/** Extract the master block from <code>problem</code>. * The constructor also sets up the solver for the newly created master * block. The master block can only be extracted if all sub-blocks have * already been extracted. * @param problem The problem from which to extract the master. * @param blocks The sub blocks that have already been extracted. */ BendersOpt::Block::Block(Problem const *problem, BlockVector const &blocks) : env(), number(-1), vars(0), rows(0), cplex(0), cb(0) { IloNumVarArray problemVars = problem->getVariables(); IloRangeArray problemRanges = problem->getRows(); IloExpr masterObj(env); IloNumVarArray masterVars(env); IloRangeArray masterRows(env); // Find columns that do not intersect block variables and // copy them to the master block. IdxMap idxMap; RowSet rowSet; for (IloInt j = 0; j < problemVars.getSize(); ++j) { IloNumVar x = problemVars[j]; if ( problem->getBlock(x) < 0 ) { // Column is not in a block. Copy it to the master. IloNumVar v(env, x.getLB(), x.getUB(), x.getType(), x.getName()); varMap.insert(VarMap::value_type(v, x)); masterObj += problem->getObjCoef(x) * v; idxMap[x] = masterVars.getSize(); masterVars.add(v); } else { // Column is in a block. Collect all rows that intersect // this column. RowSet const &intersected = problem->getIntersectedRows(x); for (RowSet::const_iterator it = intersected.begin(); it != intersected.end(); ++it) rowSet.insert(*it); idxMap[x] = -1; } } // Pick up the rows that we need to copy. // These are the rows that are only intersected by master variables, // that is, the rows that are not in any block's rowset. for (IloInt i = 0; i < problemRanges.getSize(); ++i) { IloRange r = problemRanges[i]; if ( rowSet.find(r) == rowSet.end() ) { IloRange masterRow(env, r.getLB(), r.getUB(), r.getName()); IloExpr lhs(env); for (IloExpr::LinearIterator it = r.getLinearIterator(); it.ok(); ++it) { lhs += it.getCoef() * masterVars[idxMap[it.getVar()]]; } masterRow.setExpr(lhs); masterRows.add(masterRow); } } // Adjust variable indices in blocks so that reference to variables // in the original problem become references to variables in the master. for (BlockVector::const_iterator b = blocks.begin(); b != blocks.end(); ++b) { for (std::vector<FixData>::iterator it = (*b)->fixed.begin(); it != (*b)->fixed.end(); ++it) it->col = idxMap[problemVars[it->col]]; } // Create the eta variables, one for each block. // See the comments at the top of this file for details about the // eta variables. IloInt const firsteta = masterVars.getSize(); for (BlockVector::size_type i = 0; i < blocks.size(); ++i) { std::stringstream s; s << "_eta" << i; IloNumVar eta(env, 0.0, IloInfinity, s.str().c_str()); masterObj += eta; masterVars.add(eta); } // Create model and solver instance vars = masterVars; rows = masterRows; IloModel model(env); model.add(obj = IloObjective(env, masterObj, problem->getObjSense())); model.add(vars); model.add(rows); cplex = IloCplex(model); cplex.use(cb = new (env) LazyConstraintCallback(env, this, blocks, firsteta)); for (IloExpr::LinearIterator it = obj.getLinearIterator(); it.ok(); ++it) objMap.insert(ObjMap::value_type(it.getVar(), it.getCoef())); }
/** Create the dual of a linear program. * The function can only dualize programs of the form * <code>Ax <= b, x >= 0</code>. The data in <code>primalVars</code> and * <code>dualRows</code> as well as in <code>primalRows</code> and * <code>dualVars</code> is in 1-to-1-correspondence. * @param primalObj Objective function of primal problem. * @param primalVars Variables in primal problem. * @param primalRows Rows in primal problem. * @param dualObj Objective function of dual will be stored here. * @param dualVars All dual variables will be stored here. * @param dualRows All dual rows will be stored here. */ void BendersOpt::makeDual(IloObjective const &primalObj, IloNumVarArray const &primalVars, IloRangeArray const &primalRows, IloObjective *dualObj, IloNumVarArray *dualVars, IloRangeArray *dualRows) { // To keep the code simple we only support problems // of the form Ax <= b, b >= 0 here. We leave it as a reader's // exercise to extend the function to something that can handle // any kind of linear model. for (IloInt j = 0; j < primalVars.getSize(); ++j) if ( primalVars[j].getLB() != 0 || primalVars[j].getUB() < IloInfinity ) { std::stringstream s; s << "Cannot dualize variable " << primalVars[j]; throw s.str(); } for (IloInt i = 0; i < primalRows.getSize(); ++i) if ( primalRows[i].getLB() > -IloInfinity || primalRows[i].getUB() >= IloInfinity ) { std::stringstream s; s << "Cannot dualize constraint " << primalRows[i]; std::cerr << s.str() << std::endl; throw s.str(); } // The dual of // min/max c^T x // Ax <= b // x >= 0 // is // max/min y^T b // y^T A <= c // y <= 0 // We scale y by -1 to get >= 0 IloEnv env = primalVars.getEnv(); IloObjective obj(env, 0.0, primalObj.getSense() == IloObjective::Minimize ? IloObjective::Maximize : IloObjective::Minimize); IloRangeArray rows(env); IloNumVarArray y(env); std::map<IloNumVar,IloInt,ExtractableLess<IloNumVar> > v2i; for (IloInt j = 0; j < primalVars.getSize(); ++j) { IloNumVar x = primalVars[j]; v2i.insert(std::map<IloNumVar,IloInt,ExtractableLess<IloNumVar> >::value_type(x, j)); rows.add(IloRange(env, -IloInfinity, 0, x.getName())); } for (IloExpr::LinearIterator it = primalObj.getLinearIterator(); it.ok(); ++it) rows[v2i[it.getVar()]].setUB(it.getCoef()); for (IloInt i = 0; i < primalRows.getSize(); ++i) { IloRange r = primalRows[i]; IloNumColumn col(env); col += obj(-r.getUB()); for (IloExpr::LinearIterator it = r.getLinearIterator(); it.ok(); ++it) col += rows[v2i[it.getVar()]](-it.getCoef()); y.add(IloNumVar(col, 0, IloInfinity, IloNumVar::Float, r.getName())); } *dualObj = obj; *dualVars = y; *dualRows = rows; }
/** Extract sub block number <code>n</code> from <code>problem</code>. * The constructor creates a representation of block number <code>n</code> * as described in <code>problem</code>. * The constructor will also connect the newly created block to a remote * object solver instance. * @param problem The problem from which the block is to be extracted. * @param n Index of the block to be extracted. * @param argc Argument for IloCplex constructor. * @param argv Argument for IloCplex constructor. * @param machines List of machines to which to connect. If the code is * compiled for the TCP/IP transport then the block will * be connected to <code>machines[n]</code>. */ BendersOpt::Block::Block(Problem const *problem, IloInt n, int argc, char const *const *argv, std::vector<char const *> const &machines) : env(), number(n), vars(0), rows(0), cplex(0), cb(0) { IloNumVarArray problemVars = problem->getVariables(); IloRangeArray problemRanges = problem->getRows(); // Create a map that maps variables in the original model to their // respective index in problemVars. std::map<IloNumVar,IloInt,ExtractableLess<IloNumVar> > origIdxMap; for (IloInt j = 0; j < problemVars.getSize(); ++j) origIdxMap.insert(std::map<IloNumVar,IloInt,ExtractableLess<IloNumVar> >::value_type(problemVars[j], j)); // Copy non-fixed variables from original problem into primal problem. IloExpr primalObj(env); IloNumVarArray primalVars(env); IloRangeArray primalRows(env); IdxMap idxMap; // Index of original variable in block's primal model RowSet rowSet; for (IloInt j = 0; j < problemVars.getSize(); ++j) { IloNumVar x = problemVars[j]; if ( problem->getBlock(x) == number ) { // Create column in block LP with exactly the same data. if ( x.getType() != IloNumVar::Float ) { std::stringstream s; s << "Cannot create non-continuous block variable " << x; std::cerr << s.str() << std::endl; throw s.str(); } IloNumVar v(env, x.getLB(), x.getUB(), x.getType(), x.getName()); // Normalize objective function to 'minimize' double coef = problem->getObjCoef(x); if ( problem->getObjSense() != IloObjective::Minimize ) coef *= -1.0; primalObj += coef * v; // Record the index that the copied variable has in the // block model. idxMap.insert(IdxMap::value_type(x, primalVars.getSize())); primalVars.add(v); // Mark the rows that are intersected by this column // so that we can collect them later. RowSet const &intersected = problem->getIntersectedRows(x); for (RowSet::const_iterator it = intersected.begin(); it != intersected.end(); ++it) rowSet.insert(*it); } else idxMap.insert(IdxMap::value_type(x, -1)); } // Now copy all rows that intersect block variables. for (IloInt i = 0; i < problemRanges.getSize(); ++i) { IloRange r = problemRanges[i]; if ( rowSet.find(r) == rowSet.end() ) continue; // Create a copy of the row, normalizing it to '<=' double factor = 1.0; if ( r.getLB() > -IloInfinity ) factor = -1.0; IloRange primalR(env, factor < 0 ? -r.getUB() : r.getLB(), factor < 0 ? -r.getLB() : r.getUB(), r.getName()); IloExpr lhs(env); for (IloExpr::LinearIterator it = r.getLinearIterator(); it.ok(); ++it) { IloNumVar v = it.getVar(); double const val = factor * it.getCoef(); if ( problem->getBlock(v) != number ) { // This column is not explicitly in this block. This means // that it is a column that will be fixed by the master. // We collect all such columns so that we can adjust the // dual objective function according to concrete fixings. // Store information about variables in this block that // will be fixed by master solves. fixed.push_back(FixData(primalRows.getSize(), origIdxMap[v], -val)); } else { // The column is an ordinary in this block. Just copy it. lhs += primalVars[idxMap[v]] * val; } } primalR.setExpr(lhs); primalRows.add(primalR); lhs.end(); } // Create the dual of the primal model we just created. // Note that makeDual _always_ returns a 'maximize' objective. IloObjective objective(env, primalObj, IloObjective::Minimize); makeDual(objective, primalVars, primalRows, &obj, &vars, &rows); objective.end(); primalRows.endElements(); primalRows.end(); primalVars.endElements(); primalVars.end(); primalObj.end(); // Create a model. IloModel model(env); model.add(obj); model.add(vars); model.add(rows); for (IloExpr::LinearIterator it = obj.getLinearIterator(); it.ok(); ++it) objMap.insert(ObjMap::value_type(it.getVar(), it.getCoef())); // Finally create the IloCplex instance that will solve // the problems associated with this block. char const **transargv = new char const *[argc + 3]; for (int i = 0; i < argc; ++i) transargv[i] = argv[i]; #if defined(USE_MPI) char extra[128]; sprintf (extra, "-remoterank=%d", static_cast<int>(number + 1)); transargv[argc++] = extra; (void)machines; #elif defined(USE_PROCESS) char extra[128]; sprintf (extra, "-logfile=block%04d.log", static_cast<int>(number)); transargv[argc++] = extra; (void)machines; #elif defined(USE_TCPIP) transargv[argc++] = machines[number]; #endif cplex = IloCplex(model, TRANSPORT, argc, transargv); delete[] transargv; // Suppress output from this block's solver. cplex.setOut(env.getNullStream()); cplex.setWarning(env.getNullStream()); }