// 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
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);
}
}
}
}
int main()
{
// Generate output.
ofstream output;
output.open("numknapcov.txt");
// Generate input.
ifstream input;
input.open("list.txt");
// Check if input is opened succesfully.
if (input.is_open() == false) {
cerr << "Input file read error." << endl;
output << "Input file read error." << endl;
exit(0);
}
/********************************************************************************/
// Headers for output data.
output << "Statistics of knapsack cover cuts applied to root relaxation." << endl;
output << "problem " << "vars " << "cons " << "lincons " << "knapcons " << "knapcov "
<< "knaps " << "totalcuts " << "cuts " << "violknapcuts " << "initobj "
<< "endobj " << "gapclosed " << "timeinit " << "timecut " << "timemod"
<< endl;
/********************************************************************************/
// loop to test all problems in list.txt
while (input.good()) {
// problem name
string pname;
getline(input, pname);
// At the end of file just exit from loop.
if (pname.empty()) {
break;
}
cout << "Problem considered is: " << pname << endl;
// Real stuff begins.
// Ampl interface, jacobian and hessian.
MINOTAUR_AMPL::AMPLInterfacePtr iface = MINOTAUR_AMPL::AMPLInterfacePtr();
JacobianPtr jPtr; //! Jacobian read from AMPL
HessianOfLagPtr hPtr; //! Hessian read from AMPL
// environment, timers and options:
EnvPtr env = (EnvPtr) new Environment();
OptionDBPtr options;
// problem to be solved.
ProblemPtr minlp;
// solver pointers, including status.
FilterSQPEngine e(env);
EngineStatus status;
// Presolver.
PresolverPtr pres;
// give parameters.
UInt argc2 = 2;
std::string arg1 = "bnb";
std::string arg2 = pname;
char** argv2 = new char* [2];
argv2[0] = &arg1[0];
argv2[1] = &arg2[0];
// Default options
env->getOptions()->findBool("presolve")->setValue(false);
env->getOptions()->findBool("use_native_cgraph")->setValue(true);
env->getOptions()->findBool("nl_presolve")->setValue(false);
// parse options
env->readOptions(argc2, argv2);
options = env->getOptions();
options->findString("interface_type")->setValue("AMPL");
// read minlp from AMPL.
iface = (MINOTAUR_AMPL::AMPLInterfacePtr) new MINOTAUR_AMPL::AMPLInterface(env);
minlp = iface->readInstance(pname);
// Timer is obtained.
Timer * timer = env->getNewTimer();
// Nonlinearize objective function.
Bool MIPCONSIDERED = false;
if (MIPCONSIDERED == true) {
ObjectivePtr initobjfun = minlp->getObjective();
if (initobjfun->getObjectiveType() == Maximize) {
cerr << "Objective type is Maximize, change it to Minimize." << endl;
exit(0);
}
LinearFunctionPtr lfinitobj = initobjfun->getLinearFunction();
// NonlinearFunctionPtr nlfobj = (NonlinearFunctionPtr) new NonlinearFunction();
CGraphPtr nlfobj = (CGraphPtr) new CGraph();
logobj(lfinitobj, nlfobj);
FunctionPtr logobjfun = (FunctionPtr) new Function(nlfobj);
ObjectiveType otyp = Minimize;
minlp->changeObj(logobjfun, 0);
}
minlp->calculateSize();
minlp->prepareForSolve();
// Change format of problem to be suitable for Minotaur.
HandlerVector handlers;
// Use presolver to standardize problem.
//pres = (PresolverPtr) new Presolver(minlp, env, handlers);
//pres->standardize();
minlp->calculateSize();
minlp->prepareForSolve();
minlp->setJacobian(jPtr);
minlp->setHessian(hPtr);
minlp->setNativeDer();
minlp->calculateSize();
minlp->prepareForSolve();
minlp->setNativeDer();
//minlp->write(std::cout);
/**************************************************************/
// Given problem statistics .
// Number of variables.
UInt numvars = minlp->getNumVars();
// number of constraints.
UInt numcons = minlp->getNumCons();
// linear constraints.
UInt numlin = minlp->getNumLinCons();
/*************************************************************/
// set option for engine to resolve to solve NLP repeatedly.
// Probbaly does nothing.
e.setOptionsForRepeatedSolve();
// load problem.
e.load(minlp);
// Solve problem.
timer->start();
status = e.solve();
/********************************************************************/
// Solution time of relaxation.
Double timeinit = timer->query();
timer->stop();
// Solution objective value
Double initobj = e.getSolutionValue();
/********************************************************************/
std::cout << "Relaxation objective value = " << initobj << std::endl;
// Get solution from engine.
ConstSolutionPtr sol = e.getSolution();
// Construct relaxation.
RelaxationPtr rel = (RelaxationPtr) new Relaxation(minlp);
// Time for cut generation.
timer->start();
// Generate kanpsack cover cuts.
CoverCutGeneratorPtr knapgen =
(CoverCutGeneratorPtr) new CoverCutGenerator(rel, sol, env);
/*******************************************************************/
Double timecut = timer->query();
timer->stop();
/*******************************************************************/
// Get statistics of cut generator.
ConstCovCutGenStatsPtr knapstats = knapgen->getStats();
/*******************************************************************/
// Knapsack cut generator statistics.
// knapsack constraints.
UInt numknap = (knapgen->getKnapsackList())->getNumKnaps();
// knapsacks that has cover sets.
UInt numknapcov = knapgen->getNumCons();
// knapsack subproblems solved, i.e number of lifting subproblems solved.
UInt knaps = knapstats->knaps;
// cover cuts including duplicates.
UInt totalcuts = knapstats->totalcuts;
// cuts without duplicates.
UInt numknapcuts = knapstats->cuts;
// violated cuts.
UInt violknapcuts = knapstats->violated;
/*******************************************************************/
std::cout << "Number of knapsack cover cuts to be applied is: "
<< knapstats->violated << std::endl;
// Get the violated cuts from generator.
CutVector knapcuts = knapgen->getViolatedCutList();
// Iterators for cuts
CutVectorConstIter it;
CutVectorConstIter begin = knapcuts.begin();
CutVectorConstIter end = knapcuts.end();
// Apply the cuts to the problem.
// Violation list.
DoubleVector knapviols = knapgen->getViolList();
UInt curknap = 0;
Double maxviol = 0.0;
for (it=begin; it!=end; ++it) {
std::cout << "Violation obtained from this constraint is: "
<< knapviols[curknap] << std::endl;
ConstraintPtr newcons = rel->newConstraint((*it)->getFunction(), (*it)->getLb(), (*it)->getUb());
if (maxviol < knapviols[curknap]) {
maxviol = knapviols[curknap];
}
// add constraint to engine does not do anything.
// Thus, we add constraint to the relaxation and reload it to engine.
// e.addConstraint(newcons);
}
/*******************************************************************/
// Solution time of knapsack cover cuts added problem.
Double timemod = 0.0;
// Objective value after adding knapsack cover cuts.
Double endobj = 0.0;
// Gap closed by using knapsack cover cuts.
Double gapknap = 0.0;
/*******************************************************************/
if (violknapcuts >= 1) {
// Reload problem to engine.
// Check if we should reload the modified problem.
e.clear();
const Double * xupdated;
if (WARMSTART == 1) {
// Set initial point as the solution of root solution.
xupdated = sol->getPrimal();
rel->setInitialPoint(xupdated);
}
// Load the modified problem.
e.load(rel);
// warmstart continues.
if (WARMSTART == 1) {
// Before presolve, we set initial primal and
// dual solutions as the root solution.
SolutionPtr solupdated = (SolutionPtr) new Solution(initobj, xupdated, rel);
// Create new dual solution.
const Double * dualofvars = sol->getDualOfVars();
solupdated->setDualOfVars(dualofvars);
const Double * initdualofcons = sol->getDualOfCons();
UInt numconsupdated = rel->getNumCons();
Double * dualofcons = new Double[numconsupdated];
memcpy(dualofcons, initdualofcons, numcons*sizeof(Double));
for (UInt indexx = numcons; indexx < numconsupdated; ++indexx) {
dualofcons[indexx] = 0.0;
}
solupdated->setDualOfCons(dualofcons);
FilterWSPtr warmstart = (FilterWSPtr) new FilterSQPWarmStart();
warmstart->setPoint(solupdated);
e.loadFromWarmStart(warmstart);
delete [] dualofcons;
}
// Solution time after adding knapsack cover cuts to relaxation.
timer->start();
// Resolve the problem.
e.solve();
/*******************************************************************/
// Solution time of knapsack cover cuts added problem.
timemod = timer->query();
timer->stop();
// Objective value after adding knapsack cover cuts.
endobj = e.getSolutionValue();
// Gap closed by using knapsack cover cuts.
gapknap = (endobj-initobj)/fabs(initobj) * 100;
/*******************************************************************/
} else {
/*******************************************************************/
// Solution time of knapsack cover cuts added problem.
timemod = timeinit;
// Objective value after adding knapsack cover cuts.
endobj = initobj;
// Gap closed by using knapsack cover cuts.
gapknap = 0.0;
/*******************************************************************/
}
std::cout << "Objective value of relaxation after adding cuts: "
<< endobj << std::endl;
cout << pname << " " << numvars << " " << numcons << " " << numlin
<< " " << numknap
<< " " << numknapcov << " " << knaps << " " << totalcuts
<< " " << numknapcuts << " " << violknapcuts
<< std::fixed << std::setprecision(2)
<< " " << initobj << " " << endobj
<< " " << gapknap << " " << timeinit << " " << timecut
<< " " << timemod << endl;
if (numknap >= 1) {
// Save output data.
output << pname << " " << numvars << " " << numcons << " " << numlin
<< " " << numknap
<< " " << numknapcov << " " << knaps << " " << totalcuts
<< " " << numknapcuts << " " << violknapcuts
<< std::fixed << std::setprecision(2)
<< " " << initobj << " " << endobj
<< " " << gapknap << " " << timeinit << " " << timecut
<< " " << timemod << endl;
}
delete iface;
delete [] argv2;
}
output.close();
input.close();
return 0;
}
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::relaxInitInc(RelaxationPtr relaxation, bool *)
{
// General notes...
// Use Id to order variables
// x[v->getIndex()] returns solution.
/*
0) Create "terms" map using the relaxation variables, not the original
problem variables
1) Create groups based on container of terms
2) Add all lambda variables based on groups.
(Be sure to keep a container of which constraints are associated with
which groups)
*/
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
cout << "In MultilinearTermHandler::relaxInitInc()" << endl << " Current Relaxation: " << endl;
relaxation->write(cout);
cout << "And current terms: " << endl;
for(ConstTermIterator it = termsO_.begin(); it != termsO_.end(); ++it) {
std::cout << "zvar: ";
it->first->write(std::cout);
std::cout << "Contains vars: " << std::endl;
for(SetOfVars::const_iterator it2 = it->second.begin();
it2 != it->second.end(); ++it2) {
(*it2)->write(cout);
}
}
#endif
// Copy the original variable pointers into a data structure consisting of
// relaxation variables (It just makes likfe easier to keep things in
// terms of relaxation variables).
for (ConstTermIterator it = termsO_.begin(); it != termsO_.end(); ++it) {
ConstVariablePtr ov = it->first;
SetOfVars const &ovset = it->second;
ConstVariablePtr rv = relaxation->getRelaxationVar(ov);
SetOfVars rvset;
for(SetOfVars::const_iterator it2 = ovset.begin(); it2 != ovset.end(); ++it2) {
rvset.insert( relaxation->getRelaxationVar(*it2));
}
termsR_.insert(make_pair(rv, rvset));
}
// First we make the groups.
makeGroups_();
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
cout << "After making groups: " << endl;
for (ConstGroupIterator it = groups_.begin(); it != groups_.end(); ++it) {
cout << "Group of: " << endl;
for(set<ConstVariablePtr>::const_iterator it2 = it->begin(); it2 != it->end(); ++it2) {
(*it2)->write(cout);
}
}
// Just checking groups now. Stop here.
//exit(1);
#endif
/* This chunk of code creates the (powerset) representation
* of the extreme points in the groups, adds the lambda variables,
* and adds the convexity constraints
*/
lambdavars_.resize(groups_.size());
for(UInt gix = 0; gix < groups_.size(); ++gix) {
LinearFunctionPtr lf = (LinearFunctionPtr) new LinearFunction();
std::set<SetOfVars> p = powerset_(groups_[gix]);
int pix = 0;
for (std::set<SetOfVars>::iterator it2 = p.begin(); it2 != p.end(); ++it2) {
std::string name;
std::stringstream name_stream;
name_stream << "lam_" << gix << "_" << pix;
name = name_stream.str();
VariablePtr lam;
lam = relaxation->newVariable(0.0, 1.0, Continuous, name);
lf->addTerm(lam, 1.0);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER2)
std::cout << "Adding: " << name << std::endl;
#endif
lambdavars_[gix].push_back(lam);
pix++;
}
points_.push_back(p);
FunctionPtr f = (FunctionPtr) new Function(lf);
relaxation->newConstraint(f, 1.0, 1.0);
}
ModVector mods; // Not used in initialization
handleXDefConstraints_(relaxation, relaxInit_Call, mods);
handleZDefConstraints_(relaxation, relaxInit_Call, mods);
#if defined(DEBUG_MULTILINEARTERMS_HANDLER)
std::cout << "In MultilinearTermHandler::relaxInitInc()" << std::endl << " Final Relaxation: " << std::endl;
relaxation->write(std::cout);
#endif
}
