// This chunk of code adds
// z_t = \sum_{k=1}^{2 |V_g|} \lambda_k^g, \Prod_{j \in J_t} \chi_j^{g,k}
// \forall J_t \subseteq V_g
void
MultilinearTermsHandler::handleZDefConstraints_(RelaxationPtr relaxation, HandleCallingFunction wherefrom, ModVector &mods)
{
for(ConstTermIterator it = termsR_.begin(); it != termsR_.end(); ++it) {
ConstVariablePtr zt = it->first;
SetOfVars const &jt = it->second;
for (UInt gix = 0; gix < groups_.size(); ++gix) {
SetOfVars &vg = groups_[gix];
if (std::includes(vg.begin(), vg.end(), jt.begin(), jt.end())) {
// jt is a subset of vg, add constraint
LinearFunctionPtr lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(zt, -1.0);
int pix = 0;
for (std::set<SetOfVars>::iterator it2 = points_[gix].begin();
it2 != points_[gix].end(); ++it2) {
double prodval = 1.0;
VariablePtr lam = lambdavars_[gix][pix];
for(SetOfVars::const_iterator jt_it = jt.begin(); jt_it != jt.end(); ++jt_it) {
ConstVariablePtr xvar = *jt_it;
double tmp = varIsAtLowerBoundAtPoint_(xvar, *it2) ? xvar->getLb() : xvar->getUb();
prodval *= tmp;
}
lf->addTerm(lam, prodval);
++pix;
}
FunctionPtr f = (FunctionPtr) new Function(lf);
if (wherefrom == relaxInit_Call) {
ConstraintPtr c = relaxation->newConstraint(f, 0.0, 0.0);
zConMap_.insert(std::make_pair(IntVarPtrPair(gix, zt), c));
}
else {
IntVarPtrPairConstraintMap::iterator pos;
pos = zConMap_.find(IntVarPtrPair(gix, zt));
if (pos == zConMap_.end()) {
assert(0);
}
ConstraintPtr c = pos->second;
//XXX Here you should just check if the constraint really was going to
//change and do nothing if it doesn't... (will be faster).
if (wherefrom == relaxNodeInc_Call) {
relaxation->changeConstraint(c, lf, 0.0, 0.0);
}
LinConModPtr lcmod = (LinConModPtr) new LinConMod(c, lf, 0.0, 0.0);
mods.push_back(lcmod);
}
}
}
}
}
void
MultilinearFormulation::boundsOnProduct(ConstVariablePtr x1, ConstVariablePtr x2,
double &lb, double &ub)
{
double l1 = x1->getLb();
double u1 = x1->getUb();
double l2 = x2->getLb();
double u2 = x2->getUb();
lb = l1 * l2;
ub = l1 * l2;
lb = std::min(lb, u1*l2);
ub = std::max(ub, u1*l2);
lb = std::min(lb, u1*u2);
ub = std::max(ub, u1*u2);
lb = std::min(lb, l1*u2);
ub = std::max(ub, l1*u2);
}
void
MultilinearTermsHandler::handleXDefConstraints_(RelaxationPtr relaxation, HandleCallingFunction wherefrom, ModVector &mods)
{
for (UInt gix = 0; gix < groups_.size(); ++gix) {
for(SetOfVars::const_iterator it = groups_[gix].begin(); it != groups_[gix].end(); ++it) {
ConstVariablePtr xvar = *it;
LinearFunctionPtr lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(xvar, -1.0);
int pix = 0;
for (std::set<SetOfVars>::iterator it2 = points_[gix].begin(); it2 != points_[gix].end(); ++it2) {
VariablePtr lam = lambdavars_[gix][pix];
double val = varIsAtLowerBoundAtPoint_(xvar, *it2) ? xvar->getLb() : xvar->getUb();
lf->addTerm(lam, val);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << xvar->getName() << ", lam: " << gix << "," << pix << " value is: "
<< val << std::endl;
#endif
++pix;
}
FunctionPtr f = (FunctionPtr) new Function(lf);
if (wherefrom == relaxInit_Call) {
ConstraintPtr c = relaxation->newConstraint(f, 0.0, 0.0);
xConMap_.insert(std::make_pair(IntVarPtrPair(gix, xvar), c));
}
else {
IntVarPtrPairConstraintMap::iterator pos;
pos = xConMap_.find(IntVarPtrPair(gix, xvar));
if (pos == xConMap_.end()) {
assert(0);
}
ConstraintPtr c = pos->second;
//XXX Here you should just check if the constraint really was going to
//change and do nothing if it doesn't... (will be faster).
if (wherefrom == relaxNodeInc_Call) {
relaxation->changeConstraint(c, lf, 0.0, 0.0);
}
else {
assert(0);
}
LinConModPtr lcmod = (LinConModPtr) new LinConMod(c, lf, 0.0, 0.0);
mods.push_back(lcmod);
}
}
}
}
void CxUnivarConstraintData::addSecant(RelaxationPtr rel,
ConstVariablePtr riv,
ConstVariablePtr rov,
FunctionPtr fn, DoubleVector& tmpX,
bool init, ModVector &mods)
{
int error;
double xlb, xub, fxlb, fxub, m, intercept;
LinearFunctionPtr lf;
FunctionPtr f;
// First add the secant inequalities based on variable bounds
xlb = riv->getLb();
xub = riv->getUb();
#if defined(DEBUG_CXUNIVARHANDLER)
std::cout << "Adding secant on variable rix index: " << riv->getIndex()
<< " rov index: " << rov->getIndex()
<< " xlb: " << xlb << " xub: " << xub << std::endl;
#endif
// no secant if unbounded either way
if (xlb <= -0.9*INFINITY || xub >= 0.9*INFINITY) {
std::cout << "Cannot add secant -- bound is infinite" << std::endl;
return;
}
// TODO: Check the error value!
tmpX[riv->getIndex()] = xlb;
fxlb = fn->eval(tmpX, &error);
tmpX[riv->getIndex()] = xub;
fxub = fn->eval(tmpX, &error);
tmpX[riv->getIndex()] = 0.0;
// TODO: check/remedy numerical issues in this division
if (xub - xlb > 10e-7) {
m = (fxub - fxlb)/(xub - xlb);
}
else {
m = 0.0;
}
intercept = fxlb - m*xlb;
lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(rov, 1.0);
lf->addTerm(riv, -m);
// rovar <= m*rivar + intercept
if (init) {
f = (FunctionPtr) new Function(lf);
secCon_ = rel->newConstraint(f, -INFINITY, intercept);
}
else {
rel->changeConstraint(secCon_, lf, -INFINITY, intercept);
LinConModPtr lcmod = (LinConModPtr) new LinConMod(secCon_, lf, -INFINITY,
intercept);
mods.push_back(lcmod);
}
}
void CxUnivarConstraintData::addLin(RelaxationPtr rel, ConstVariablePtr riv,
ConstVariablePtr rov, FunctionPtr fn,
DoubleVector& tmpX, DoubleVector& grad,
bool init, ModVector &mods)
{
int error;
ConstraintPtr cons;
double xlb = riv->getLb();
double xub = riv->getUb();
double fxlbval=0, fxubval=0, dfxlbval=0, dfxubval=0;
double tmpxval, fxval, dfxval;
LinearFunctionPtr lf;
FunctionPtr f;
// More sophisticated strategies hopefully could be obtained by simply
// changing this array
int npts = 3;
double xvals[] = {xlb, xub, (xub-xlb)/2.0};
#if defined(DEBUG_CXUNIVARHANDLER)
std::cout << "Adding linearizations. rix id: " << riv->getId()
<< " rix index: " << riv->getIndex() << " rov id: " << rov->getId()
<< " rov index: " << rov->getIndex()
<< " xlb: " << xlb << " xub: " << xub << std::endl;
#endif
for (int i = 0; i < npts; i++) {
// Zero out tmpX and grad each time, or else bad things happen
for (UInt j = 0; j < tmpX.size(); ++j) {
tmpX[j] = 0.0;
grad[j] = 0.0;
}
if (i == 2) {
// Third linearization point taken to be where first two intersect:
// x3 = (f'(xub)*xub - f'(xlb)*xlb + f(xlb) - f(xub))/(f'(xub) - f'(xlb))
// Unless this would put it too close to one of the end points
if (dfxubval - dfxlbval > 0.0001 || dfxubval - dfxlbval < -0.0001) {
tmpxval = (dfxubval*xub - dfxlbval*xlb + fxlbval - fxubval)/
(dfxubval - dfxlbval);
if (tmpxval < xlb + (xub-xlb)*0.05) {
xvals[2] = xlb + (xub-xlb)*0.05;
}
else if (tmpxval > xub - (xub-xlb)*0.05) {
xvals[2] = xub - (xub-xlb)*0.05;
}
else {
xvals[2] = tmpxval;
}
}
}
tmpX[riv->getIndex()] = xvals[i];
error = 0;
fxval = fn->eval(tmpX, &error);
fn->evalGradient(&tmpX[0], &grad[0], &error);
#if defined(DEBUG_CXUNIVARHANDLER2)
for (UInt j = 0; j < tmpX.size(); ++j) {
std::cout << "x[" << j << "] = " << tmpX[j] << " dfdx[" << j << "] = "
<< grad[j] << std::endl;
}
#endif
dfxval = grad[riv->getIndex()];
if (i == 0) {
fxlbval = fxval;
dfxlbval = dfxval;
}
else if (i == 1) {
fxubval = fxval;
dfxubval = dfxval;
}
// linearization: rov >= f(xval) + f'(xval)(riv - xval)
// rov - f'(xval)*riv >= f(xval) - f'(xval)*xval
lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(rov, 1.0);
lf->addTerm(riv, -dfxval);
if (init) {
f = (FunctionPtr) new Function(lf);
cons = rel->newConstraint(f, fxval - dfxval*xvals[i], INFINITY);
linCons_.push_back(cons);
}
else {
#if defined(DEBUG_CXUNIVARHANDLER)
std::cout << "Will change 'linearization ' constraint to have "
<< "linear function: ";
lf->write(std::cout);
std::cout << std::endl;
#endif
rel->changeConstraint(linCons_[i], lf, fxval - dfxval*xvals[i], INFINITY);
LinConModPtr lcmod = (LinConModPtr) new LinConMod(linCons_[i], lf,
fxval -
dfxval*xvals[i],
INFINITY);
mods.push_back(lcmod);
}
}
tmpX[riv->getIndex()] = 0.0;
grad[riv->getIndex()] = 0.0;
}
void MultilinearTermsHandler::getBranchingCandidates(RelaxationPtr,
const DoubleVector &x,
ModVector &,
BrVarCandSet &cands,
BrCandVector &, bool &is_inf)
{
// Implementation notes:
// (1) You must insert into the set cands
// (2) Super naive implmentation: Just pick the variable from infeasible
// terms whose total 'bound product' is largest
std::set<ConstVariablePtr> candidates;
for (ConstTermIterator it = termsR_.begin(); it != termsR_.end(); ++it) {
ConstVariablePtr zt = it->first;
SetOfVars const &jt = it->second;
if (allVarsBinary_(jt)) continue;
double zval = x[zt->getIndex()];
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "Relaxation term variable: ";
zt->write(std::cout);
std::cout << " Has LP value: " << zval << std::endl;
#endif
double termval = 1.0;
double largest_score = eTol_;
ConstVariablePtr largest_score_var;
for(SetOfVars::const_iterator jt_it = jt.begin(); jt_it != jt.end(); ++jt_it) {
ConstVariablePtr termvar = *jt_it;
termval *= x[termvar->getIndex()];
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "Term variable: ";
termvar->write(std::cout);
std::cout << " has value: " << x[termvar->getIndex()] << std::endl;
#endif
double score = (termvar->getUb() - x[termvar->getIndex()])*
(x[termvar->getIndex()] - termvar->getLb());
if (score > largest_score) {
largest_score = score;
largest_score_var = termvar;
}
}
if (fabs(zval - termval) > eTol_) {
candidates.insert(largest_score_var);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
largest_score_var->write(std::cout);
std::cout << " will be a candidate" << std::endl;
#endif
}
}
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "Branching candidates are: " << std::endl;
for(SetOfVars::const_iterator it = candidates.begin(); it != candidates.end(); ++it) {
(*it)->write(std::cout);
}
#endif
for(SetOfVars::const_iterator it = candidates.begin(); it != candidates.end(); ++it) {
ConstVariablePtr v = *it;
BrVarCandPtr br_can = (BrVarCandPtr) new BrVarCand(v, v->getIndex(), 0.5, 0.5);
cands.insert(br_can);
}
is_inf = false;
}
ModificationPtr MultilinearTermsHandler::getBrMod(BrCandPtr cand, DoubleVector &xval,
RelaxationPtr , BranchDirection dir)
{
LinModsPtr linmods;
//XXX Put (bool init) back in handle{x,z}def...
BrVarCandPtr vcand = boost::dynamic_pointer_cast <BrVarCand> (cand);
VariablePtr v = vcand->getVar();
double branching_value = xval[v->getIndex()];
BoundType lu;
VariableType vtype = v->getType();
// Change bounds on the x var (called v here)
if (dir == DownBranch) {
lu = Upper;
if (vtype != Continuous) branching_value = floor(branching_value);
}
else {
lu = Lower;
if (vtype != Continuous) branching_value = ceil(branching_value);
}
linmods = (LinModsPtr) new LinMods();
VarBoundModPtr vmod = (VarBoundModPtr) new VarBoundMod(v, lu, branching_value);
linmods->insert(vmod);
// This chunk of code changes the
// x_{V_g} = \sum_{k=1}^{2 |V_g|} \lambda_k^g \chi^{k,g} \forall g \in G
for (UInt gix = 0; gix < groups_.size(); ++gix) {
for(SetOfVars::const_iterator it = groups_[gix].begin(); it != groups_[gix].end(); ++it) {
ConstVariablePtr xvar = *it;
if (v != xvar) continue;
LinearFunctionPtr lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(xvar, -1.0);
UInt pix = 0;
for (std::set<SetOfVars>::iterator it2 = points_[gix].begin(); it2 != points_[gix].end(); ++it2) {
VariablePtr lam = lambdavars_[gix][pix];
double val = -INFINITY;
bool atLower = varIsAtLowerBoundAtPoint_(v, *it2);
bool atUpper = !atLower;
if (lu == Upper && atUpper) val = branching_value;
else if (lu == Lower && atLower) val = branching_value;
else val = (atLower ? v->getLb() : v->getUb());
lf->addTerm(lam, val);
++pix;
}
FunctionPtr f = (FunctionPtr) new Function(lf);
IntVarPtrPairConstraintMap::iterator pos;
pos = xConMap_.find(IntVarPtrPair(gix, xvar));
if (pos == xConMap_.end()) {
assert(0);
}
ConstraintPtr c = pos->second;
LinConModPtr lcmod = (LinConModPtr) new LinConMod(c, lf, 0.0, 0.0);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "getBrMod(). Will change 'x =' constraint to have linear function ";
lf->write(std::cout);
std::cout << std::endl;
#endif
linmods->insert(lcmod);
}
}
// This will change the z_t = sum \sum_{k=1}^{2|V_g} \lambda_k^g \chi^{k,g}.
// Probably not very efficient way to do this...
for(ConstTermIterator it = termsR_.begin(); it != termsR_.end(); ++it) {
SetOfVars const &jt = it->second;
for (UInt gix = 0; gix < groups_.size(); ++gix) {
SetOfVars &vg = groups_[gix];
std::set<ConstVariablePtr>::iterator pos1;
pos1 = jt.find(v);
if (pos1 == jt.end()) continue; // J_t does not contain v, go to next group
// J_t is not in V_g, go to next group
if (! std::includes(vg.begin(), vg.end(), jt.begin(), jt.end())) continue;
ConstVariablePtr zvar = it->first;
LinearFunctionPtr lf = (LinearFunctionPtr) new LinearFunction();
lf->addTerm(zvar, -1.0);
// Get ConstraintToChange
IntVarPtrPairConstraintMap::iterator pos2;
pos2 = zConMap_.find(IntVarPtrPair(gix, zvar));
if (pos2 == zConMap_.end()) {
assert(0);
}
ConstraintPtr c = pos2->second;
UInt pix = 0;
for (std::set<SetOfVars>::iterator it2 = points_[gix].begin();
it2 != points_[gix].end(); ++it2) {
double prodval = 1.0;
VariablePtr lam = lambdavars_[gix][pix];
// Compute new extreme point value for this lambda
for(SetOfVars::const_iterator jt_it = jt.begin(); jt_it != jt.end(); ++jt_it) {
ConstVariablePtr xvar = *jt_it;
double val = 0.0;
bool atLower = varIsAtLowerBoundAtPoint_(xvar, *it2);
bool atUpper = !atLower;
if (xvar == v) {
if (lu == Upper && atUpper) val = branching_value;
else if (lu == Lower && atLower) val = branching_value;
else val = (atLower ? xvar->getLb() : xvar->getUb());
}
else {
val = atLower ? xvar->getLb() : xvar->getUb();
}
prodval *= val;
}
lf->addTerm(lam, prodval);
++pix;
}
// Add new mod
LinConModPtr lcmod = (LinConModPtr) new LinConMod(c, lf, 0.0, 0.0);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "getBrMod(): Will change 'zt = ' constraint to have linear function: ";
lf->write(std::cout);
std::cout << std::endl;
#endif
linmods->insert(lcmod);
}
}
return linmods;
return ModificationPtr();
}