; i++)
        vars[i][i].set(GRB.DoubleAttr.UB, 0.0);

      model.setCallback(new Tsp(vars));
      model.optimize();

      if (model.get(GRB.IntAttr.SolCount) > 0) {
        int[] tour = findsubtour(model.get(GRB.DoubleAttr.X, vars));
        assert tour.length == n;

        System.out.print("Tour: ");
        for (int i = 0; i < tour.length; i++)
          System.out.print(String.valueOf(tour[i]) + " ");
        System.out.println();
      }

      // Dispose of model and environment
      model.dispose();
      env.dispose();

    } catch (GRBException e) {
      System.out.println("Error code: " + e.getErrorCode() + ". " +
          e.getMessage());
      e.printStackTrace();
    }
  }
}

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