C++ IloRangeArray::getSize方法代码示例

// This function creates the following model:
//   Minimize
//    obj: x1 + x2 + x3 + x4 + x5 + x6
//   Subject To
//    c1: x1 + x2      + x5      = 8
//    c2:           x3 + x5 + x6 = 10
//    q1: [ -x1^2 + x2^2 + x3^2 ] <= 0
//    q2: [ -x4^2 + x5^2 ] <= 0
//   Bounds
//    x2 Free
//    x3 Free
//    x5 Free
//   End
// which is a second order cone program in standard form.
// The function returns objective, variables and constraints in the
// values obj, vars and rngs.
// The function also sets up cone so that for a column j we have
// cone[j] >= 0               Column j is in a cone constraint and is the
//                            cone's head variable.
// cone[j] == NOT_CONE_HEAD   Column j is in a cone constraint but is
//                            not the cone's head variable..
// cone[j] == NOT_IN_CONE     Column j is not contained in any cone constraint.
static void
createmodel (IloModel& model, IloObjective &obj, IloNumVarArray &vars,
             IloRangeArray &rngs, IloIntArray& cone)
{
   // The indices we assign as user objects to the modeling objects.
   // We define them as static data so that we don't have to worry about
   // dynamic memory allocation/leakage.
   static int indices[] = { 0, 1, 2, 3, 4, 5, 6 };

   IloEnv env = model.getEnv();

   // Create variables.
   IloNumVar x1(env,            0, IloInfinity, "x1");
   IloNumVar x2(env, -IloInfinity, IloInfinity, "x2");
   IloNumVar x3(env, -IloInfinity, IloInfinity, "x3");
   IloNumVar x4(env,            0, IloInfinity, "x4");
   IloNumVar x5(env, -IloInfinity, IloInfinity, "x5");
   IloNumVar x6(env,            0, IloInfinity, "x6");

   // Create objective function and immediately store it in return value.
   obj = IloMinimize(env, x1 + x2 + x3 + x4 + x5 + x6);

   // Create constraints.
   IloRange c1(env, 8,  x1 + x2      + x5,       8, "c1");
   IloRange c2(env, 10,           x3 + x5 + x6, 10, "c2");
   IloRange q1(env, -IloInfinity, -x1*x1 + x2*x2 + x3*x3, 0, "q1");
   cone.add(2);             // x1, cone head of constraint at index 2
   cone.add(NOT_CONE_HEAD); // x2
   cone.add(NOT_CONE_HEAD); // x3
   IloRange q2(env, -IloInfinity, -x4*x4 + x5*x5, 0, "q2");
   cone.add(3);             // x4, cone head of constraint at index 3
   cone.add(NOT_CONE_HEAD); // x5

   cone.add(NOT_IN_CONE);   // x6

   // Setup model.
   model.add(obj);
   model.add(obj);
   model.add(c1);
   model.add(c2);
   model.add(q1);
   model.add(q2);

   // Setup return values.
   vars.add(x1);
   vars.add(x2);
   vars.add(x3);
   vars.add(x4);
   vars.add(x5);
   vars.add(x6);

   rngs.add(c1);
   rngs.add(c2);
   rngs.add(q1);
   rngs.add(q2);

   // We set the user object for each modeling object to its index in the
   // respective array. This makes the code in checkkkt a little simpler.
   for (IloInt i = 0; i < vars.getSize(); ++i)
      vars[i].setObject(&indices[i]);
   for (IloInt i = 0; i < rngs.getSize(); ++i)
      rngs[i].setObject(&indices[i]);
}

// Test KKT conditions on the solution.
// The function returns true if the tested KKT conditions are satisfied
// and false otherwise.
// The function assumes that the model currently extracted to CPLEX is fully
// described by obj, vars and rngs.
static bool
checkkkt (IloCplex& cplex, IloObjective const& obj, IloNumVarArray const& vars,
          IloRangeArray const& rngs, IloIntArray const& cone, double tol)
{
   IloEnv env = cplex.getEnv();
   IloModel model = cplex.getModel();
   IloNumArray x(env), dslack(env);
   IloNumArray pi(env, rngs.getSize()), slack(env);

   // Read primal and dual solution information.
   cplex.getValues(x, vars);
   cplex.getSlacks(slack, rngs);

   // pi for second order cone constraints.
   getsocpconstrmultipliers(cplex, vars, rngs, pi, dslack);

   // pi for linear constraints.
   for (IloInt i = 0; i < rngs.getSize(); ++i) {
      IloRange r = rngs[i];
      if ( !r.getQuadIterator().ok() )
         pi[idx(r)] = cplex.getDual(r);
   }

   // Print out the data we just fetched.
   streamsize oprec = env.out().precision(3);
   ios_base::fmtflags oflags = env.out().setf(ios::fixed | ios::showpos);
   env.out() << "x      = [";
   for (IloInt i = 0; i < x.getSize(); ++i)
      env.out() << " " << x[i];
   env.out() << " ]" << endl;
   env.out() << "dslack = [";
   for (IloInt i = 0; i < dslack.getSize(); ++i)
      env.out() << " " << dslack[i];
   env.out() << " ]" << endl;
   env.out() << "pi     = [";
   for (IloInt i = 0; i < rngs.getSize(); ++i)
      env.out() << " " << pi[i];
   env.out() << " ]" << endl;
   env.out() << "slack  = [";
   for (IloInt i = 0; i < rngs.getSize(); ++i)
      env.out() << " " << slack[i];
   env.out() << " ]" << endl;
   env.out().precision(oprec);
   env.out().flags(oflags);

   // Test primal feasibility.
   // This example illustrates the use of dual vectors returned by CPLEX
   // to verify dual feasibility, so we do not test primal feasibility
   // here.

   // Test dual feasibility.
   // We must have
   // - for all <= constraints the respective pi value is non-negative,
   // - for all >= constraints the respective pi value is non-positive,
   // - the dslack value for all non-cone variables must be non-negative.
   // Note that we do not support ranged constraints here.
   for (IloInt i = 0; i < vars.getSize(); ++i) {
      IloNumVar v = vars[i];
      if ( cone[i] == NOT_IN_CONE && dslack[i] < -tol ) {
         env.error() << "Dual multiplier for " << v << " is not feasible: "
                     << dslack[i] << endl;
         return false;
      }
   }
   for (IloInt i = 0; i < rngs.getSize(); ++i) {
      IloRange r = rngs[i];
      if ( fabs (r.getLB() - r.getUB()) <= tol ) {
         // Nothing to check for equality constraints.
      }
      else if ( r.getLB() > -IloInfinity && pi[i] > tol ) {
         env.error() << "Dual multiplier " << pi[i] << " for >= constraint"
                     << endl << r << endl
                     << "not feasible"
                     << endl;
         return false;
      }
      else if ( r.getUB() < IloInfinity && pi[i] < -tol ) {
         env.error() << "Dual multiplier " << pi[i] << " for <= constraint"
                     << endl << r << endl
                     << "not feasible"
                     << endl;
         return false;
      }
   }

   // Test complementary slackness.
   // For each constraint either the constraint must have zero slack or
   // the dual multiplier for the constraint must be 0. We must also
   // consider the special case in which a variable is not explicitly
   // contained in a second order cone constraint.
   for (IloInt i = 0; i < vars.getSize(); ++i) {
      if ( cone[i] == NOT_IN_CONE ) {
         if ( fabs(x[i]) > tol && dslack[i] > tol ) {
            env.error() << "Invalid complementary slackness for " << vars[i]
                        << ":" << endl
//.........这里部分代码省略.........

/** 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();
//.........这里部分代码省略.........