 FICO Xpress Optimization Examples Repository
 FICO Optimization Community FICO Xpress Optimization Home   Wagon - MIP start solution heuristic

Description
Load balancing of train wagons. A heuristic solution obtained via a Longest processing time heuristic is loaded as start solution into Xpress Optimizer.

Further explanation of this example: The start solution heuristic is described in the book 'Applications of optimization with Xpress-MP', Section 9.1 Wagon load balancing

Source Files

xbd1wagon2.c

```/********************************************************
BCL Example Problems
====================

file d1wagon2.c
``````````````
(second version, using heuristic solution as
start solution for MIP)

(c) 2014 Fair Isaac Corporation
author: L. Bertacco, September 2014
********************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "xprb.h"
#include "xprs.h"

#define NBOXES (sizeof(WEIGHT)/sizeof(*WEIGHT)) /* Number of boxes                       */
#define NWAGONS 3                               /* Number of wagons                      */

/* Box weights                           */
int WEIGHT[] = { 34, 6, 8, 17, 16, 5, 13, 21, 25, 31, 14, 13, 33, 9, 25, 25 };
int WMAX = 100;                                 /* Weight limit of the wagons            */

int HeurSol[NBOXES];                            /* Heuristic solution: for each box      */
/* specifies in which wagon it is loaded */

/****VARIABLES****/
XPRBvar load[NBOXES][NWAGONS];                  /* 1 if box loaded on wagon, 0 otherwise */
XPRBvar maxweight;                              /* Weight of the heaviest wagon load     */

XPRBprob prob;

void XPRS_CC solnotify(XPRSprob my_prob, void* my_object, const char* solname, int status);

void d1w2_model(XPRBprob prob)
{
int b, w;
double sum_weights = 0;
XPRBctr ctr;

/****VARIABLES****/

for (b = 0; b < NBOXES; b++) for(w = 0; w < NWAGONS; w++)

/* Create maxweight (continuous with lb=ceil((sum(b in BOXES) WEIGHT(b))/NBOXES) */
for (b = 0; b < NBOXES; b++) sum_weights += WEIGHT[b];
maxweight = XPRBnewvar(prob, XPRB_PL, "maxweight", ceil(sum_weights/NBOXES), XPRB_INFINITY);

/****CONSTRAINTS****/

/* Every box into one wagon: forall(b in BOXES) sum(w in WAGONS) load(b,w) = 1 */
for (b = 0; b < NBOXES; b++) {
ctr = XPRBnewctr(prob, NULL, XPRB_E);
}

/* Limit the weight loaded into every wagon: forall(w in WAGONS) sum(b in BOXES) WEIGHT(b)*load(b,w) <= maxweight */
for (w = 0; w < NWAGONS; w++) {
ctr = XPRBnewctr(prob, NULL, XPRB_L);
}

/****OBJECTIVE****/

ctr = XPRBnewctr(prob, "MaxWeight", XPRB_N);
XPRBsetobj(prob, ctr);
XPRBsetsense(prob, XPRB_MINIM);
}

void d1w2_solve(XPRBprob prob)
{
int b, w;
int statmip;
XPRBsol sol;

/* Alternative to lower bound on maxweight: adapt the optimizer cutoff value  */

/* Comment out the following line to enable the optimizer log */

/* Create a BCL solution from the heuristic solution we have found */
sol = XPRBnewsol(prob);
/* Set the solution values for all discrete variables that are non-zero */
for (b = 0; b < NBOXES; b++) XPRBsetsolvar(sol, load[b][HeurSol[b]], 1);

/* It is possible, but not necessary, to set values for ALL discrete vars  */
/* by uncommenting the following line. In this case, the usersolnotify     */
/* callback would return status equal to 2 (instead of 3), as the solution */
/* would be feasible without the need of a local search.                   */
/* for (b=0; b<NBOXES; b++) for (w=0; w<NWAGONS; w++) XPRBsetsolvar(sol, load[b][w], w==HeurSol[b]); */

XPRBaddmipsol(prob, sol, "heurSol"); /* Send the solution to the optimizer */
XPRBdelsol(sol);                     /* Free the solution object */
/* Request notification of solution status after processing */

/* Parameter settings to make use of loaded solution */

XPRBmipoptimize(prob,"c");       /* Solve the LP-problem */
statmip = XPRBgetmipstat(prob); /* Get the problem status */
if (statmip == XPRB_MIP_SOLUTION || statmip == XPRB_MIP_OPTIMAL) { /* An integer solution has been found */
printf("Optimal solution:\n Max weight: %g\n", XPRBgetobjval(prob));
for (w = 0; w < NWAGONS; w++) {
int tot_weight = 0;
printf(" %d:", w + 1);
for (b = 0; b < NBOXES; b++) if (XPRBgetsol(load[b][w]) > .5) {
printf(" %d", b+1);
tot_weight += WEIGHT[b];
}
printf(" (total weight: %d)\n", tot_weight);
}
}
}

/***********************************************************************/

/* LPT (Longest processing time) heuristic:     */
/* One at a time, place the heaviest unassigned */
/* box onto the wagon with the least load       */
int weight_cmp(const int *arg1, const int *arg2) { return WEIGHT[*arg2] - WEIGHT[*arg1]; }
double solve_heur()
{
int b, w, i;
int ORDERW[NBOXES];                   /* Box indices sorted in decreasing weight order                                              */
int CurNum[NWAGONS] = { 0 };          /* For each wagon w, this is the number of boxes currently loaded                             */
int CurWeight[NWAGONS] = { 0 };       /* For each wagon w, this is the current weight, i.e. the sum of weights of loaded boxes      */
int Load[NWAGONS][NBOXES] = { 0 };    /* Load[w][i] (for i=0..CurNum[w]-1) contains the box index of the i-th box loaded on wagon w */
double heurobj = 0;                   /* heuristic solution objective value (max wagon weight) */

/* Copy the box indices into array ORDERW and sort them in decreasing     */
/* order of box weights (the sorted indices are returned in array ORDERW) */
for (b = 0; b < NBOXES; b++) ORDERW[b] = b;
qsort(ORDERW, NBOXES, sizeof(*ORDERW), weight_cmp);

/* Distribute the loads to the wagons using the LPT heuristic  */
for (b = 0; b < NBOXES; b++) {
int v = 0;                          /* Find wagon v with the smallest load */
for (w = 0; w < NWAGONS; w++) if (CurWeight[w] <= CurWeight[v]) v = w;
CurNum[v]++;                        /* Increase the counter of boxes on v */
CurWeight[v] += WEIGHT[ORDERW[b]];  /* Update current weight of the wagon */
}

/* Calculate the solution value */
for (w = 0; w < NWAGONS; w++) if (CurWeight[w]>heurobj) heurobj = CurWeight[w];

/* Solution printing */
printf("Heuristic solution:\n Max weight: %g\n", heurobj);
for (w = 0; w < NWAGONS; w++) {
printf(" %d:", w + 1);
for (i = 0; i < CurNum[w]; i++) printf(" %d", Load[w][i]+1);
printf(" (total weight: %d)\n", CurWeight[w]);
}

/* Save the heuristic solution into the HeurSol array */
for (w = 0; w < NWAGONS; w++) for (i = 0; i < CurNum[w]; i++) HeurSol[Load[w][i]] = w;

return heurobj;
}

/* Callback function reporting loaded solution status */
void XPRS_CC solnotify(XPRSprob my_prob, void* my_object, const char* solname, int status)
{
printf("Optimizer loaded solution %s with status=%d\n", solname, status);
}

/***********************************************************************/

int main(int argc, char **argv)
{
XPRBprob prob = XPRBnewprob("d1wagon2"); /* Initialize a new problem in BCL */

if (solve_heur() <= WMAX) {
printf("Heuristic solution fits capacity limits\n");
exit(0);
}

d1w2_model(prob);             /* Model the problem */
d1w2_solve(prob);             /* Solve the problem */

return 0;
}

```   