/* Copyright 2025, 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 <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "gurobi_c.h"
/* Define structure to pass data to the callback function */
struct callback_data {
int n;
};
/* Given an integer-feasible solution 'sol', find the smallest
sub-tour. Result is returned in 'tour', and length is
returned in 'tourlenP'. */
static void
findsubtour(int n,
double *sol,
int *tourlenP,
int *tour)
{
int i, node, len, start;
int bestind, bestlen;
int *seen = NULL;
seen = (int *) malloc(n*sizeof(int));
if (seen == NULL) {
fprintf(stderr, "Out of memory\n");
exit(1);
}
for (i = 0; i < n; i++)
seen[i] = 0;
start = 0;
bestlen = n+1;
bestind = -1;
while (start < n) {
for (node = 0; node < n; node++)
if (seen[node] == 0)
break;
if (node == n)
break;
for (len = 0; len < n; len++) {
tour[start+len] = node;
seen[node] = 1;
for (i = 0; i < n; i++) {
if (sol[node*n+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;
free(seen);
}
/* Subtour elimination callback. Whenever a feasible solution is found,
find the shortest subtour, and add a subtour elimination constraint
if that tour doesn't visit every node. */
int __stdcall
subtourelim(GRBmodel *model,
void *cbdata,
int where,
void *usrdata)
{
struct callback_data *mydata = (struct callback_data *) usrdata;
int n = mydata->n;
int *tour = NULL;
double *sol = NULL;
int i, j, len, nz;
int error = 0;
if (where == GRB_CB_MIPSOL) {
sol = (double *) malloc(n*n*sizeof(double));
tour = (int *) malloc(n*sizeof(int));
if (sol == NULL || tour == NULL) {
fprintf(stderr, "Out of memory\n");
exit(1);
}
GRBcbget(cbdata, where, GRB_CB_MIPSOL_SOL, sol);
findsubtour(n, sol, &len, tour);
if (len < n) {
int *ind = NULL;
double *val = NULL;
ind = (int *) malloc(len*(len-1)/2*sizeof(int));
val = (double *) malloc(len*(len-1)/2*sizeof(double));
if (ind == NULL || val == NULL) {
fprintf(stderr, "Out of memory\n");
exit(1);
}
/* Add subtour elimination constraint */
nz = 0;
for (i = 0; i < len; i++)
for (j = i+1; j < len; j++)
ind[nz++] = tour[i]*n+tour[j];
for (i = 0; i < nz; i++)
val[i] = 1.0;
error = GRBcblazy(cbdata, nz, ind, val, GRB_LESS_EQUAL, len-1);
free(ind);
free(val);
}
free(sol);
free(tour);
}
return error;
}
/* Euclidean distance between points 'i' and 'j'. */
static 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[])
{
GRBenv *env = NULL;
GRBmodel *model = NULL;
int i, j, len, n, solcount;
int error = 0;
char name[100];
double *x = NULL;
double *y = NULL;
int *ind = NULL;
double *val = NULL;
struct callback_data mydata;
if (argc < 2) {
fprintf(stderr, "Usage: tsp_c size\n");
exit(1);
}
n = atoi(argv[1]);
if (n == 0) {
fprintf(stderr, "Argument must be a positive integer.\n");
} else if (n > 100) {
printf("It will be a challenge to solve a TSP this large.\n");
}
x = (double *) malloc(n*sizeof(double));
y = (double *) malloc(n*sizeof(double));
ind = (int *) malloc(n*sizeof(int));
val = (double *) malloc(n*sizeof(double));
if (x == NULL || y == NULL || ind == NULL || val == NULL) {
fprintf(stderr, "Out of memory\n");
exit(1);
}
/* Create random points */
for (i = 0; i < n; i++) {
x[i] = ((double) rand())/RAND_MAX;
y[i] = ((double) rand())/RAND_MAX;
}
/* Create environment */
error = GRBloadenv(&env, "tsp.log");
if (error) goto QUIT;
/* Create an empty model */
error = GRBnewmodel(env, &model, "tsp", 0, NULL, NULL, NULL, NULL, NULL);
if (error) goto QUIT;
/* Add variables - one for every pair of nodes */
/* Note: If edge from i to j is chosen, then x[i*n+j] = x[j*n+i] = 1. */
/* The cost is split between the two variables. */
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
sprintf(name, "x_%d_%d", i, j);
error = GRBaddvar(model, 0, NULL, NULL, distance(x, y, i, j)/2,
0.0, 1.0, GRB_BINARY, name);
if (error) goto QUIT;
}
}
/* Degree-2 constraints */
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
ind[j] = i*n+j;
val[j] = 1.0;
}
sprintf(name, "deg2_%d", i);
error = GRBaddconstr(model, n, ind, val, GRB_EQUAL, 2, name);
if (error) goto QUIT;
}
/* Forbid edge from node back to itself */
for (i = 0; i < n; i++) {
error = GRBsetdblattrelement(model, GRB_DBL_ATTR_UB, i*n+i, 0);
if (error) goto QUIT;
}
/* Symmetric TSP */
for (i = 0; i < n; i++) {
for (j = 0; j < i; j++) {
ind[0] = i*n+j;
ind[1] = i+j*n;
val[0] = 1;
val[1] = -1;
error = GRBaddconstr(model, 2, ind, val, GRB_EQUAL, 0, NULL);
if (error) goto QUIT;
}
}
/* Set callback function */
mydata.n = n;
error = GRBsetcallbackfunc(model, subtourelim, (void *) &mydata);
if (error) goto QUIT;
/* Must set LazyConstraints parameter when using lazy constraints */
error = GRBsetintparam(GRBgetenv(model), GRB_INT_PAR_LAZYCONSTRAINTS, 1);
if (error) goto QUIT;
/* Optimize model */
error = GRBoptimize(model);
if (error) goto QUIT;
/* Extract solution */
error = GRBgetintattr(model, GRB_INT_ATTR_SOLCOUNT, &solcount);
if (error) goto QUIT;
if (solcount > 0) {
int *tour = NULL;
double *sol = NULL;
sol = (double *) malloc(n*n*sizeof(double));
tour = (int *) malloc(n*sizeof(int));
if (sol == NULL || tour == NULL) {
fprintf(stderr, "Out of memory\n");
exit(1);
}
error = GRBgetdblattrarray(model, GRB_DBL_ATTR_X, 0, n*n, sol);
if (error) goto QUIT;
/* Print tour */
findsubtour(n, sol, &len, tour);
printf("Tour: ");
for (i = 0; i < len; i++)
printf("%d ", tour[i]);
printf("\n");
free(tour);
free(sol);
}
QUIT:
/* Free data */
free(x);
free(y);
free(ind);
free(val);
/* Error reporting */
if (error) {
printf("ERROR: %s\n", GRBgeterrormsg(env));
exit(1);
}
/* Free model */
GRBfreemodel(model);
/* Free environment */
GRBfreeenv(env);
return 0;
}