Linear Programming: Modulo constraint

I am using Coin-Or's rehearse to implement linear programming.

I need a modulo constraint. Example: x shall be a multiple of 3.

OsiCbcSolverInterface solver;
CelModel model(solver);
CelNumVar x;
CelIntVar z;

unsigned int mod = 3;

// Maximize

solver.setObjSense(-1.0);

model.setObjective(x);

model.addConstraint(x <= 7.5);

// The modulo constraint:

model.addConstraint(x == z * mod);

The result for x should be 6. However, z is set to 2.5, which should not be possible as I declared it as a CellIntVar.

How can I enforce z to be an integer?

Solution

I never used that lib, but you i think you should follow the tests.

The core message comes from the readme:

If you want some of your variables to be integers, use CelIntVar instead of CelNumVar. You must bind the solver to an Integer Linear Programming solver as well, for example Coin-cbc.

Looking at Rehearse/tests/testRehearse.cpp -> exemple4() (here presented: incomplete code; no copy-paste):

OsiClpSolverInterface *solver = new OsiClpSolverInterface();

CelModel model(*solver);

...
CelIntVar x1("x1");
...
solver->initialSolve();       // this is the relaxation (and maybe presolving)!
...
CbcModel cbcModel(*solver);   // MIP-solver
cbcModel.branchAndBound();    // Use MIP-solver

printf("Solution for x1 : %g\n", model.getSolutionValue(x1, *cbcModel.solver()));
printf("Solution objvalue = : %g\n", cbcModel.solver()->getObjValue());

This kind of usage (use Osi to get LP-solver; build MIP-solver on top of that Osi-provided-LP-solver and call brandAndBound) basically follows Cbc's internal interface (with python's cylp this looks similar).

Just as reference: This is the official CoinOR Cbc (Rehearse-free) example from here:

// Copyright (C) 2005, International Business Machines
// Corporation and others.  All Rights Reserved.

#include "CbcModel.hpp"

// Using CLP as the solver
#include "OsiClpSolverInterface.hpp"

int main (int argc, const char *argv[])
{
  OsiClpSolverInterface solver1;

  // Read in example model in MPS file format
  // and assert that it is a clean model
  int numMpsReadErrors = solver1.readMps("../../Mps/Sample/p0033.mps","");
  assert(numMpsReadErrors==0);

  // Pass the solver with the problem to be solved to CbcModel 
  CbcModel model(solver1);

  // Do complete search
  model.branchAndBound();

  /* Print the solution.  CbcModel clones the solver so we
     need to get current copy from the CbcModel */
  int numberColumns = model.solver()->getNumCols();

  const double * solution = model.bestSolution();

  for (int iColumn=0;iColumn<numberColumns;iColumn++) {
    double value=solution[iColumn];
    if (fabs(value)>1.0e-7&&model.solver()->isInteger(iColumn)) 
      printf("%d has value %g\n",iColumn,value);
   }
  return 0;
}