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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.java

```/********************************************************
Xpress-BCL Java Example Problems
================================

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

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

import java.util.*;
import com.dashoptimization.*;

public class xbd1wagon2
{
/* Box weights */
static final int[] WEIGHT = { 34, 6, 8, 17, 16, 5, 13, 21, 25, 31, 14, 13, 33, 9, 25, 25 };
static final int NBOXES = WEIGHT.length;       /* Number of boxes                       */
static final int NWAGONS = 3;                  /* Number of wagons                      */
static final int WMAX = 100;                   /* Weight limit of the wagons            */
static final int[] HeurSol = new int[NBOXES];  /* Heuristic solution: for each box      */

static XPRB bcl;
static XPRBprob prob;

/****VARIABLES****/
static final XPRBvar[][] load = new XPRBvar[NBOXES][NWAGONS];
static XPRBvar maxweight;

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

static void d1w2_model() throws XPRSexception
{
/****VARIABLES****/

for (int b = 0; b < NBOXES; b++) for (int w = 0; w < NWAGONS; w++)
load[b][w] = prob.newVar("load_" + (b + 1) + "_" + (w + 1), XPRB.BV);

/* Create maxweight (continuous with lb=ceil((sum(b in BOXES) WEIGHT(b))/NBOXES) */
double sum_weights = 0;
for (int b = 0; b < NBOXES; b++) sum_weights += WEIGHT[b];
maxweight = prob.newVar("maxweight", XPRB.PL, Math.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 (int b = 0; b < NBOXES; b++) {
XPRBexpr eq = new XPRBexpr();
prob.newCtr(eq.eql(1));
}

/* Limit the weight loaded into every wagon: forall(w in WAGONS) sum(b in BOXES) WEIGHT(b)*load(b,w) <= maxweight */
for (int w = 0; w < NWAGONS; w++) {
XPRBexpr le = new XPRBexpr();
prob.newCtr(le.lEql(maxweight));
}

/****OBJECTIVE****/

prob.setObj(maxweight);
prob.setSense(XPRB.MINIM);
}

static void d1w2_solve()
{
int b, w;
XPRSprob oprob = prob.getXPRSprob(); /* Get Optimizer problem */

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

/* Comment out the following line to enable the optimizer log */
oprob.setIntControl(XPRS.OUTPUTLOG, 0);

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

prob.addMIPSol(sol, "heurSol");      /* Send the solution to the optimizer */
/* Request notification of solution status after processing */

/* Parameter settings to make use of loaded solution */
oprob.setDblControl(XPRS.HEURSEARCHEFFORT, 2);
oprob.setIntControl(XPRS.HEURSEARCHROOTSELECT, 31);
oprob.setIntControl(XPRS.HEURSEARCHTREESELECT, 19);

prob.mipOptimize("c");          /* Solve the LP-problem */
int statmip = prob.getMIPStat(); /* Get the problem status */
if (statmip == XPRB.MIP_SOLUTION || statmip == XPRB.MIP_OPTIMAL) { /* An integer solution has been found */
System.out.printf("Optimal solution:\n Max weight: %.0f\n", prob.getObjVal());
for (w = 0; w < NWAGONS; w++) {
int tot_weight = 0;
System.out.print(" " + (w+1) + ":");
for (b = 0; b < NBOXES; b++) if (load[b][w].getSol() > .5) {
System.out.print(" "+(b+1));
tot_weight += WEIGHT[b];
}
System.out.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       */
static double solve_heur() {
Integer[] ORDERW = new Integer[NBOXES];   /* Box indices sorted in decreasing weight order                                              */
int[] CurNum = new int[NWAGONS];          /* For each wagon w, this is the number of boxes currently loaded                             */
int[] CurWeight = new int[NWAGONS];       /* For each wagon w, this is the current weight, i.e. the sum of weights of loaded boxes      */
int[][] Load = new int[NWAGONS][NBOXES];  /* Load[w][i] (for i=0..CurNum[w]-1) contains the box index of the i-th box loaded on wagon w */

/* 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 (int b = 0; b < NBOXES; b++) ORDERW[b] = b;
Arrays.sort(ORDERW, new Comparator<Integer>() {
public int compare(Integer i1, Integer i2) { return ((Integer)WEIGHT[i2]).compareTo(WEIGHT[i1]); }
});

/* Distribute the loads to the wagons using the LPT heuristic  */
for (int b = 0; b < NBOXES; b++) {
int v = 0;                          /* Find wagon v with the smallest load */
for (int 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 */
double heurobj = 0;                   /* heuristic solution objective value (max wagon weight) */
for (int w = 0; w < NWAGONS; w++) if (CurWeight[w] > heurobj) heurobj = CurWeight[w];

/* Solution printing */
System.out.printf("Heuristic solution:\n Max weight: %.0f\n", heurobj);

for (int w = 0; w < NWAGONS; w++) {
System.out.printf(" %d:", w + 1);
for (int i = 0; i < CurNum[w]; i++) System.out.print(" " + (Load[w][i] + 1));
System.out.printf(" (total weight: %d)\n", CurWeight[w]);
}

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

/* Callback function reporting loaded solution status */
static class UserSolNotifyCallback implements XPRSuserSolNotifyListener
{
public void XPRSuserSolNotifyEvent(XPRSprob oprob, Object data, String name, int status)
{
System.out.printf("Optimizer loaded solution %s with status=%d\n", name, status);
}
}
/***********************************************************************/

public static void main(String[] args) throws XPRSexception
{
if (solve_heur() <= WMAX) {
System.out.println("Heuristic solution fits capacity limits");
}
else {
XPRS.init();                      /* Initialize Xpress-Optimizer */
bcl = new XPRB();                 /* Initialize BCL */
prob = bcl.newProb("d1wagon2");   /* Create a new problem in BCL */
d1w2_model();                     /* Model the problem */
d1w2_solve();                     /* Solve the problem */
}
}

}
```