void
MultilinearFormulation::makeTermByTerm()
{
// First we do some processing of the instance to determine how many
// multilinear or quadratic constraints, and we store the indicies
// in the instance for later
vector<int> lcid;
vector<int> mlcid;
for(ConstConstraintIterator it = originalInstance_->consBegin();
it != originalInstance_->consEnd(); ++it) {
FunctionType ft = (*it)->getFunctionType();
if (ft == Multilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Bilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Linear) {
lcid.push_back((*it)->getId());
}
}
// add x variables
vector<double> lb;
vector<double> ub;
vector<VariablePtr> xvars;
int nv = 0;
for (ConstVariableIterator it = originalInstance_->varsBegin();
it != originalInstance_->varsEnd(); ++it) {
VariablePtr v = *it;
VariablePtr vnew = VariablePtr(new Variable(nv, v->getLb(), v->getUb(), v->getType()));
lb.push_back(v->getLb());
ub.push_back(v->getUb());
variableMapping_.insert(make_pair(vnew,v));
variables_.push_back(vnew);
xvars.push_back(vnew);
nv++;
}
// Add the linear constraints
for(int i = 0; i < lcid.size(); i++) {
const ConstraintPtr mlc = originalInstance_->getConstraint(lcid[i]);
const LinearFunctionPtr olf = mlc->getLinearFunction();
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
for(ConstVariableGroupIterator it = olf->varsBegin(); it != olf->varsEnd(); ++it) {
lf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, mlc->getLb(), mlc->getUb());
constraints_.push_back(c);
#if defined(DEBUG_TERM_BY_TERM)
c->display();
#endif
}
// The w variables
vector<VariablePtr> wvars;
// This holds a map between the 'w' variable added and indices of x vars in multilinear product
map <VariablePtr, vector<int> > mlterms;
// Go through multilinear rows. Add constraints, and create maps
for(int i = 0; i < mlcid.size(); i++) {
const ConstraintPtr omlc = originalInstance_->getConstraint(mlcid[i]);
const LinearFunctionPtr olf = omlc->getLinearFunction();
const QuadraticFunctionPtr oqf = omlc->getQuadraticFunction();
const NonlinearFunctionPtr onlf = omlc->getNonlinearFunction();
//!!! Don't make this shared by boost, it will get confused in counting
MultilinearFunction *omlf = dynamic_cast<MultilinearFunction *>(onlf.get());
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
// Linear part of constraint remains the same
for(ConstVariableGroupIterator it = olf->varsBegin(); it != olf->varsEnd(); ++it) {
lf->addTerm(xvars[it->first->getId()], it->second);
}
// Quadratic part gets a new variable for every term
for(ConstVariablePairGroupIterator it = oqf->begin(); it != oqf->end(); ++it) {
vector<int> mlix;
mlix.push_back(it->first.first->getId());
mlix.push_back(it->first.second->getId());
VariablePtr w = VariablePtr(new Variable(nv, -INFINITY,INFINITY, Continuous));
nv++;
variables_.push_back(w);
wvars.push_back(w);
//XXX Need to store term for evaluation
mlterms.insert(make_pair(w,mlix));
lf->addTerm(w,it->second);
}
// Multilinear part gets a new var for every term
for(constMultilinearTermContainerIterator it = omlf->termsBegin();
it != omlf->termsEnd(); ++it) {
vector<int> mlix;
for(set<ConstVariablePtr>::const_iterator it2 = it->second.begin();
it2 != it->second.end(); ++it2) {
mlix.push_back((*it2)->getId());
}
VariablePtr w = VariablePtr(new Variable(nv, -INFINITY, INFINITY, Continuous));
nv++;
variables_.push_back(w);
wvars.push_back(w);
mlterms.insert(make_pair(w,mlix));
lf->addTerm(w,it->first);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, omlc->getLb(), omlc->getUb());
constraints_.push_back(c);
#if defined(DEBUG_TERM_BY_TERM)
c->display();
#endif
}
// Now add all the constraints for each new bilinear/multilinear term
for(map<VariablePtr, vector<int> >::iterator it = mlterms.begin();
it != mlterms.end(); ++it) {
ConstVariablePtr w = it->first;
vector<int> &mlix = it->second;
#if defined(DEBUG_TERM_BY_TERM)
cout << "mlix: ";
copy(mlix.begin(), mlix.end(), ostream_iterator<int>(cout, " "));
cout << endl;
#endif
// Enumerate extreme points
vector<vector<double> > V;
vector<VariablePtr> lambdavars;
allExtreme(mlix, lb, ub, V);
// Add lambda vars
for(UInt j = 0; j < V.size(); j++) {
VariablePtr vnew = VariablePtr(new Variable(nv,0.0,1.0,Continuous));
variables_.push_back(vnew);
nv++;
lambdavars.push_back(vnew);
}
// Write x as convex combination of lambda (for each component)
for(UInt k = 0; k < mlix.size(); k++) {
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
lf->addTerm(xvars[mlix[k]], -1.0);
for(UInt j = 0; j < V.size(); j++) {
lf->addTerm(lambdavars[j], V[j][k]);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, 0.0, 0.0);
constraints_.push_back(c);
#if defined(DEBUG_TERM_BY_TERM)
c->display();
#endif
}
// Write w (term) as convex combination of function values at extreme points
LinearFunctionPtr wlf = LinearFunctionPtr(new LinearFunction());
wlf->addTerm(w, -1.0);
for(int j = 0; j < V.size(); j++) {
// Evaluation at extreme point is just the product
double product = 1.0;
for(int k = 0; k < V[j].size(); k++) {
product *= V[j][k];
}
if (product > 1.0e-9 || product < -1.0e-9) {
wlf->addTerm(lambdavars[j], product);
}
}
FunctionPtr wf = (FunctionPtr) new Function(wlf);
ConstraintPtr wc = (ConstraintPtr) new Constraint(wf, 0.0, 0.0);
constraints_.push_back(wc);
#if defined(DEBUG_TERM_BY_TERM)
wc->display();
#endif
// Also add sum (lambda) = 1
LinearFunctionPtr convex_lf = LinearFunctionPtr(new LinearFunction());
for(int j = 0; j < V.size(); j++) {
convex_lf->addTerm(lambdavars[j], 1.0);
}
FunctionPtr convex_f = (FunctionPtr) new Function(convex_lf);
ConstraintPtr convex_c = (ConstraintPtr) new Constraint(convex_f, 1.0, 1.0);
constraints_.push_back(convex_c);
#if defined(DEBUG_TERM_BY_TERM)
convex_c->display();
#endif
}
LinearFunctionPtr olf = LinearFunctionPtr(new LinearFunction());
const LinearFunctionPtr originalInstance_olf = originalInstance_->getObjective()->getLinearFunction();
for (ConstVariableGroupIterator it = originalInstance_olf->varsBegin();
it != originalInstance_olf->varsEnd(); ++it) {
olf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr of = (FunctionPtr) new Function(olf);
objective_ = ObjectivePtr(new Objective(of, 0));
}
void
MultilinearFormulation::makeConvexHull()
{
// First we do some processing of the instance to determine how many
// multilinear or quadratic constraints, and we store the indicies
// in the instance for later
vector<int> lcid;
vector<int> mlcid;
for(ConstConstraintIterator it = originalInstance_->consBegin();
it != originalInstance_->consEnd(); ++it) {
FunctionType ft = (*it)->getFunctionType();
if (ft == Multilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Bilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Linear) {
lcid.push_back((*it)->getId());
}
}
// add x variables
vector<double> lb;
vector<double> ub;
vector<VariablePtr> xvars;
int nv = 0;
for (ConstVariableIterator it = originalInstance_->varsBegin();
it != originalInstance_->varsEnd(); ++it) {
VariablePtr v = *it;
VariablePtr vnew = VariablePtr(new Variable(nv, v->getLb(), v->getUb(), v->getType()));
lb.push_back(v->getLb());
ub.push_back(v->getUb());
variableMapping_.insert(make_pair(vnew,v));
variables_.push_back(vnew);
xvars.push_back(vnew);
nv++;
}
// Add z vars
vector<VariablePtr> zvars;
for(UInt i = 0; i < mlcid.size(); i++) {
const ConstraintPtr mlc = originalInstance_->getConstraint(mlcid[i]);
VariablePtr vnew = VariablePtr(new Variable(nv,mlc->getLb(),mlc->getUb(),Continuous));
variables_.push_back(vnew);
zvars.push_back(vnew);
nv++;
}
// Enumerate all extreme points
int origNumVars = originalInstance_->getNumVars();
vector<int> S(origNumVars);
for(int i = 0; i < origNumVars; i++) {
S[i] = i;
}
vector<vector<double> > V;
allExtreme(S, lb, ub, V);
// Add lambda variables
vector<VariablePtr> lambdavars;
for(UInt i = 0; i < V.size(); i++) {
VariablePtr vnew = VariablePtr(new Variable(nv,0.0,1.0,Continuous));
variables_.push_back(vnew);
lambdavars.push_back(vnew);
nv++;
}
// Add the original linear constraints (on x)
for(int i = 0; i < lcid.size(); i++) {
const ConstraintPtr mlc = originalInstance_->getConstraint(lcid[i]);
const LinearFunctionPtr olf = mlc->getLinearFunction();
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
for(ConstVariableGroupIterator it = olf->varsBegin(); it != olf->varsEnd(); ++it) {
lf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, mlc->getLb(), mlc->getUb());
constraints_.push_back(c);
#if defined(DEBUG_CONVEX_HULL)
c->display();
#endif
}
// Write x in terms of extreme points
for(int i = 0; i < origNumVars; i++) {
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
lf->addTerm(xvars[i], -1.0);
for(int j = 0; j < V.size(); j++) {
lf->addTerm(lambdavars[j], V[j][i]);
}
//lf->display();
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, 0.0, 0.0);
constraints_.push_back(c);
//XXX Should I set the ID?
#if defined(DEBUG_CONVEX_HULL)
c->display();
#endif
}
// Write z in terms of extreme points
for(int i = 0; i < mlcid.size(); i++) {
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
lf->addTerm(zvars[i], -1.0);
const ConstraintPtr mlc = originalInstance_->getConstraint(mlcid[i]);
const FunctionPtr mlf = mlc->getFunction();
for(int j = 0; j < V.size(); j++) {
double zval = mlf->eval(V[j]);
//cout << "zval = " << zval << endl;
lf->addTerm(lambdavars[j], zval);
}
//lf->display(); cout << endl << endl;
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, 0.0, 0.0);
constraints_.push_back(c);
#if defined(DEBUG_CONVEX_HULL)
c->display();
#endif
}
// Add convexity constraint
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
for(int j = 0; j < V.size(); j++) {
lf->addTerm(lambdavars[j], 1.0);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, 1.0, 1.0);
constraints_.push_back(c);
#if defined(DEBUG_CONVEX_HULL)
c->display();
#endif
LinearFunctionPtr olf = LinearFunctionPtr(new LinearFunction());
// Add objective (on x vars only)
const LinearFunctionPtr originalInstance_olf = originalInstance_->getObjective()->getLinearFunction();
for (ConstVariableGroupIterator it = originalInstance_olf->varsBegin();
it != originalInstance_olf->varsEnd(); ++it) {
olf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr of = (FunctionPtr) new Function(olf);
objective_ = ObjectivePtr(new Objective(of, 0));
}
void
MultilinearFormulation::makeRowByRow()
{
// First we do some processing of the instance to determine how many
// multilinear or quadratic constraints, and we store the indicies
// for later
vector<int> lcid;
vector<int> mlcid;
for(ConstConstraintIterator it = originalInstance_->consBegin();
it != originalInstance_->consEnd(); ++it) {
FunctionType ft = (*it)->getFunctionType();
if (ft == Multilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Bilinear) {
mlcid.push_back((*it)->getId());
}
else if (ft == Linear) {
lcid.push_back((*it)->getId());
}
}
// add x variables
vector<double> lb;
vector<double> ub;
vector<VariablePtr> xvars;
int nv = 0;
for (ConstVariableIterator it = originalInstance_->varsBegin();
it != originalInstance_->varsEnd(); ++it) {
VariablePtr v = *it;
VariablePtr vnew = VariablePtr(new Variable(nv, v->getLb(), v->getUb(), v->getType()));
lb.push_back(v->getLb());
ub.push_back(v->getUb());
variableMapping_.insert(make_pair(vnew,v));
variables_.push_back(vnew);
xvars.push_back(vnew);
nv++;
}
// Add the linear constraints
for(int i = 0; i < lcid.size(); i++) {
const ConstraintPtr mlc = originalInstance_->getConstraint(lcid[i]);
const LinearFunctionPtr olf = mlc->getLinearFunction();
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
for(ConstVariableGroupIterator it = olf->varsBegin(); it != olf->varsEnd(); ++it) {
lf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, mlc->getLb(), mlc->getUb());
constraints_.push_back(c);
}
vector<VariablePtr> zvars;
vector<vector< VariablePtr> > lambdavars(mlcid.size());
for(UInt i = 0; i < mlcid.size(); i++) {
// One 'z' var per row
VariablePtr zvar = VariablePtr(new Variable(nv, -INFINITY, INFINITY, Continuous));
variables_.push_back(zvar);
zvars.push_back(zvar);
nv++;
// Determine what variables appear nonlinearly...
const ConstraintPtr mlc = originalInstance_->getConstraint(mlcid[i]);
vector<int> nlvars = nonlinearVarsInConstraint(mlc);
#if defined(DEBUG_ROW_BY_ROW)
cout << "Vars in ml constraint " << i << " have ix: ";
for(vector<int>::iterator it = nlvars.begin(); it != nlvars.end(); ++it) {
cout << (*it) << " ";
}
cout << endl;
#endif
// Add lambda vars for this row
vector<vector<double> > V;
allExtreme(nlvars, lb, ub, V);
for(UInt j = 0; j < V.size(); j++) {
VariablePtr vnew = VariablePtr(new Variable(nv,0.0,1.0,Continuous));
variables_.push_back(vnew);
lambdavars[i].push_back(vnew);
nv++;
}
for(UInt k = 0; k < nlvars.size(); k++) {
// Create 'x' portion of this constraint
LinearFunctionPtr lf = LinearFunctionPtr(new LinearFunction());
lf->addTerm(xvars[nlvars[k]], -1.0);
for(UInt j = 0; j < V.size(); j++) {
lf->addTerm(lambdavars[i][j], V[j][k]);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, 0.0, 0.0);
constraints_.push_back(c);
#if defined(DEBUG_ROW_BY_ROW)
c->display();
#endif
}
// Now add the 'z' var definition
LinearFunctionPtr tlf = LinearFunctionPtr(new LinearFunction());
tlf->addTerm(zvar, -1.0);
const FunctionPtr mlf = mlc->getFunction();
const LinearFunctionPtr mlf_lf = mlf->getLinearFunction();
for(int j = 0; j < V.size(); j++) {
//XXX Kludgy, but just create a vector for the (full) point
int onv = originalInstance_->getNumVars();
vector<double> xe(onv,0.0);
for(UInt k = 0; k < nlvars.size(); k++) {
xe[nlvars[k]] = V[j][k];
}
double zval = mlf->eval(xe);
// Need to subtract off linear part, since yuo keep those variables in
zval -= mlf_lf->eval(xe);
tlf->addTerm(lambdavars[i][j], zval);
}
FunctionPtr tf = (FunctionPtr) new Function(tlf);
ConstraintPtr tc = (ConstraintPtr) new Constraint(tf, 0.0, 0.0);
constraints_.push_back(tc);
#if defined(DEBUG_ROW_BY_ROW)
tc->display();
#endif
// Now add the linear constraint involving linear x and t
LinearFunctionPtr xtlf = LinearFunctionPtr(new LinearFunction());
for(ConstVariableGroupIterator it = mlf_lf->varsBegin(); it != mlf_lf->varsEnd(); ++it) {
xtlf->addTerm(xvars[it->first->getId()], it->second);
}
xtlf->addTerm(zvar,1.0);
FunctionPtr xtf = (FunctionPtr) new Function(xtlf);
ConstraintPtr xtc = (ConstraintPtr) new Constraint(xtf, mlc->getLb(), mlc->getUb());
constraints_.push_back(xtc);
#if defined(DEBUG_ROW_BY_ROW)
xtc->display();
#endif
// Also add sum (lambda) = 1
LinearFunctionPtr convex_lf = LinearFunctionPtr(new LinearFunction());
for(int j = 0; j < V.size(); j++) {
convex_lf->addTerm(lambdavars[i][j], 1.0);
}
FunctionPtr convex_f = (FunctionPtr) new Function(convex_lf);
ConstraintPtr convex_c = (ConstraintPtr) new Constraint(convex_f, 1.0, 1.0);
constraints_.push_back(convex_c);
#if defined(DEBUG_ROW_BY_ROW)
convex_c->display();
#endif
}
LinearFunctionPtr olf = LinearFunctionPtr(new LinearFunction());
const LinearFunctionPtr originalInstance_olf = originalInstance_->getObjective()->getLinearFunction();
for (ConstVariableGroupIterator it = originalInstance_olf->varsBegin();
it != originalInstance_olf->varsEnd(); ++it) {
olf->addTerm(xvars[it->first->getId()], it->second);
}
FunctionPtr of = (FunctionPtr) new Function(olf);
objective_ = ObjectivePtr(new Objective(of, 0));
}