/********************************************************
* Xpress-BCL Java Example Problems
* ================================
*
* file d1wagon2.java
* `````````````````
* Load balancing of train wagons
* (second version, using heuristic solution as
* start solution for MIP)
*
* (c) 2014-2024 Fair Isaac Corporation
* author: L.Bertacco, 2014
********************************************************/
import com.dashoptimization.*;
import java.util.*;
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 */
/****VARIABLES****/
static final XPRBvar[][] load = new XPRBvar[NBOXES][NWAGONS];
static XPRBvar maxweight;
/***********************************************************************/
static void d1w2_model(XPRBprob prob) throws XPRSexception {
/****VARIABLES****/
/* Create load[box,wagon] (binary) */
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();
for (int w = 0; w < NWAGONS; w++) eq.add(load[b][w]);
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();
for (int b = 0; b < NBOXES; b++) le.add(load[b][w].mul(WEIGHT[b]));
prob.newCtr(le.lEql(maxweight));
}
/****OBJECTIVE****/
prob.setObj(maxweight);
prob.setSense(XPRB.MINIM);
}
static void d1w2_solve(XPRBprob prob) {
int b, w;
XPRSprob oprob = prob.getXPRSprob(); /* Get Optimizer problem */
/* Alternative to lower bound on maxweight: adapt the optimizer cutoff value */
/* oprob.setDblControl(XPRS.MIPADDCUTOFF, -0.99999); */
/* 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 */
oprob.addUserSolNotifyListener(new UserSolNotifyCallback());
/* 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 MIP 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;
Load[v][CurNum[v]] = ORDERW[b]; /* Add current box to wagon v */
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 {
try (XPRBprob prob = new XPRBprob("d1wagon2"); /* Initialize BCL and create a new problem */
XPRBexprContext context =
new XPRBexprContext(); /* Release XPRBexpr instances at end of block. */
XPRS xprs = new XPRS()) {
/* Initialize Xpress-Optimizer */
d1w2_model(prob); /* Model the problem */
d1w2_solve(prob); /* Solve the problem */
}
}
}
}
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