vector<int>
MultilinearFormulation::nonlinearVarsInConstraint(const ConstraintPtr c)
{
set<int> ix;
const QuadraticFunctionPtr qf = c->getQuadraticFunction();
const NonlinearFunctionPtr nlf = c->getNonlinearFunction();
const MultilinearFunction *mlf = dynamic_cast<MultilinearFunction *>(nlf.get());
for(ConstVariablePairGroupIterator it = qf->begin(); it != qf->end(); ++it) {
ix.insert(it->first.first->getId());
ix.insert(it->first.second->getId());
}
for(constMultilinearTermContainerIterator it = mlf->termsBegin();
it != mlf->termsEnd();
++it) {
for(set<ConstVariablePtr>::const_iterator it2 = it->second.begin();
it2 != it->second.end(); ++it2) {
ix.insert((*it2)->getId());
}
}
vector<int> vix;
for(set<int>::const_iterator it = ix.begin(); it != ix.end(); ++it) {
vix.push_back(*it);
}
return vix;
}
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::makeMcCormick()
{
// 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);
}
// The w variables
vector<VariablePtr> wvars;
// The z vars: These are what you put in the objective
vector<ConstVariablePtr> zvars;
// The bilinear terms
map <VariablePtr, ConstVariablePair> blterms;
// Go through multilinear rows. Add constraints, and create maps
// for mccormick vars
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) {
ConstVariablePtr x1 = it->first.first;
ConstVariablePtr x2 = it->first.second;
//Bounds on product depend on whether variable bounds are < 0, > 0
double lb = 0.0;
double ub = 0.0;
boundsOnProduct(x1,x2,lb,ub);
VariablePtr w = VariablePtr(new Variable(nv, lb, ub, Continuous));
nv++;
variables_.push_back(w);
wvars.push_back(w);
blterms.insert(make_pair(w,ConstVariablePair(x1,x2)));
lf->addTerm(w,it->second);
}
// Multilinear part gets d-1 new vars.
// We do mccormick (for now) in the FIFO way
for(constMultilinearTermContainerIterator it = omlf->termsBegin();
it != omlf->termsEnd(); ++it) {
set<ConstVariablePtr>::const_iterator it2 = it->second.begin();
ConstVariablePtr x1 = *it2;
++it2;
for( ; it2 != it->second.end(); ++it2) {
ConstVariablePtr x2 = *it2;
double lb = 0.0;
double ub = 0.0;
boundsOnProduct(x1,x2,lb,ub);
VariablePtr w = VariablePtr(new Variable(nv, lb, ub, Continuous));
nv++;
variables_.push_back(w);
wvars.push_back(w);
blterms.insert(make_pair(w,ConstVariablePair(x1,x2)));
x1 = w;
}
// Now x1 is the var you should add to the linear constraint
lf->addTerm(x1,it->first);
zvars.push_back(x1);
}
FunctionPtr f = (FunctionPtr) new Function(lf);
ConstraintPtr c = (ConstraintPtr) new Constraint(f, omlc->getLb(), omlc->getUb());
constraints_.push_back(c);
}
// Now add all the constraints for each new bilinear term
for(map<VariablePtr, ConstVariablePair>::iterator it = blterms.begin();
it != blterms.end(); ++it) {
ConstVariablePtr w = it->first;
ConstVariablePtr x1 = it->second.first;
ConstVariablePtr x2 = it->second.second;
LinearFunctionPtr lf1 = LinearFunctionPtr(new LinearFunction());
LinearFunctionPtr lf2 = LinearFunctionPtr(new LinearFunction());
LinearFunctionPtr lfw = LinearFunctionPtr(new LinearFunction());
// Create new lambda variables
VariablePtr lamll = VariablePtr(new Variable(nv, 0.0, 1.0, Continuous));
nv++;
variables_.push_back(lamll);
VariablePtr lamul = VariablePtr(new Variable(nv, 0.0, 1.0, Continuous));
nv++;
variables_.push_back(lamul);
VariablePtr lamuu = VariablePtr(new Variable(nv, 0.0, 1.0, Continuous));
nv++;
variables_.push_back(lamuu);
VariablePtr lamlu = VariablePtr(new Variable(nv, 0.0, 1.0, Continuous));
nv++;
variables_.push_back(lamlu);
// Just enumerate extreme points yourself
lf1->addTerm(x1,-1.0);
lf1->addTerm(lamll, x1->getLb());
lf1->addTerm(lamul, x1->getUb());
lf1->addTerm(lamuu, x1->getUb());
lf1->addTerm(lamlu, x1->getLb());
// Just enumerate extreme points yourself
lf2->addTerm(x2,-1.0);
lf2->addTerm(lamll, x2->getLb());
lf2->addTerm(lamul, x2->getLb());
lf2->addTerm(lamuu, x2->getUb());
lf2->addTerm(lamlu, x2->getUb());
lfw->addTerm(w, -1.0);
lfw->addTerm(lamll, x1->getLb()*x2->getLb());
lfw->addTerm(lamul, x1->getUb()*x2->getLb());
lfw->addTerm(lamuu, x1->getUb()*x2->getUb());
lfw->addTerm(lamlu, x1->getLb()*x2->getUb());
// Add the x1,x2,and w rows
FunctionPtr f1 = (FunctionPtr) new Function(lf1);
ConstraintPtr c1 = (ConstraintPtr) new Constraint(f1, 0.0, 0.0);
constraints_.push_back(c1);
FunctionPtr f2 = (FunctionPtr) new Function(lf2);
ConstraintPtr c2 = (ConstraintPtr) new Constraint(f2, 0.0, 0.0);
constraints_.push_back(c2);
FunctionPtr fw = (FunctionPtr) new Function(lfw);
ConstraintPtr cw = (ConstraintPtr) new Constraint(fw, 0.0, 0.0);
constraints_.push_back(cw);
// Add the convexity constraint
LinearFunctionPtr convex_lf = LinearFunctionPtr(new LinearFunction());
convex_lf->addTerm(lamll, 1.0);
convex_lf->addTerm(lamul, 1.0);
convex_lf->addTerm(lamuu, 1.0);
convex_lf->addTerm(lamlu, 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);
}
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));
}