vector<const Match *> OptimalConstrainedMatches::calculateSubset()
{
_score = -1;
vector<const Match*> result;
if (_matches.size() == 0)
{
return result;
}
// figure out all the pairs of matches that conflict.
_calculateMatchConflicts();
// if there are no conflicts, then there is nothing to solve.
if (_conflicts.size() == 0)
{
LOG_DEBUG("No match conflicts found.");
return _matches;
}
// populate the solver with
IntegerProgrammingSolver solver;
_populateSolver(solver);
if (_timeLimit > 0)
{
solver.setTimeLimit(_timeLimit);
}
LOG_INFO("Calculating optimal match conflicts with an Integer Programming solution...");
// solve the Integer Programming problem.
solver.solve();
_score = solver.getObjectiveValue();
result.reserve(_matches.size());
// go through all the columns (variables)
for (int i = 0; i < solver.getNumColumns(); i++)
{
// if the value is close to 1 (as opposed to 0)
if (solver.getColumnPrimalValue(i + 1) > 0.99)
{
// it is a keeper
result.push_back(_matches[i]);
}
else
{
LOG_TRACE("Removing match: " << _matches[i]);
}
}
return result;
}
void OptimalConstrainedMatches::_populateSolver(IntegerProgrammingSolver& solver)
{
// try to maximize the score.
solver.setObjectiveDirection(GLP_MAX);
// each match is a column (variable) in the function that we want to maximize.
solver.addColumns(_matches.size());
for (size_t i = 0; i < _matches.size(); i++)
{
solver.setColumnKind(i + 1, GLP_BV);
//solver.setColumnBounds(i + 1, GLP_DB, 0.0, 1.0);
// The score of a match is the coefficient. This makes higher score matches worth
// more in the function.
solver.setObjectiveCoefficient(i + 1, _matches[i]->getScore() + EPSILON);
}
// there is one row (constraint) for each conflict.
solver.addRows(_conflicts.size());
vector<int> ia(_conflicts.size() * 2 + 1);
vector<int> ja(_conflicts.size() * 2 + 1);
vector<double> ra(_conflicts.size() * 2 + 1);
int i = 0;
for (MatchConflicts::ConflictMap::const_iterator it = _conflicts.constBegin();
it != _conflicts.constEnd(); ++it)
{
// Set the coefficients to 1 for each of the conflicting pairs and set the max value to 1. This
// will make it so only one of the values can be 1 at a time, or they can both be 0.
solver.setRowBounds(i + 1, GLP_DB, 0.0, 1.0);
ia[i * 2 + 1] = i + 1;
ja[i * 2 + 1] = (int)it.key() + 1;
ra[i * 2 + 1] = 1.0;
ia[i * 2 + 2] = i + 1;
ja[i * 2 + 2] = (int)it.value() + 1;
ra[i * 2 + 2] = 1.0;
i++;
}
// Populate the row coefficients.
solver.loadMatrix(ia, ja, ra);
}
void runTest()
{
double z, x1, x2, x3;
IntegerProgrammingSolver solver;
solver.setProblemName("sample");
solver.setObjectiveDirection(GLP_MAX);
solver.addRows(2);
solver.setRowName(1, "p");
solver.setRowBounds(1, GLP_DB, 0.0, 1.0);
solver.setRowName(2, "q");
solver.setRowBounds(2, GLP_DB, 0.0, 1.0);
solver.addColumns(3);
solver.setColumnName(1, "x1");
solver.setColumnKind(1, GLP_BV);
solver.setColumnBounds(1, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(1, 0.4);
solver.setColumnName(2, "x2");
solver.setColumnKind(2, GLP_BV);
solver.setColumnBounds(2, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(2, 0.9);
solver.setColumnName(3, "x3");
solver.setColumnKind(3, GLP_BV);
solver.setColumnBounds(3, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(3, 0.6);
vector<int> ia, ja;
vector<double> ar;
ia.push_back(-1);
ja.push_back(-1);
ar.push_back(-1);
ia.push_back(1); ja.push_back(1); ar.push_back(1.0);
ia.push_back(1); ja.push_back(2); ar.push_back(1.0);
ia.push_back(1); ja.push_back(3); ar.push_back(0.0);
//ia.push_back(2); ja.push_back(1); ar.push_back(0.0);
ia.push_back(2); ja.push_back(2); ar.push_back(1.0);
ia.push_back(2); ja.push_back(3); ar.push_back(1.0);
solver.loadMatrix(ia, ja, ar);
solver.solve();
z = solver.getObjectiveValue();
x1 = solver.getColumnPrimalValue(1);
x2 = solver.getColumnPrimalValue(2);
x3 = solver.getColumnPrimalValue(3);
//LOG_INFO("z: " << z << " x1: " << x1 << " x2: " << x2 << " x3: " << x3);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, z, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, x1, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, x2, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, x3, 1e-5);
solver.setObjectiveCoefficient(3, 0.4);
solver.solve();
z = solver.getObjectiveValue();
x1 = solver.getColumnPrimalValue(1);
x2 = solver.getColumnPrimalValue(2);
x3 = solver.getColumnPrimalValue(3);
//LOG_INFO("z: " << z << " x1: " << x1 << " x2: " << x2 << " x3: " << x3);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.9, z, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, x1, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, x2, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, x3, 1e-5);
}
void runTest2()
{
double z, x1, x2, x3;
IntegerProgrammingSolver solver;
solver.setProblemName("sample");
solver.setObjectiveDirection(GLP_MAX);
solver.addRows(1);
// 0.0 <= p <= 1.1
solver.setRowName(1, "p");
// make sure it properly solves an integer problem.
solver.setRowBounds(1, GLP_DB, 0.0, 1.1);
// z = x1 + 2 * x2 + x3
solver.addColumns(3);
solver.setColumnName(1, "x1");
solver.setColumnKind(1, GLP_BV);
solver.setColumnBounds(1, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(1, 1.0);
solver.setColumnName(2, "x2");
solver.setColumnKind(2, GLP_BV);
solver.setColumnBounds(2, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(2, 2.0);
solver.setColumnName(3, "x3");
solver.setColumnKind(3, GLP_BV);
solver.setColumnBounds(3, GLP_DB, 0.0, 1.0);
solver.setObjectiveCoefficient(3, 1.0);
vector<int> ia, ja;
vector<double> ar;
ia.push_back(-1);
ja.push_back(-1);
ar.push_back(-1);
// subject to constraint:
// p = x1 + x2 + 0 * x3
ia.push_back(1); ja.push_back(1); ar.push_back(1.0);
ia.push_back(1); ja.push_back(2); ar.push_back(1.0);
ia.push_back(1); ja.push_back(3); ar.push_back(0.0);
solver.loadMatrix(ia, ja, ar);
solver.solve();
z = solver.getObjectiveValue();
x1 = solver.getColumnPrimalValue(1);
x2 = solver.getColumnPrimalValue(2);
x3 = solver.getColumnPrimalValue(3);
//LOG_INFO("z: " << z << " x1: " << x1 << " x2: " << x2 << " x3: " << x3);
CPPUNIT_ASSERT_DOUBLES_EQUAL(3.0, z, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, x1, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, x2, 1e-5);
CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, x3, 1e-5);
}
