Linear Programming: Modulo constraint - c++

Question

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?

Answer 1

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;
}