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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

xbd1wagonjava.zip[download all files]

Source Files
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xbd1wagon2.java[download]





xbd1wagon2.java

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

    /****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 */
                 XPRS xprs = new XPRS()) {                  /* Initialize Xpress-Optimizer */
                d1w2_model(prob);                     /* Model the problem */
                d1w2_solve(prob);                     /* Solve the problem */
            }
        }
    }
}

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