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UG - Examples from 'BCL Reference Manual'

Description
The following examples are discussed in detail in the 'BCL User Guide and Reference Manual':
  • modeling and solving a small MIP scheduling problem (xbexpl1 version BASIC)
  • using variable arrays and constraint templates (xbexpl1 versions ARRAY and ARRAYC)
  • definition of SOS-1 (xbexpl1 version SOS)
  • data input from file, index sets (xbexpl1i)
  • user error handling, output redirection (xbexpl3)
  • solving multiple scenarios of a transportation problem in parallel (xbexpl2: standard, single thread version)
  • cut generation / adding cuts at MIP tree nodes (xbcutex)
  • quadratic programming (quadratic objective: xbqpr12, quadratic constraints: xbairport)
  • combine BCL problem input with problem solving in Xpress Optimizer (xbcontr1)
  • use an Xpress Optimizer solution callback with a BCL model (xbcontr2s: single MIP thread; xbcontr2: multiple MIP threads)
Further explanation of this example: 'BCL Reference Manual', Appendix B Using BCL with the Optimizer library


Source Files

Data Files





xbairport.java

/********************************************************
  BCL Example Problems
  ====================

  file xbairport.java
  ```````````````````
  QCQP problem by
      Rodrigo de Barros Nabholz & Maria Aparecida Diniz Ehrhardt
      November 1994, DMA - IMECC- UNICAMP.
  Based on AMPL model airport.mod by Hande Y. Benson
  (Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/ )

  (c) 2008-2024 Fair Isaac Corporation
      author: S.Heipcke, June 2008, rev. Dec. 2011
********************************************************/

import java.io.*;
import com.dashoptimization.*;

public class xbairport {
    static final int N = 42;

    static final double CX[] = {-6.3, -7.8, -9, -7.2, -5.7, -1.9, -3.5, -0.5, 1.4,
                                4, 2.1, 5.5, 5.7, 5.7, 3.8, 5.3, 4.7, 3.3, 0, -1, -0.4, 4.2,
                                3.2, 1.7, 3.3, 2, 0.7, 0.1, -0.1, -3.5, -4, -2.7, -0.5, -2.9,
                                -1.2, -0.4, -0.1, -1, -1.7, -2.1, -1.8, 0};
    static final double CY[] = {8, 5.1, 2, 2.6, 5.5, 7.1, 5.9, 6.6, 6.1, 5.6, 4.9,
                                4.7, 4.3, 3.6, 4.1, 3, 2.4, 3, 4.7, 3.4, 2.3, 1.5, 0.5, -1.7, -2,
                                -3.1, -3.5, -2.4, -1.3, 0, -1.7, -2.1, -0.4, -2.9, -3.4, -4.3,
                                -5.2, -6.5, -7.5, -6.4, -5.1, 0};
    static final double R[] = {0.09, 0.3, 0.09, 0.45, 0.5, 0.04, 0.1, 0.02, 0.02,
                               0.07, 0.4, 0.045, 0.05, 0.056, 0.36, 0.08, 0.07, 0.36, 0.67, 0.38,
                               0.37, 0.05, 0.4, 0.66, 0.05, 0.07, 0.08, 0.3, 0.31, 0.49, 0.09,
                               0.46, 0.12, 0.07, 0.07, 0.09, 0.05, 0.13, 0.16, 0.46, 0.25, 0.1};

    public static void main(String[] args) throws IOException {
        int i,j;
        XPRBvar[] x,y;                        /* x-/y-coordinates to determine */
        XPRBexpr qe;
        XPRBctr cobj, c;

        try (XPRBprob prob = new XPRBprob("airport")) { /* Initialize BCL and create a new problem */

            /**** VARIABLES ****/
            x = new XPRBvar[N];
            for(i=0;i<N;i++)
                x[i] = prob.newVar("x(" + (i+1) + ")", XPRB.PL, -10, 10);
            y = new XPRBvar[N];
            for(i=0;i<N;i++)
                y[i] = prob.newVar("y(" + (i+1) + ")", XPRB.PL, -10, 10);

            /****OBJECTIVE****/
            /* Minimize the total distance between all points */
            /*  sum(i in 1..N-1,j in i+1..N) ((x(i)-x(j))^2+(y(i)-y(j))^2)  */
            qe = new XPRBexpr();
            for(i=0;i<N-1;i++)
                for(j=i+1;j<N;j++) qe .add((x[i].add(x[j].mul(-1))).sqr())
                                       .add((y[i].add(y[j].mul(-1))).sqr());
            cobj = prob.newCtr("TotDist", qe);
            prob.setObj(cobj);                     /* Set objective function */

            /**** CONSTRAINTS ****/
            /* All points within given distance of their target location */
            /*  (x(i)-CX(i))^2+(y(i)-CY(i))^2 <= R(i)  */
            for(i=0;i<N;i++)
                c = prob.newCtr("LimDist", (x[i].add(-CX[i])).sqr()
                                .add( (y[i].add(-CY[i])).sqr()) .lEql(R[i]) );

            /****SOLVING + OUTPUT****/
            prob.setSense(XPRB.MINIM);             /* Choose the sense of optimization */

            /* Problem printing and matrix output: */
            /*
              prob.print();
              prob.exportProb(XPRB.MPS, "airport");
              prob.exportProb(XPRB.LP, "airport");
            */

            prob.lpOptimize("");                   /* Solve the problem */

            System.out.println("Solution: " + prob.getObjVal());
            for(i=0;i<N;i++)
                System.out.println(x[i].getName() + ": " + x[i].getSol() + ", " +
                                   y[i].getName() + ": " + y[i].getSol());
        }
    }
}

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