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

  file xbairport.cxx
  ``````````````````
  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 Fair Isaac Corporation
      author: S.Heipcke, June 2008, rev. Mar. 2011
********************************************************/

#include <iostream>
#include "xprb_cpp.h"
#include "xprs.h"

using namespace std;
using namespace ::dashoptimization;

#define N 42

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};
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};
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};

int main(int argc, char **argv)
{
 int i,j;
 XPRBvar x[N],y[N];
 XPRBexpr qe;
 XPRBctr cobj, c;
 XPRBprob prob("airport");              // Initialize a new problem in BCL

/**** VARIABLES ****/
 for(i=0;i<N;i++) 
  x[i] = prob.newVar(XPRBnewname("x(%d)",i+1), XPRB_PL, -10, 10);
 for(i=0;i<N;i++) 
  y[i] = prob.newVar(XPRBnewname("y(%d)",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=0;
 for(i=0;i<N-1;i++)
  for(j=i+1;j<N;j++) qe+= sqr(x[i]-x[j])+sqr(y[i]-y[j]);
 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", sqr(x[i]-CX[i])+sqr(y[i]-CY[i]) <= 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

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

 return 0;
}