[Osi] How to use integer/binary variables with coin-or OSI interface (cplex)

[T L]

Hi List members,

I am learning coin OSI programming using the C++ interface (using CPLEX). I
have the following example code that works for continuous variables and
Linear Programming (LP) (based on online coin examples).

But I couldn't find instructions on how to use integer decision variables.

Could anyone help explain how to change the two decision variables x0 and
x1 to integer and/or binary variables?

Also, I am currently use CPLEX and have clp installed. To use MILP with
coin-or instead of CPLEX, what additional package do I need?

Thanks and regards,

// Example of using COIN-OR OSI, building the instance internally
// with sparse matrix object
#include <iostream>
//#include <coin/OsiClpSolverInterface.hpp>
#include <coin/OsiCpxSolverInterface.hpp>
#include <coin/CoinPackedMatrix.hpp>
#include <coin/CoinPackedVector.hpp>

int
main(void)
{
  // Create a problem pointer. We use the base class here.
  OsiSolverInterface *si;
  // When we instantiate the object, we need a specific derived class.
  //si = new OsiClpSolverInterface;
  si = new OsiCpxSolverInterface;
  // Build our own instance from scratch
/*
* This section adapted from Matt Galati's example
* on thise COIN-OR Tutorial website.
*
* Problem from Bertsimas, Tsitsiklis page 21
*
* optimal solution: x* = (1,1)
*
* minimize -1 x0 - 1 x1
* s.t 1 x0 + 2 x1 <= 3
* 2 x0 + 1 x1 <= 3
* x0 >= 0
* x1 >= 0
*/
  int n_cols = 2;
  double * col_lb = new double[n_cols];//the column lower bounds
  double * col_ub = new double[n_cols];//the column upper bounds
  //Define the variable lower/upper bounds.
  // x0 >= 0 => 0 <= x0 <= infinity
  // x1 >= 0 => 0 <= x1 <= infinity
  col_lb[0] = 0.0;
  col_lb[1] = 0.0;
  col_ub[0] = si->getInfinity();
  col_ub[1] = si->getInfinity();

  //Define the objective coefficients.
  //minimize -1 x0 - 1 x1
//  double * objective = new double[n_cols];//the objective coefficients
  std::vector<double> objective(n_cols, 0.0); //the objective coefficients
  objective[0] = -1.0;
  objective[1] = -1.0;

  int n_rows = 2;
  double * row_lb = new double[n_rows]; //the row lower bounds
  double * row_ub = new double[n_rows]; //the row upper bounds
  //Define the constraint matrix.
  CoinPackedMatrix * matrix = new CoinPackedMatrix(false,0,0);
  matrix->setDimensions(0, n_cols);
  //1 x0 + 2 x1 <= 3 => -infinity <= 1 x0 + 2 x2 <= 3
  CoinPackedVector row1;
  row1.insert(0, 1.0);
  row1.insert(1, 2.0);
  row_lb[0] = -1.0 * si->getInfinity();
  row_ub[0] = 3.0;

  matrix->appendRow(row1);
  //2 x0 + 1 x1 <= 3 => -infinity <= 2 x0 + 1 x1 <= 3
  CoinPackedVector row2;
  row2.insert(0, 2.0);
  row2.insert(1, 1.0);
  row_lb[1] = -1.0 * si->getInfinity();
  row_ub[1] = 3.0;
  matrix->appendRow(row2);
  //load the problem to OSI
  si->loadProblem(*matrix, col_lb, col_ub, objective.data(), row_lb,
row_ub);
  //write the MPS file to a file called example.mps
  si->writeMps("example");
  // Solve the (relaxation of the) problem
  si->initialSolve();
  // Check the solution
  if ( si->isProvenOptimal() )
  {
    std::cout << "Found optimal solution!" << std::endl;
    std::cout << "Objective value is " << si->getObjValue() << std::endl;
    int n = si->getNumCols();
    const double *solution;
    solution = si->getColSolution();
    // We could then print the solution or examine it.
  }
  else
  {
    std::cout << "Didn't find optimal solution." << std::endl;
    // Could then check other status functions.
  }
  return 0;
}
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