/********************************************************
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 XPRB bcl;
static XPRBprob p;
/***********************************************************************/
static void modCutStock() throws XPRSexception
{
int i,j;
XPRBexpr le;
bcl = new XPRB(); /* Initialize BCL */
p = bcl.newProb("CutStock"); /* Create a new problem in BCL */
XPRS.init();
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() 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(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(int N, double[] c, double[] a, double R, int[] d, int[] xbest)
{
int j;
double zbest = 0.0;
XPRBvar[] x;
XPRBexpr klobj, knap;
XPRBprob pk;
/*
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);
*/
pk = bcl.newProb("Knapsack");
x = new XPRBvar[N];
for(j=0;j<N;j++) x[j]=pk.newVar("x", XPRB.UI, 0, d[j]);
klobj = new XPRBexpr();
for(j=0;j<N;j++) klobj.add(x[j].mul(c[j]));
pk.setObj(klobj);
knap = new XPRBexpr();
for(j=0;j<N;j++) knap.add(x[j].mul(a[j]));
pk.newCtr("KnapXPRBctr", knap.lEql(R) );
pk.setSense(XPRB.MAXIM);
pk.mipOptimize("");
zbest = pk.getObjVal();
for(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();
*/
x = null;
pk = null;
return (zbest);
}
/***********************************************************************/
public static void main(String[] args) throws XPRSexception
{
modCutStock(); /* Model the problem */
solveCutStock(); /* Solve the problem */
}
}
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