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Cutstk - Column generation for a cutting stock problem

Description
This example features iteratively adding new variables, basis in/output and working with subproblems. The column generation algorithm is implemented as a loop over the root node of the MIP problem.

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Source Files
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xbcutstk.java

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

  file xbcutstk.java
  ``````````````````
  Cutting stock problem, solved by column (= cutting
  pattern) generation heuristic looping over the
  root node.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, 2001, rev. Mar. 2014
********************************************************/

import java.lang.*;
import com.dashoptimization.*;

public class xbcutstk {
    static final int NWIDTHS = 5;
    static final int MAXWIDTH = 94;

    static final double EPS = 1e-6;
    static final int MAXCOL = 10;

    /****DATA****/
    static final double[] WIDTH = {17, 21, 22.5,  24, 29.5}; /* Possible widths */
    static final int[] DEMAND = {150, 96,   48, 108,  227};  /* Demand per width */
    static int[][] PATTERNS;    /* (Basic) cutting patterns */

    static XPRBvar[] pat;              /* Rolls per pattern */
    static XPRBctr[] dem;              /* Demand constraints */
    static XPRBctr cobj;               /* Objective function */

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

    static void modCutStock(XPRBprob p) throws XPRSexception {
        int i,j;
        XPRBexpr le;

        PATTERNS = new int[NWIDTHS][NWIDTHS];
        for(j=0;j<NWIDTHS;j++)
            PATTERNS[j][j] = (int)Math.floor((double)MAXWIDTH/WIDTH[j]);

        /****VARIABLES****/
        pat = new XPRBvar[NWIDTHS+MAXCOL];
        for(j=0;j<NWIDTHS;j++)
            pat[j]=p.newVar("pat_"+(j+1), XPRB.UI, 0,
                            (int)Math.ceil((double)DEMAND[j]/PATTERNS[j][j]));

        /****OBJECTIVE****/
        le = new XPRBexpr();
        for(j=0;j<NWIDTHS;j++) le.add(pat[j]);
        cobj = p.newCtr("OBJ", le);
        p.setObj(cobj);                  /* Minimize total number of rolls */

        /****CONSTRAINTS****/
        dem = new XPRBctr[NWIDTHS];
        for(i=0;i<NWIDTHS;i++) {            /* Satisfy the demand per width */
            le = new XPRBexpr();
            for(j=0;j<NWIDTHS;j++)
                le .add(pat[j].mul(PATTERNS[i][j]));
            dem[i] = p.newCtr("Demand", le.gEql(DEMAND[i]) );
        }
    }

    /**************************************************************************/
    /*  Column generation loop at the top node:                               */
    /*    solve the LP and save the basis                                     */
    /*    get the solution values                                             */
    /*    generate new column(s) (=cutting pattern)                           */
    /*    load the modified problem and load the saved basis                  */
    /**************************************************************************/
    static void solveCutStock(XPRB bcl, XPRBprob p)  throws XPRSexception {
        double objval=0;                /* Objective value */
        int i,j;
        int starttime;
        int npatt, npass;               /* Counters for columns and passes */
        double[] solpat;                /* Solution values for variables pat */
        double[] dualdem;               /* Dual values of demand constraints */
        XPRBbasis basis;
        double dw,z;
        int[] x;

        x = new int[NWIDTHS];
        solpat = new double[NWIDTHS+MAXCOL];
        dualdem = new double[NWIDTHS];

        starttime=XPRB.getTime();
        npatt = NWIDTHS;

        for(npass=0;npass<MAXCOL;npass++) {
            p.lpOptimize("");               /* Solve the LP */
            basis = p.saveBasis();          /* Save the current basis */
            objval = p.getObjVal();         /* Get the objective value */

            /* Get the solution values: */
            for(j=0;j<npatt;j++)  solpat[j]=pat[j].getSol();
            for(i=0;i<NWIDTHS;i++)  dualdem[i]=dem[i].getDual();

            /* Solve integer knapsack problem  z = min{cx : ax<=r, x in Z^n}
               with r=MAXWIDTH, n=NWIDTHS */
            z = knapsack(bcl, NWIDTHS, dualdem, WIDTH, (double)MAXWIDTH, DEMAND, x);
            /* Force garbage collection to clean up subproblem: */
            /*   System.gc();
                 System.runFinalization();
            */
            System.out.print("(" + (XPRB.getTime()-starttime)/1000.0 + " sec) Pass " +
                             (npass+1) + ": ");

            if(z < 1+EPS) {
                System.out.println("no profitable column found.");
                System.out.println();
                basis=null;                     /* No need to keep the basis any longer */
                break;
            }
            else {
                /* Print the new pattern: */
                System.out.println("new pattern found with marginal cost " + (z-1) );
                System.out.print("   Widths distribution: ");
                dw=0;
                for(i=0;i<NWIDTHS;i++) {
                    System.out.print(WIDTH[i] +":"+ x[i] +"  ");
                    dw += WIDTH[i]*x[i];
                }
                System.out.println("Total width: " + dw);

                /* Create a new variable for this pattern: */
                pat[npatt]=p.newVar("pat_"+(npatt+1),XPRB.UI);

                cobj .add(pat[npatt]);          /* Add new var. to the objective */
                dw=0;
                for(i=0; i<NWIDTHS; i++)        /* Add new var. to demand constraints*/
                    if(x[i] > EPS) {
                        dem[i].add(pat[npatt].mul(x[i]));
                        if((int)Math.ceil((double)DEMAND[i]/x[i]) > dw)
                            dw = (int)Math.ceil((double)DEMAND[i]/x[i]);
                    }
                pat[npatt].setUB(dw);           /* Change the upper bound on the new var.*/
                npatt++;

                p.loadMat();                    /* Reload the problem */
                p.loadBasis(basis);             /* Load the saved basis */
                basis=null;                     /* No need to keep the basis any longer */
            }
        }

        p.mipOptimize("");                /* Solve the MIP */

        System.out.println("(" + (XPRB.getTime()-starttime)/1000.0 +
                           " sec) Optimal solution: " + p.getObjVal() + " rolls, " + npatt +
                           " patterns");
        System.out.print("   Rolls per pattern: ");
        for(i=0;i<npatt;i++) System.out.print(pat[i].getSol() + ", ");
        System.out.println();
    }

    /**************************************************************************/
    /* Integer Knapsack Algorithm for solving the integer knapsack problem    */
    /*    z = max{cx : ax <= R, x <= d, x in Z^N}                             */
    /*                                                                        */
    /* Input data:                                                            */
    /*   N:        Number of item types                                       */
    /*   c[i]:     Unit profit of item type i, i=1..n                         */
    /*   a[i]:     Unit resource use of item type i, i=1..n                   */
    /*   R:        Total resource available                                   */
    /*   d[i]:     Demand for item type i, i=1..n                             */
    /* Return values:                                                         */
    /*   xbest[i]: Number of items of type i used in optimal solution         */
    /*   zbest:    Value of optimal solution                                  */
    /**************************************************************************/
    static double knapsack(XPRB bcl, int N, double[] c, double[] a, double R, int[] d, int[] xbest) {
        /*
          System.out.println("Solving z = max{cx : ax <= b; x in Z^n}");
          System.out.print("   c   =");
          for(j = 0; j < N; j++)  System.out.print(" " + c[j] + ",");
          System.out.println();
          System.out.print("   a   =");
          for(j = 0; j < N; j++)  System.out.print(" " + a[j] + ",");
          System.out.println();
          System.out.print("   c/a =");
          for (j = 0; j < N; j++)  System.out.print(" " + c[j]/a[j] + ",");
          System.out.println();
          System.out.print("   b   = " + R);
        */

        try (XPRBprob pk = bcl.newProb("Knapsack")) {
            XPRBvar[] x = new XPRBvar[N];
            for(int j=0;j<N;j++) x[j]=pk.newVar("x", XPRB.UI, 0, d[j]);

            XPRBexpr klobj = new XPRBexpr();
            for(int j=0;j<N;j++) klobj.add(x[j].mul(c[j]));
            pk.setObj(klobj);
            XPRBexpr knap = new XPRBexpr();
            for(int j=0;j<N;j++) knap.add(x[j].mul(a[j]));
            pk.newCtr("KnapXPRBctr", knap.lEql(R) );
            pk.setSense(XPRB.MAXIM);
            pk.mipOptimize("");

            double zbest = pk.getObjVal();
            for(int j=0;j<N;j++) xbest[j]=(int)Math.floor(x[j].getSol() + 0.5);
            /*
              System.out.println("   z = " + zbest);
              System.out.print("   x =");
              for(j=0; j<N; j++) System.out.print(" " + xbest[j] + ",");
              System.out.println();
            */

            return (zbest);
        }
    }

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

    public static void main(String[] args) throws XPRSexception {
        try (XPRB bcl = new XPRB();            /* Initialize BCL */
             XPRBprob p = bcl.newProb("Els");  /* Create a new problem */
             XPRS xprs = new XPRS()) {         /* Initialize Xpress-Optimizer */
            modCutStock(p);                    /* Model the problem */
            solveCutStock(bcl, p);             /* Solve the problem */
        }
    }
}

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