void profit_create_vars(graph g, IloModel model, IloNumVarArray x, IloNumVarArray p, IloNumVarArray z, int **columns) { IloEnv env = model.getEnv(); string s; assignment_vars(g, model, x, columns); for(int j = 0; j < g->items; j++) { s = "p_" + itos(j); p.add(IloNumVar(env, 0.0, boundp(j), ILOFLOAT, s.c_str())); // p.add(IloNumVar(env, lowerp(j), boundp(j), ILOFLOAT, s.c_str())); } for(int i = 0; i < g->bidders; i++) { s = "z_" + itos(i); z.add(IloNumVar(env, 0.0, boundu(i), ILOFLOAT, s.c_str())); } }
void addInitColumn(IloNumVarArray lambda, IloObjective rmpObj, IloRangeArray maintConEng, IloRangeArray removeMod, IloRangeArray convex, IloNumArray2 addXCol, IloNumArray addZCol, const IloNumArray compCosts, const IloNumArray convexityCoef) { // loop counter IloInt t; // counter for objective function coefficient for lambda // variable to be added. IloNum lambdaObjCoef = 0; // function assumes addXCol and addZCol contains proper values. // calculate objective function coefficient lambdaObjCoef for (t = 0; t < TIME_SPAN; t++) { // for each fixed t: scalar product of x[m]* vector and // component costs vector compCosts[m]: lambdaObjCoef += IloScalProd(addXCol[t],compCosts); // also clear the addXCol subarrays as soon as they // have been used addXCol[t].clear(); } // now add this column and it's associated lambda variable to the RMP. lambda.add(IloNumVar(rmpObj(lambdaObjCoef) + maintConEng(addZCol) + removeMod(addZCol) + convex(convexityCoef), 0.0, 1.0)); // clear addZCol num array. addZCol.clear(); } // END of addColumn
static void populatebycolumn (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); IloObjective obj = IloMaximize(env); c.add(IloRange(env, -IloInfinity, 20.0)); c.add(IloRange(env, -IloInfinity, 30.0)); x.add(IloNumVar(obj(1.0) + c[0](-1.0) + c[1]( 1.0), 0.0, 40.0)); x.add(obj(2.0) + c[0]( 1.0) + c[1](-3.0)); x.add(obj(3.0) + c[0]( 1.0) + c[1]( 1.0)); model.add(obj); model.add(c); } // END populatebycolumn
void addColumn(IloCplex subSolver, IloNumVarArray2 x, IloNumVarArray z, IloNumVarArray lambda, IloObjective rmpObj, IloRangeArray maintConEng, IloRangeArray removeMod, IloRangeArray convex, IloNumArray2 addXCol, IloNumArray addZCol, const IloNumArray compCosts, const IloNumArray convexityCoef) { // loop counter IloInt t; // counter for objective function coefficient for lambda // variable to be added. IloNum lambdaObjCoef = 0; // extract subproblem-optimal solution values // (into IloNumArrays addXCol (2d) and addZCol (1d)). // z values: subSolver.getValues(addZCol,z); //cout << endl << endl << "z = " << endl << addZCol << endl; //cin.get(); // !!! OBS !!! // here we might want to save these z values some column pool's custom-nitted class // array. Or to be specific, we want to add the indexes for NON-ZERO-ENTRIES in addZCol // to our class that keep place of columns. // E.g., given variable lambda(m)_(q_m), we want to know in our own class object, // given (m)(q_m), the indexes of non-zeros in that Z column. // and for each t... for (t = 0; t < TIME_SPAN; t++) { // x values: subSolver.getValues(addXCol[t],x[t]); //cout << endl << endl << "x[t=" << t << "] =" << endl << addXCol[t] << endl; } //cin.get(); // calculate objective function coefficient lambdaObjCoef for (t = 0; t < TIME_SPAN; t++) { // for each fixed t: scalar product of x[m]* vector and // component costs vector compCosts[m]: lambdaObjCoef += IloScalProd(addXCol[t],compCosts); // also clear the addXCol subarrays as soon as they // have been used addXCol[t].clear(); } // now add this column and it's associated lambda variable to the RMP. lambda.add(IloNumVar(rmpObj(lambdaObjCoef) + maintConEng(addZCol) + removeMod(addZCol) + convex(convexityCoef), 0.0, 1.0)); // clear addZCol num array. addZCol.clear(); } // END of addColumn
static void populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); x.add(IloNumVar(env, 0.0, 40.0)); x.add(IloNumVar(env)); x.add(IloNumVar(env)); x.add(IloNumVar(env, 2.0, 3.0, ILOINT)); model.add(IloMaximize(env, x[0] + 2 * x[1] + 3 * x[2] + x[3])); c.add( - x[0] + x[1] + x[2] + 10 * x[3] <= 20); c.add( x[0] - 3 * x[1] + x[2] <= 30); c.add( x[1] - 3.5* x[3] == 0); model.add(c); } // END populatebyrow
void PopulateFromGraph(IloModel model, IloNumVarArray s, IloRangeArray c){ IloEnv env = model.getEnv(); // Used n+1 for accomodating an extra variable // For being able to write the objective function for(int i = 0; i <= n; i++) s.add(IloNumVar(env)); }
static void populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); x.add(IloNumVar(env, 0.0, 40.0)); x.add(IloNumVar(env)); x.add(IloNumVar(env)); model.add(IloMaximize(env, x[0] + 2 * x[1] + 3 * x[2] - 0.5 * (33*x[0]*x[0] + 22*x[1]*x[1] + 11*x[2]*x[2] - 12*x[0]*x[1] - 23*x[1]*x[2] ) )); c.add( - x[0] + x[1] + x[2] <= 20); c.add( x[0] - 3 * x[1] + x[2] <= 30); model.add(c); } // END populatebyrow
IloExpr minBeamletStr(IloEnv & env, IloNumVarArray & w, Sparse_Matrix<IloInt> & vox) { IloExpr obj(env); for(int i=0;i<w.getSize();++i) { obj += w[i]/IloNum(100); } return obj; }
void generateProblem(const ILPModel& m, IloModel& model, IloNumVarArray& x, IloRangeArray& con) { IloEnv env = model.getEnv(); IloObjective obj = (m.obj == MINIMIZE ? IloMinimize(env) : IloMaximize(env)); for (unsigned long v = 0; v < m.numberOfVariables(); ++v) { switch (m.x[v].type) { case FLT: x.add(IloNumVar(env, m.x[v].lowerBound, m.x[v].upperBound, IloNumVar::Float)); break; case BIN: x.add(IloNumVar(env, m.x[v].lowerBound, m.x[v].upperBound, IloNumVar::Bool)); break; default: x.add(IloNumVar(env, m.x[v].lowerBound, m.x[v].upperBound, IloNumVar::Int)); } obj.setLinearCoef(x[v], m.c[v]); x[v].setName(m.varDesc[v].c_str()); } for (unsigned long c = 0; c < m.numberOfConstraints(); ++c) { switch (m.ops[c]) { case LESS_EQUAL: con.add(IloRange(env, -IloInfinity, m.b[c])); break; case EQUAL: con.add(IloRange(env, m.b[c], m.b[c])); break; case GREATER_EQUAL: con.add(IloRange(env, m.b[c], IloInfinity)); } for (const pair<uint32_t, double>& p : m.A[c]) con[c].setLinearCoef(x[p.first], p.second); con[c].setName(m.conDesc[c].c_str()); } model.add(obj); model.add(con); }
static void populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); x.add(IloNumVar(env, -1.0, 1.0)); x.add(IloNumVar(env, 0.0, 1.0)); model.add(IloMinimize(env, 0.5 * (-3*x[0]*x[0] - 3*x[1]*x[1] + - 1*x[0]*x[1] ) )); c.add( - x[0] + x[1] >= 0); c.add( x[0] + x[1] >= 0); model.add(c); } // END populatebyrow
/** Destructor. */ ~Worker() { if ( handle ) { handle.kill(); handle.join(); } if ( cplex.getImpl() ) { cplex.userfunction(USERACTION_REMOVECALLBACK, 0, NULL, 0, 0, NULL); cplex.end(); } rng.end(); x.end(); obj.end(); model.end(); }
static void populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); x.add(IloNumVar(env, 0.0, 40.0)); x.add(IloNumVar(env, 0.0, IloInfinity, ILOINT)); x.add(IloNumVar(env, 0.0, IloInfinity, ILOINT)); x.add(IloNumVar(env, 2.0, 3.0, ILOINT)); model.add(IloMaximize(env, x[0] + 2 * x[1] + 3 * x[2] + x[3])); c.add( - x[0] + x[1] + x[2] + 10 * x[3] <= 20); c.add( x[0] - 3 * x[1] + x[2] <= 30); c.add( x[1] - 3.5* x[3] == 0); model.add(c); IloNumVarArray sosvar(env, 2); IloNumArray sosval(env, 2); sosvar[0] = x[2]; sosvar[1] = x[3]; sosval[0] = 25.0; sosval[1] = 18.0; model.add(IloSOS1(model.getEnv(), sosvar, sosval)); } // END populatebyrow
/** 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()); }
// This routine set up the IloCplex algorithm to solve the worker LP, and // creates the worker LP (i.e., the dual of flow constraints and // capacity constraints of the flow MILP) // // Modeling variables: // forall k in V0, i in V: // u(k,i) = dual variable associated with flow constraint (k,i) // // forall k in V0, forall (i,j) in A: // v(k,i,j) = dual variable associated with capacity constraint (k,i,j) // // Objective: // minimize sum(k in V0) sum((i,j) in A) x(i,j) * v(k,i,j) // - sum(k in V0) u(k,0) + sum(k in V0) u(k,k) // // Constraints: // forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j) // // Nonnegativity on variables v(k,i,j) // forall k in V0, forall (i,j) in A: v(k,i,j) >= 0 // void createWorkerLP(IloCplex cplex, IloNumVarArray v, IloNumVarArray u, IloObjective obj, IloInt numNodes) { IloInt i, j, k; IloEnv env = cplex.getEnv(); IloModel mod(env, "atsp_worker"); // Set up IloCplex algorithm to solve the worker LP cplex.extract(mod); cplex.setOut(env.getNullStream()); // Turn off the presolve reductions and set the CPLEX optimizer // to solve the worker LP with primal simplex method. cplex.setParam(IloCplex::Reduce, 0); cplex.setParam(IloCplex::RootAlg, IloCplex::Primal); // Create variables v(k,i,j) forall k in V0, (i,j) in A // For simplicity, also dummy variables v(k,i,i) are created. // Those variables are fixed to 0 and do not partecipate to // the constraints. IloInt numArcs = numNodes * numNodes; IloInt vNumVars = (numNodes-1) * numArcs; IloNumVarArray vTemp(env, vNumVars, 0, IloInfinity); for (k = 1; k < numNodes; ++k) { for (i = 0; i < numNodes; ++i) { vTemp[(k-1)*numArcs + i *numNodes + i].setBounds(0, 0); } } v.clear(); v.add(vTemp); vTemp.end(); mod.add(v); // Set names for variables v(k,i,j) for (k = 1; k < numNodes; ++k) { for(i = 0; i < numNodes; ++i) { for(j = 0; j < numNodes; ++j) { char varName[100]; sprintf(varName, "v.%d.%d.%d", (int) k, (int) i, (int) j); v[(k-1)*numArcs + i*numNodes + j].setName(varName); } } } // Associate indices to variables v(k,i,j) IloIntArray vIndex(env, vNumVars); for (j = 0; j < vNumVars; ++j) { vIndex[j] = j; v[j].setObject(&vIndex[j]); } // Create variables u(k,i) forall k in V0, i in V IloInt uNumVars = (numNodes-1) * numNodes; IloNumVarArray uTemp(env, uNumVars, -IloInfinity, IloInfinity); u.clear(); u.add(uTemp); uTemp.end(); mod.add(u); // Set names for variables u(k,i) for (k = 1; k < numNodes; ++k) { for(i = 0; i < numNodes; ++i) { char varName[100]; sprintf(varName, "u.%d.%d", (int) k, (int) i); u[(k-1)*numNodes + i].setName(varName); } } // Associate indices to variables u(k,i) IloIntArray uIndex(env, uNumVars); for (j = 0; j < uNumVars; ++j) { uIndex[j] = vNumVars + j; u[j].setObject(&uIndex[j]); } // Initial objective function is empty obj.setSense(IloObjective::Minimize); mod.add(obj); // Add constraints: // forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j) for (k = 1; k < numNodes; ++k) { for(i = 0; i < numNodes; ++i) { for(j = 0; j < numNodes; ++j) { if ( i != j ) { IloExpr expr(env); expr -= v[(k-1)*numArcs + i*(numNodes) + j]; expr += u[(k-1)*numNodes + i]; expr -= u[(k-1)*numNodes + j]; mod.add(expr <= 0); expr.end(); } } } } }// END createWorkerLP
Example(IloEnv env) : nblocks(0), model(env), vars(env), ranges(env) { // Model data. // fixed[] is the fixed cost for opening a facility, // cost[i,j] is the cost for serving customer i from facility j. static double const fixed[] = { 2.0, 3.0, 3.0 }; static double const cost[] = { 2.0, 3.0, 4.0, 5.0, 7.0, 4.0, 3.0, 1.0, 2.0, 6.0, 5.0, 4.0, 2.0, 1.0, 3.0 }; #define NFACTORY ((CPXDIM)(sizeof(fixed) / sizeof(fixed[0]))) #define NCUSTOMER ((CPXDIM)((sizeof(cost) / sizeof(cost[0])) / NFACTORY)) nblocks = NCUSTOMER; IloExpr obj(env); // Create integer y variables. IloNumVarArray y(env); for (IloInt f = 0; f < NFACTORY; ++f) { std::stringstream s; s << "y" << f; IloIntVar v(env, 0, 1, s.str().c_str()); obj += fixed[f] * v; objMap[v] = fixed[f]; y.add(v); blockMap.insert(BlockMap::value_type(v, -1)); intersectMap.insert(IntersectMap::value_type(v, RowSet())); } // Create continuous x variables. IloNumVarArray x(env); for (IloInt f = 0; f < NFACTORY; ++f) { for (IloInt c = 0; c < NCUSTOMER; ++c) { std::stringstream s; s << "x" << f << "#" << c; IloNumVar v(env, 0.0, IloInfinity, s.str().c_str()); obj += v * cost[f * NCUSTOMER + c]; objMap[v] = cost[f * NCUSTOMER + c]; x.add(v); blockMap.insert(BlockMap::value_type(v, c)); intersectMap.insert(IntersectMap::value_type(v, RowSet())); } } vars.add(y); vars.add(x); model.add(vars); // Add objective function. model.add(IloMinimize(env, obj, "obj")); objSense = IloObjective::Minimize; obj.end(); // Satisfy each customer's demand. for (IloInt c = 0; c < NCUSTOMER; ++c) { std::stringstream s; s << "c1_" << c; IloRange r(env, 1.0, IloInfinity, s.str().c_str()); IloExpr lhs(env); for (IloInt f = 0; f < NFACTORY; ++f) { lhs += x[f * NCUSTOMER + c]; intersectMap[x[f * NCUSTOMER + c]].insert(r); } r.setExpr(lhs); ranges.add(r); lhs.end(); } // A factory must be open if we service from it. for (IloInt c = 0; c < NCUSTOMER; ++c) { for (IloInt f = 0; f < NFACTORY; ++f) { std::stringstream s; s << "c2_" << c << "#" << f; IloRange r(env, 0.0, IloInfinity, s.str().c_str()); intersectMap[x[f * NCUSTOMER + c]].insert(r); intersectMap[y[f]].insert(r); r.setExpr(-x[f * NCUSTOMER + c] + y[f]); ranges.add(r); } } // Capacity constraint. IloRange r(env, -IloInfinity, NFACTORY - 1, "c3"); IloExpr lhs(env); for (IloInt f = 0; f < NFACTORY; ++f) { lhs += y[f]; intersectMap[y[f]].insert(r); } r.setExpr(lhs); ranges.add(r); lhs.end(); model.add(ranges); #undef NFACTORY #undef NCUSTOMER }
void makeCuts(const IloNumVarArray vars, IloExprArray lhs, IloNumArray rhs) { IloNumVar x11, x12, x13, x14, x15; IloNumVar x21, x22, x23, x24, x25; IloNumVar x31, x32, x33, x34, x35; IloNumVar x41, x42, x43, x44, x45; IloNumVar x51, x52, x53, x54, x55; IloNumVar w11, w12, w13, w14, w15; IloNumVar w21, w22, w23, w24, w25; IloNumVar w31, w32, w33, w34, w35; IloNumVar w41, w42, w43, w44, w45; IloNumVar w51, w52, w53, w54, w55; IloInt num = vars.getSize(); for (IloInt i = 0; i < num; i++) { if ( strcmp(vars[i].getName(), "X11") == 0 ) x11 = vars[i]; else if ( strcmp(vars[i].getName(), "X12") == 0 ) x12 = vars[i]; else if ( strcmp(vars[i].getName(), "X13") == 0 ) x13 = vars[i]; else if ( strcmp(vars[i].getName(), "X14") == 0 ) x14 = vars[i]; else if ( strcmp(vars[i].getName(), "X15") == 0 ) x15 = vars[i]; else if ( strcmp(vars[i].getName(), "X21") == 0 ) x21 = vars[i]; else if ( strcmp(vars[i].getName(), "X22") == 0 ) x22 = vars[i]; else if ( strcmp(vars[i].getName(), "X23") == 0 ) x23 = vars[i]; else if ( strcmp(vars[i].getName(), "X24") == 0 ) x24 = vars[i]; else if ( strcmp(vars[i].getName(), "X25") == 0 ) x25 = vars[i]; else if ( strcmp(vars[i].getName(), "X31") == 0 ) x31 = vars[i]; else if ( strcmp(vars[i].getName(), "X32") == 0 ) x32 = vars[i]; else if ( strcmp(vars[i].getName(), "X33") == 0 ) x33 = vars[i]; else if ( strcmp(vars[i].getName(), "X34") == 0 ) x34 = vars[i]; else if ( strcmp(vars[i].getName(), "X35") == 0 ) x35 = vars[i]; else if ( strcmp(vars[i].getName(), "X41") == 0 ) x41 = vars[i]; else if ( strcmp(vars[i].getName(), "X42") == 0 ) x42 = vars[i]; else if ( strcmp(vars[i].getName(), "X43") == 0 ) x43 = vars[i]; else if ( strcmp(vars[i].getName(), "X44") == 0 ) x44 = vars[i]; else if ( strcmp(vars[i].getName(), "X45") == 0 ) x45 = vars[i]; else if ( strcmp(vars[i].getName(), "X51") == 0 ) x51 = vars[i]; else if ( strcmp(vars[i].getName(), "X52") == 0 ) x52 = vars[i]; else if ( strcmp(vars[i].getName(), "X53") == 0 ) x53 = vars[i]; else if ( strcmp(vars[i].getName(), "X54") == 0 ) x54 = vars[i]; else if ( strcmp(vars[i].getName(), "X55") == 0 ) x55 = vars[i]; else if ( strcmp(vars[i].getName(), "W11") == 0 ) w11 = vars[i]; else if ( strcmp(vars[i].getName(), "W12") == 0 ) w12 = vars[i]; else if ( strcmp(vars[i].getName(), "W13") == 0 ) w13 = vars[i]; else if ( strcmp(vars[i].getName(), "W14") == 0 ) w14 = vars[i]; else if ( strcmp(vars[i].getName(), "W15") == 0 ) w15 = vars[i]; else if ( strcmp(vars[i].getName(), "W21") == 0 ) w21 = vars[i]; else if ( strcmp(vars[i].getName(), "W22") == 0 ) w22 = vars[i]; else if ( strcmp(vars[i].getName(), "W23") == 0 ) w23 = vars[i]; else if ( strcmp(vars[i].getName(), "W24") == 0 ) w24 = vars[i]; else if ( strcmp(vars[i].getName(), "W25") == 0 ) w25 = vars[i]; else if ( strcmp(vars[i].getName(), "W31") == 0 ) w31 = vars[i]; else if ( strcmp(vars[i].getName(), "W32") == 0 ) w32 = vars[i]; else if ( strcmp(vars[i].getName(), "W33") == 0 ) w33 = vars[i]; else if ( strcmp(vars[i].getName(), "W34") == 0 ) w34 = vars[i]; else if ( strcmp(vars[i].getName(), "W35") == 0 ) w35 = vars[i]; else if ( strcmp(vars[i].getName(), "W41") == 0 ) w41 = vars[i]; else if ( strcmp(vars[i].getName(), "W42") == 0 ) w42 = vars[i]; else if ( strcmp(vars[i].getName(), "W43") == 0 ) w43 = vars[i]; else if ( strcmp(vars[i].getName(), "W44") == 0 ) w44 = vars[i]; else if ( strcmp(vars[i].getName(), "W45") == 0 ) w45 = vars[i]; else if ( strcmp(vars[i].getName(), "W51") == 0 ) w51 = vars[i]; else if ( strcmp(vars[i].getName(), "W52") == 0 ) w52 = vars[i]; else if ( strcmp(vars[i].getName(), "W53") == 0 ) w53 = vars[i]; else if ( strcmp(vars[i].getName(), "W54") == 0 ) w54 = vars[i]; else if ( strcmp(vars[i].getName(), "W55") == 0 ) w55 = vars[i]; } lhs.add(x21 - x22); rhs.add(0.0); lhs.add(x22 - x23); rhs.add(0.0); lhs.add(x23 - x24); rhs.add(0.0); lhs.add(2.08*x11 + 2.98*x21 + 3.47*x31 + 2.24*x41 + 2.08*x51 + 0.25*w11 + 0.25*w21 + 0.25*w31 + 0.25*w41 + 0.25*w51); rhs.add(20.25); lhs.add(2.08*x12 + 2.98*x22 + 3.47*x32 + 2.24*x42 + 2.08*x52 + 0.25*w12 + 0.25*w22 + 0.25*w32 + 0.25*w42 + 0.25*w52); rhs.add(20.25); lhs.add(2.08*x13 + 2.98*x23 + 3.47*x33 + 2.24*x43 + 2.08*x53 + 0.25*w13 + 0.25*w23 + 0.25*w33 + 0.25*w43 + 0.25*w53); rhs.add(20.25); lhs.add(2.08*x14 + 2.98*x24 + 3.47*x34 + 2.24*x44 + 2.08*x54 + 0.25*w14 + 0.25*w24 + 0.25*w34 + 0.25*w44 + 0.25*w54); rhs.add(20.25); lhs.add(2.08*x15 + 2.98*x25 + 3.47*x35 + 2.24*x45 + 2.08*x55 + 0.25*w15 + 0.25*w25 + 0.25*w35 + 0.25*w45 + 0.25*w55); rhs.add(16.25); }
// 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]); }
void LpSolver::populatebyrow (CplexConverter& cplexConverter, IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); // CAPITAL LETTERS MEAN I NEED YOUR HELP, here is help // IloExpr cost(env); // Create Variables // cout << "size of var: " << cplexConverter.variables.size() << endl; for (int i = 0; i < cplexConverter.variables.size(); ++i){ IloNumVar iloVar(env, 0.0, cplexConverter.capacities[i], IloNumVar::Int); // cout << iloVar << endl; x.add(iloVar); } //Capacity Constraints for (auto &it : cplexConverter.atomicIdToVarIdDict){ IloExpr t(env); // cout << "adding constraint "; for (int j = 0; j < it.second.size(); j++){ // cout << "x[" << it.second[j] << "] + "; t += x[it.second[j]]; } // cout << endl; c.add(t <= cplexConverter.graph->atomicEdges[it.first]->capacity); // cout << c << endl; t.end(); } // other constraints for (auto nodePair : cplexConverter.graph->nodes){ // For all nodes Node* n = nodePair.second; if(n == cplexConverter.src){ // source constraints // IloExpr inFlow(env); IloExpr outFlow(env); for(auto &atoIn : n->atomicEdge_in){ int aeId = atoIn.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; outFlow += x[vId]; // cost += cplexConverter.graph->atomicEdges[cplexConverter.variables[vId].atomicEdgeId]->interest_rate * x[vId]; } } for (auto &atoOut : n->atomicEdge_out){ int aeId = atoOut.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; // inFlow += x[vId]; c.add(x[vId] == 0); // cost -= cplexConverter.graph->atomicEdges[cplexConverter.variables[vId].atomicEdgeId]->interest_rate * x[vId]; } } c.add(outFlow == cplexConverter.request); // inFlow.end(); outFlow.end(); } else if(n == cplexConverter.dest){ // destination constraints IloExpr inFlow(env); // IloExpr outFlow(env); for(auto &atoIn : n->atomicEdge_in){ int aeId = atoIn.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; // outFlow += x[vId]; c.add(x[vId] == 0); } } for (auto &atoOut : n->atomicEdge_out){ int aeId = atoOut.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; inFlow += x[vId]; } } c.add(inFlow == cplexConverter.request); inFlow.end(); // outFlow.end(); } else { // Monotonicity Constraints for (int i = 0; i < credNetConstants.totalIrs.size(); ++i){ IloExpr tempin(env); IloExpr tempout(env); for (auto &atoIn : n->atomicEdge_in){ int aeId = atoIn.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; if (cplexConverter.variables[vId].interest_rate <= credNetConstants.totalIrs[i]){ tempout += x[vId]; } } } for (auto &atoOut : n->atomicEdge_out){ int aeId = atoOut.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; if (cplexConverter.variables[vId].interest_rate <= credNetConstants.totalIrs[i]){ tempin += x[vId]; } } } c.add(tempout - tempin >= 0); tempout.end(); tempin.end(); } //Flow Constraints IloExpr inFlow(env); IloExpr outFlow(env); for(auto &atoIn : n->atomicEdge_in){ int aeId = atoIn.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; outFlow += x[vId]; } } for (auto &atoOut : n->atomicEdge_out){ int aeId = atoOut.second->atomicEdgeId; for (int j = 0; j < cplexConverter.atomicIdToVarIdDict[aeId].size(); j++){ // var Id int vId = cplexConverter.atomicIdToVarIdDict[aeId][j]; inFlow += x[vId]; } } c.add(inFlow - outFlow == 0); inFlow.end(); outFlow.end(); } } model.add(c); // model.add(IloMinimize(env, cost)); // model.add(IloMaximize(env,cost)); //option to minimize cost // cost.end(); } // END populatebyrow
static void populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c) { IloEnv env = model.getEnv(); IloNumArray costs(env); IloNumArray time(env); IloNumArray product(env); int costs_array[] = {1,1,1,10,1,12,2,2,5,10}; int time_array[] = {10,1,7,3,2,3,2,3,7,1}; int product_array[] = {0,3,1,2,-2,0,0,0,0,0}; for(int i=0;i<10;i++) costs.add(costs_array[i]); for(int i=0;i<10;i++) time.add(time_array[i]); for(int i=0;i<10;i++) product.add(product_array[i]); x.add(IloBoolVar(env,"x12")); //0 x.add(IloBoolVar(env,"x24")); //1 x.add(IloBoolVar(env,"x46")); //2 x.add(IloBoolVar(env,"x13")); //3 x.add(IloBoolVar(env,"x32")); //4 x.add(IloBoolVar(env,"x35")); //5 x.add(IloBoolVar(env,"x56")); //6 x.add(IloBoolVar(env,"x25")); //7 x.add(IloBoolVar(env,"x34")); //8 x.add(IloBoolVar(env,"x45")); //9 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s2")); //10 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s3")); //11 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s4")); //12 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s5")); //13 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s1")); //14 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"s6")); //15 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q2")); //16 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q3")); //17 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q4")); //18 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q5")); //19 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q1")); //20 x.add(IloNumVar(env,0,IloInfinity,ILOINT,"q6")); //21 model.add(IloMinimize(env, costs[0]*x[0] + costs[1]*x[1] + costs[2]*x[2] + costs[3]*x[3] + costs[4]*x[4] + costs[5]*x[5] + costs[6]*x[6] + costs[7]*x[7] + costs[8]*x[8] + costs[9]*x[9])); c.add(x[0]+ x[3] == 1); // arcs sortant du noeud de depart c.add(x[2]+ x[6] == 1); // arcs entrant au noeud d arrivee c.add(x[1]+ x[7] - x[0] - x[4] == 0); c.add(x[8]+ x[5] + x[4] - x[3] == 0); c.add(x[9]+ x[2] - x[1] - x[8] == 0); c.add(x[6]- x[7] - x[5] - x[9] == 0); c.add(time[0]*x[0] + time[1]*x[1] + time[2]*x[2] + time[3]*x[3] + time[4]*x[4] + time[5]*x[5] + time[6]*x[6] + time[7]*x[7] + time[8]*x[8] + time[9]*x[9] <= 14); //c.add(product[0]*x[0] + product[1]*x[1] + product[2]*x[2] + product[3]*x[3] + product[4]*x[4] + product[5]*x[5] + product[6]*x[6] + product[7]*x[7] + product[8]*x[8] + product[9]*x[9] <= 4); c.add(x[14]+time[0]-1000*(1-x[0]) - x[10]<= 0); c.add(x[20]+product[0]-1000*(1-x[0]) - x[16]<= 0); c.add(x[10]+time[1]-1000*(1-x[1]) - x[12]<= 0); c.add(x[16]+product[1]-1000*(1-x[1]) - x[18]<= 0); c.add(x[18]-product[1]-1000*(1-x[1]) - x[16]<= 0); c.add(x[12]+time[2]-1000*(1-x[2]) - x[15]<= 0); c.add(x[18]+product[2]-1000*(1-x[2]) - x[21]<= 0); c.add(x[21]-product[2]-1000*(1-x[2]) - x[18]<= 0); c.add(x[14]+time[3]-1000*(1-x[3]) - x[11]<= 0); c.add(x[20]+product[3]-1000*(1-x[3]) - x[17]<= 0); c.add(x[17]-product[3]-1000*(1-x[3]) - x[20]<= 0); c.add(x[13]+time[6]-1000*(1-x[6]) - x[15]<= 0); c.add(x[19]+product[6]-1000*(1-x[6]) - x[21]<= 0); c.add(x[10]+time[7]-1000*(1-x[7]) - x[13]<= 0); c.add(x[16]+product[7]-1000*(1-x[7]) - x[19]<= 0); c.add(x[12]+time[9]-1000*(1-x[9]) - x[13]<= 0); c.add(x[18]+product[9]-1000*(1-x[9]) - x[19]<= 0); c.add(x[11]+time[4]-1000*(1-x[4]) - x[10] <=0); c.add(x[17]+product[4]-1000*(1-x[4]) - x[16]<= 0); c.add(x[16]-product[4]-1000*(1-x[4]) - x[17]<= 0); c.add(x[11]+time[8]-1000*(1-x[8]) - x[12]<= 0); c.add(x[17]+product[8]-1000*(1-x[8]) - x[18]<= 0); c.add(x[11]+time[5]-1000*(1-x[5]) - x[13]<= 0); c.add(x[17]+product[5]-1000*(1-x[5]) - x[19]<= 0); c.add(5 <= x[10] <= 7); c.add(2 <= x[11] <= 5); c.add(5 <= x[12] <= 9); c.add(0 <= x[13] <= 20); c.add(0 <= x[14] <= 0); c.add(0 <= x[15] <= 14); /* c.add(2 <= x[17] <= 4); c.add(0 <= x[16] <= 2); c.add(3 <= x[18] <= 4); c.add(0 <= x[19] <= 1000); //c.add(0 <= x[20] <= 0);*/ c.add(3 <= x[21] <= 4); c.add( x[20] == 1); model.add(c); }
/** Create a new worker. * The constructor mainly does the following: * - create an IloCplex instance that refers to a remote worker, * - load the model in <code>modelfile</code>, * - setup parameters depending on this worker's index, * - start an asynchronous solve. * If anything fails then an exception will be thrown. * @param env The environment used for instantiating Ilo* objects. * @param i The index of the worker to be created. This also * determines the parameter settings to use in this worker. * @param s A pointer to the global solve state. * @param transport The transport name for the IloCplex constructor. * @param argc The argument count for the IloCplex constructor. * @param argv The array of transport arguments for the IloCplex * constructor. * @param modelfile Name of the model to be loaded into the worker. * @param output The output mode. * @param objdiff The minimal difference between so that two * consecutive objective function values are considered * different. */ Worker(IloEnv env, int i, SolveState *s, char const *transport, int argc, char const **argv, char const *modelfile, OUTPUT output, double objdiff) : idx(i), state(s), model(env), cplex(0), handle(0), primal(IloInfinity), dual(-IloInfinity), obj(env), x(env), rng(env), infoHandler(this), outb(idx), outs(&outb) { try { // Create remote object, setup output and load the model. cplex = IloCplex(model, transport, argc, argv); switch (output) { case OUTPUT_SILENT: // Disable output on the output and warning stream. cplex.setOut(env.getNullStream()); cplex.setWarning(env.getNullStream()); break; case OUTPUT_PREFIXED: // Redirect output to our custom stream. cplex.setOut(outs); cplex.setWarning(outs); break; case OUTPUT_LOG: // Nothing to do here. By default output is enabled. break; } cplex.importModel(model, modelfile, obj, x, rng); if ( obj.getSense() == IloObjective::Minimize ) { primal = -IloInfinity; dual = IloInfinity; } // We set the thread count for each solver to 1 so that we do not // run into problems if multiple solves are performed on the same // machine. cplex.setParam(IloCplex::Param::Threads, 1); // Each worker runs with a different random seed. This way we // get different paths through the tree even if the other // parameter settings are the same. cplex.setParam(IloCplex::Param::RandomSeed, idx); // Apply parameter settings. for (class ParamValue const *vals = settings[idx % NUMSETTINGS].values; vals->isValid(); ++vals) vals->apply(cplex); // Install callback and set objective change. int status = cplex.userfunction (USERACTION_ADDCALLBACK, 0, NULL, 0, 0, NULL); if ( status ) throw status; IloCplex::Serializer s; s.add(objdiff); status = cplex.userfunction (USERACTION_CHANGEOBJDIFF, s.getRawLength(), s.getRawData(), 0, 0, NULL); if ( status ) throw status; // Register the handler that will process info messages sent // from the worker. cplex.setRemoteInfoHandler(&infoHandler); // Everything is setup. Launch the asynchronous solve. handle = cplex.solve(true); } catch (...) { // In case of an exception we need to take some special // cleanup actions. Note that if we get here then the // solve cannot have been started and we don't need to // kill or join the asynchronous solve. if ( cplex.getImpl() ) cplex.end(); rng.end(); x.end(); obj.end(); model.end(); throw; } }
// 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 << " " << x[i] << " and " << dslack[i] << endl; return false; } } } for (IloInt i = 0; i < rngs.getSize(); ++i) { if ( fabs(slack[i]) > tol && fabs(pi[i]) > tol ) { env.error() << "Invalid complementary slackness for " << endl << rngs[i] << ":" << endl << " " << slack[i] << " and " << pi[i] << endl; return false; } } // Test stationarity. // We must have // c - g[i]'(X)*pi[i] = 0 // where c is the objective function, g[i] is the i-th constraint of the // problem, g[i]'(x) is the derivate of g[i] with respect to x and X is the // optimal solution. // We need to distinguish the following cases: // - linear constraints g(x) = ax - b. The derivative of such a // constraint is g'(x) = a. // - second order constraints g(x[1],...,x[n]) = -x[1] + |(x[2],...,x[n])| // the derivative of such a constraint is // g'(x) = (-1, x[2]/|(x[2],...,x[n])|, ..., x[n]/|(x[2],...,x[n])| // (here |.| denotes the Euclidean norm). // - bound constraints g(x) = -x for variables that are not explicitly // contained in any second order cone constraint. The derivative for // such a constraint is g'(x) = -1. // Note that it may happen that the derivative of a second order cone // constraint is not defined at the optimal solution X (this happens if // X=0). In this case we just skip the stationarity test. IloNumArray sum(env, vars.getSize()); for (IloExpr::LinearIterator it = obj.getLinearIterator(); it.ok(); ++it) sum[idx(it.getVar())] = it.getCoef(); for (IloInt i = 0; i < vars.getSize(); ++i) { IloNumVar v = vars[i]; if ( cone[i] == NOT_IN_CONE ) sum[i] -= dslack[i]; } for (IloInt i = 0; i < rngs.getSize(); ++i) { IloRange r = rngs[i]; if ( r.getQuadIterator().ok() ) { // Quadratic (second order cone) constraint. IloNum norm = 0.0; for (IloExpr::QuadIterator q = r.getQuadIterator(); q.ok(); ++q) { if ( q.getCoef() > 0 ) norm += x[idx(q.getVar1())] * x[idx(q.getVar1())]; } norm = sqrt(norm); if ( fabs(norm) <= tol ) { // Derivative is not defined. Skip test. env.warning() << "Cannot test stationarity at non-differentiable point." << endl; return true; } else { for (IloExpr::QuadIterator q = r.getQuadIterator(); q.ok(); ++q) { if ( q.getCoef() < 0 ) sum[idx(q.getVar1())] -= pi[i]; else sum[idx(q.getVar1())] += pi[i] * x[idx(q.getVar1())] / norm; } } } else { // Linear constraint. for (IloExpr::LinearIterator l = r.getLinearIterator(); l.ok(); ++l) sum[idx(l.getVar())] -= pi[i] * l.getCoef(); } } // Now test that all elements in sum[] are 0. for (IloInt i = 0; i < vars.getSize(); ++i) { if ( fabs(sum[i]) > tol ) { env.error() << "Invalid stationarity " << sum[i] << " for " << vars[i] << endl; return false; } } return true; }
/** 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())); }
ILOSTLBEGIN void makeCuts(IloRangeArray cuts, const IloNumVarArray& vars) { IloNumVar x11, x12, x13, x14, x15; IloNumVar x21, x22, x23, x24, x25; IloNumVar x31, x32, x33, x34, x35; IloNumVar x41, x42, x43, x44, x45; IloNumVar x51, x52, x53, x54, x55; IloNumVar w11, w12, w13, w14, w15; IloNumVar w21, w22, w23, w24, w25; IloNumVar w31, w32, w33, w34, w35; IloNumVar w41, w42, w43, w44, w45; IloNumVar w51, w52, w53, w54, w55; IloInt num = vars.getSize(); for (IloInt i = 0; i < num; i++) { if ( strcmp(vars[i].getName(), "X11") == 0 ) x11 = vars[i]; else if ( strcmp(vars[i].getName(), "X12") == 0 ) x12 = vars[i]; else if ( strcmp(vars[i].getName(), "X13") == 0 ) x13 = vars[i]; else if ( strcmp(vars[i].getName(), "X14") == 0 ) x14 = vars[i]; else if ( strcmp(vars[i].getName(), "X15") == 0 ) x15 = vars[i]; else if ( strcmp(vars[i].getName(), "X21") == 0 ) x21 = vars[i]; else if ( strcmp(vars[i].getName(), "X22") == 0 ) x22 = vars[i]; else if ( strcmp(vars[i].getName(), "X23") == 0 ) x23 = vars[i]; else if ( strcmp(vars[i].getName(), "X24") == 0 ) x24 = vars[i]; else if ( strcmp(vars[i].getName(), "X25") == 0 ) x25 = vars[i]; else if ( strcmp(vars[i].getName(), "X31") == 0 ) x31 = vars[i]; else if ( strcmp(vars[i].getName(), "X32") == 0 ) x32 = vars[i]; else if ( strcmp(vars[i].getName(), "X33") == 0 ) x33 = vars[i]; else if ( strcmp(vars[i].getName(), "X34") == 0 ) x34 = vars[i]; else if ( strcmp(vars[i].getName(), "X35") == 0 ) x35 = vars[i]; else if ( strcmp(vars[i].getName(), "X41") == 0 ) x41 = vars[i]; else if ( strcmp(vars[i].getName(), "X42") == 0 ) x42 = vars[i]; else if ( strcmp(vars[i].getName(), "X43") == 0 ) x43 = vars[i]; else if ( strcmp(vars[i].getName(), "X44") == 0 ) x44 = vars[i]; else if ( strcmp(vars[i].getName(), "X45") == 0 ) x45 = vars[i]; else if ( strcmp(vars[i].getName(), "X51") == 0 ) x51 = vars[i]; else if ( strcmp(vars[i].getName(), "X52") == 0 ) x52 = vars[i]; else if ( strcmp(vars[i].getName(), "X53") == 0 ) x53 = vars[i]; else if ( strcmp(vars[i].getName(), "X54") == 0 ) x54 = vars[i]; else if ( strcmp(vars[i].getName(), "X55") == 0 ) x55 = vars[i]; else if ( strcmp(vars[i].getName(), "W11") == 0 ) w11 = vars[i]; else if ( strcmp(vars[i].getName(), "W12") == 0 ) w12 = vars[i]; else if ( strcmp(vars[i].getName(), "W13") == 0 ) w13 = vars[i]; else if ( strcmp(vars[i].getName(), "W14") == 0 ) w14 = vars[i]; else if ( strcmp(vars[i].getName(), "W15") == 0 ) w15 = vars[i]; else if ( strcmp(vars[i].getName(), "W21") == 0 ) w21 = vars[i]; else if ( strcmp(vars[i].getName(), "W22") == 0 ) w22 = vars[i]; else if ( strcmp(vars[i].getName(), "W23") == 0 ) w23 = vars[i]; else if ( strcmp(vars[i].getName(), "W24") == 0 ) w24 = vars[i]; else if ( strcmp(vars[i].getName(), "W25") == 0 ) w25 = vars[i]; else if ( strcmp(vars[i].getName(), "W31") == 0 ) w31 = vars[i]; else if ( strcmp(vars[i].getName(), "W32") == 0 ) w32 = vars[i]; else if ( strcmp(vars[i].getName(), "W33") == 0 ) w33 = vars[i]; else if ( strcmp(vars[i].getName(), "W34") == 0 ) w34 = vars[i]; else if ( strcmp(vars[i].getName(), "W35") == 0 ) w35 = vars[i]; else if ( strcmp(vars[i].getName(), "W41") == 0 ) w41 = vars[i]; else if ( strcmp(vars[i].getName(), "W42") == 0 ) w42 = vars[i]; else if ( strcmp(vars[i].getName(), "W43") == 0 ) w43 = vars[i]; else if ( strcmp(vars[i].getName(), "W44") == 0 ) w44 = vars[i]; else if ( strcmp(vars[i].getName(), "W45") == 0 ) w45 = vars[i]; else if ( strcmp(vars[i].getName(), "W51") == 0 ) w51 = vars[i]; else if ( strcmp(vars[i].getName(), "W52") == 0 ) w52 = vars[i]; else if ( strcmp(vars[i].getName(), "W53") == 0 ) w53 = vars[i]; else if ( strcmp(vars[i].getName(), "W54") == 0 ) w54 = vars[i]; else if ( strcmp(vars[i].getName(), "W55") == 0 ) w55 = vars[i]; } cuts.add(x21 - x22 <= 0); cuts[0].setName("cut0"); cuts.add(x22 - x23 <= 0); cuts.add(x23 - x24 <= 0); cuts.add(2.08*x11 + 2.98*x21 + 3.47*x31 + 2.24*x41 + 2.08*x51 + 0.25*w11 + 0.25*w21 + 0.25*w31 + 0.25*w41 + 0.25*w51 <= 20.25); cuts.add(2.08*x12 + 2.98*x22 + 3.47*x32 + 2.24*x42 + 2.08*x52 + 0.25*w12 + 0.25*w22 + 0.25*w32 + 0.25*w42 + 0.25*w52 <= 20.25); cuts.add(2.08*x13 + 2.98*x23 + 3.4722*x33 + 2.24*x43 + 2.08*x53 + 0.25*w13 + 0.25*w23 + 0.25*w33 + 0.25*w43 + 0.25*w53 <= 20.25); cuts.add(2.08*x14 + 2.98*x24 + 3.47*x34 + 2.24*x44 + 2.08*x54 + 0.25*w14 + 0.25*w24 + 0.25*w34 + 0.25*w44 + 0.25*w54 <= 20.25); cuts.add(2.08*x15 + 2.98*x25 + 3.47*x35 + 2.24*x45 + 2.08*x55 + 0.25*w15 + 0.25*w25 + 0.25*w35 + 0.25*w45 + 0.25*w55 <= 16.25); }
/** 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; }
/** Solve the <code>problem</code> using a distributed implementation of * Benders' decomposition. */ bool BendersOpt::solve (Problem const *problem, int argc, char const *const *argv, std::vector<char const *> const &machines) { IloEnv env = problem->getModel().getEnv(); std::vector<Block *> blocks; Block *master = 0; bool result = false; try { // Extract blocks and master problem. std::cout << "Extracting " << problem->getNBlocks() << " blocks." << std::endl; for (IloInt b = 0; b < problem->getNBlocks(); ++b) blocks.push_back(new Block(problem, b, argc, argv, machines)); master = new Block(problem, blocks); // Write out the master and all blocks (for debugging). master->cplex.exportModel("master.lp"); for (BlockVector::size_type b = 0; b < blocks.size(); ++b) { std::stringstream s; s << "block" << b << ".lp"; blocks[b]->cplex.exportModel(s.str().c_str()); } // Solve the master. // If we find a feasible solution then perform a final solve // with the original problem so that we get solution values for // all variables in the original problem. if ( master->cplex.solve() ) { // Perform a last solve to get the solution values. IloNumArray vals(env), startVals(env); IloNumVarArray startVars(env); master->cplex.getValues(vals, master->vars); IloCplex cplex(problem->getModel()); // Fix integral variables to their value in the master solution // and add them as MIP start. for (IloInt i = 0; i < vals.getSize(); ++i) if ( master->vars[i].getType() != IloNumVar::Float ) { double const v = IloRound(vals[i]); IloNumVar x = master->varMap[master->vars[i]]; startVals.add(v); startVars.add(x); // We add lazy constraints so as to make sure that // - we don't modify the original model // - the problem has only the unique optimal solution // we are interested in cplex.addLazyConstraint(x == v); } cplex.addMIPStart(startVars, startVals); cplex.solve(); // Report the results. std::cout << "#### Problem solved (" << cplex.getObjValue() << ", " << cplex.getCplexStatus() << ")." << std::endl; IloNumVarArray vars = problem->getVariables(); for (IloInt i = 0; i < vars.getSize(); ++i) std::cout << "#### \tx[" << i << "] = " << cplex.getValue(vars[i]) << std::endl; cplex.end(); result = true; } } catch (...) { if ( master ) delete master; while ( blocks.size() > 0 ) { delete blocks.back(); blocks.pop_back(); } throw; } delete master; while ( blocks.size() > 0 ) { delete blocks.back(); blocks.pop_back(); } return result; }
ILOBRANCHCALLBACK1(SOSbranch, IloSOS1Array, sos) { IloNumArray x; IloNumVarArray var; try { IloInt i; x = IloNumArray(getEnv()); var = IloNumVarArray(getEnv()); IloNum bestx = EPS; IloInt besti = -1; IloInt bestj = -1; IloInt num = sos.getSize(); for (i = 0; i < num; i++) { if ( getFeasibility(sos[i]) == Infeasible ) { var.clear(); sos[i].getVariables(var); getValues(x, var); IloInt n = var.getSize(); for (IloInt j = 0; j < n; j++) { IloNum inf = IloAbs(x[j] - IloRound(x[j])); if ( inf > bestx ) { bestx = inf; besti = i; bestj = j; } } } } if ( besti >= 0 ) { IloCplex::BranchDirectionArray dir; IloNumArray val; try { dir = IloCplex::BranchDirectionArray(getEnv()); val = IloNumArray(getEnv()); var.clear(); sos[besti].getVariables(var); IloInt n = var.getSize(); for (IloInt j = 0; j < n; j++) { if ( j != bestj ) { dir.add(IloCplex::BranchDown); val.add(0.0); } else { dir.add(IloCplex::BranchUp); val.add(1.0); } } makeBranch(var, val, dir, getObjValue()); makeBranch(var[bestj], 0.0, IloCplex::BranchDown, getObjValue()); } catch (...) { dir.end(); val.end(); throw; } dir.end(); val.end(); } } catch (...) { var.end(); x.end(); throw; } var.end(); x.end(); }