void profit_create_objective(graph g, IloModel model, IloNumVarArray x, IloNumVarArray z, int **columns) {
IloNumExpr e(model.getEnv());
for(int i = 0; i < g->bidders; i++) {
e += z[i];
}
model.add(IloMaximize(model.getEnv(), e));
}
void update()
{
switch (dir_)
{
case IP::MAX: model_.add(IloMaximize(env_, obj_)); break;
case IP::MIN: model_.add(IloMinimize(env_, obj_)); break;
}
}
void BNC::buildModelNF(){
env = new IloEnv;
model = new IloModel(*env);
variables = new IloNumVarArray(*env);
constraints = new IloRangeArray(*env);
//create variables
for( int i = 0; i < n; ++i ){
variables->add( IloIntVar( *env, 0, 1 ) );
variables->add( IloIntVar( *env, 0, 1 ) );
}
for( int i = 0, k = 0; i < n; ++i ){
for( int j = i; j < n; ++j ){
if( graph[i][j] ){
IloRange newconstraintA( *env, 0, 1 );
IloRange newconstraintB( *env, 0, 1 );
newconstraintA.setLinearCoef( (*variables)[i], 1 );
newconstraintA.setLinearCoef( (*variables)[j], 1 );
newconstraintB.setLinearCoef( (*variables)[n+i], 1 );
newconstraintB.setLinearCoef( (*variables)[n+j], 1 );
constraints->add( newconstraintA );
constraints->add( newconstraintB );
++k;
}
}
}
for( int i = 0; i < n; ++i ){
IloRange newconstraintAB( *env, 0, 1 );
newconstraintAB.setLinearCoef( (*variables)[i], 1 );
newconstraintAB.setLinearCoef( (*variables)[n+i], 1 );
constraints->add( newconstraintAB );
}
//objective function
IloObjective obj = IloMaximize(*env);
//objective
for( int i = 0 ; i < n; i++ ){
obj.setLinearCoef((*variables)[i], 1 );
obj.setLinearCoef((*variables)[n+i], 1 );
}
model->add( *constraints );
model->add( obj );
cplex = new IloCplex(*model);
configureCPLEX();
//write model in file cplexmodel.lp
cplex->exportModel("cplexmodel.lp");
}
static void
populatebynonzero (IloModel model, IloIntVarArray x, IloRangeArray c)
{
IloEnv env = model.getEnv();
IloObjective obj = IloMaximize(env);
int n, a;
scanf("%d", &n);
scanf("%d", &a);
//restrição
c.add(IloRange(env, -IloInfinity, a));
//variaveis
for(int i=0 ; i<n; i++){
x.add(IloIntVar(env, 0, 1));
}
/*x.add(IloIntVar(env, 0.0, 40.0));
x.add(IloIntVar(env));
x.add(IloIntVar(env));*/
/*obj.setLinearCoef(x[0], 1.0);
obj.setLinearCoef(x[1], 2.0);
obj.setLinearCoef(x[2], 3.0);*/
/*restricoes*/
for(int i=0 ; i<n; i++){
scanf("%d", &a);
c[0].setLinearCoef(x[i], a);
}
//objetivo
for(int i=0 ; i<n; i++){
scanf("%d", &a);
obj.setLinearCoef(x[i], a);
}
/*c[0].setLinearCoef(x[1], 1.0);
c[0].setLinearCoef(x[2], 1.0);
c[1].setLinearCoef(x[0], 1.0);
c[1].setLinearCoef(x[1], -3.0);
c[1].setLinearCoef(x[2], 1.0);*/
c[0].setName("c1");
for(int i=0; i<n; i++){
char tmp[10];
printf("x%d", i+1);
x[i].setName(tmp);
}
model.add(obj);
model.add(c);
} // END populatebynonzero
void Instance::ComputeCPLEXRevenue() {
IloEnv env;
IloInt i, j;
IloModel model(env);
IloInt nbImpressions = num_impressions_;
IloInt nbAdvertisers = num_advertisers_;
NumVarMatrix x(env, nbImpressions);
for(i = 0; i < nbImpressions; i++) {
x[i] = IloNumVarArray(env, nbAdvertisers, 0.0, 1.0, ILOFLOAT);
}
// Add impression constraints.
for(i = 0; i < nbImpressions; i++) {
model.add(IloSum(x[i]) <= 1.0);
}
// Add weighted contraint.
for(j = 0; j < nbAdvertisers; j++) {
IloExpr curr_adv_constraint(env);
for (__gnu_cxx::hash_map<int, long double>::iterator iter = bids_matrix_[j].begin();
iter != bids_matrix_[j].end();
++iter) {
curr_adv_constraint += ((double) iter->second) * ((double) weights_[j]) * x[iter->first][j];
}
model.add(curr_adv_constraint <= ((double) budgets_[j]));
}
IloExpr obj_exp(env);
for(i = 0; i < nbImpressions; i++) {
for(j = 0; j < nbAdvertisers; j++) {
obj_exp += ((double) transpose_bids_matrix_[i][j]) * x[i][j];
}
}
model.add(IloMaximize(env, obj_exp));
obj_exp.end();
IloCplex cplex(env);
cplex.setOut(env.getNullStream());
cplex.extract(model);
// Optimize the problem and obtain solution.
if ( !cplex.solve() ) {
env.error() << "Failed to optimize LP" << endl;
throw(-1);
}
cplex.exportModel("/Users/ciocan/Documents/Google/data/example.lp");
cout << "CPLEX opt is " << cplex.getObjValue() << "\n";
env.end();
}
static void
populatebynonzero(IloModel model, NumVarMatrix varOutput, NumVar3Matrix varHelp, Range3Matrix con)
{
IloEnv env = model.getEnv();
IloObjective obj = IloMaximize(env); //maximization function
for (int j = current; j < current + J; ++j)
{
for (int k = 0; k < K; ++k)
{
obj.setLinearCoef(varOutput[j][k], 1.0);//add all variables to objective function, factor 1
//constraint 0: express value of output objective variables
model.add(varOutput[j][k] + varHelp[j][k][2] - varHelp[j][k][3] == 0);
//constraint 1: Td2a>=+Td2b
model.add(varHelp[j][k][5] - varHelp[j][k][4] >= 0);
//constraint 2: Tj>=Td2a + Tdc + Tblow
model.add(varHelp[j][k][5] <= T[j] - Tdc - Tblow[j] - Tslack);
//constraint 3: Td2b = Tfa+Tfd
model.add(Tfd[k] == varHelp[j][k][4] - varHelp[j][k][3]);
//constraint 4: Td1a >= Td1b
model.add(0 <= varHelp[j][k][1] - varHelp[j][k][0]);
//constraint 5: Tfb >= Td1a+Tdf
model.add(Tdf[k] <= varHelp[j][k][2] - varHelp[j][k][1]);
//constraint 6: Td1b = T(j-a)+Tcd
model.add(T[j - a[k]] + Tcd == varHelp[j][k][0]);
//constraint 7: Td1a >= Td2b(j-b) + Tloss, 1
model.add(TlossD[k] <= varHelp[j][k][1] - varHelp[j - b[k]][k][4]);
//constraint 8: Tfb >= Tfa(j-1)+Tloss, 2
model.add(TlossF[k] <= varHelp[j][k][2] - varHelp[j - 1][k][3]);
//constraint 9: at least X s for every load
model.add(varOutput[j][k] >= TloadMin[k]);
}
//constraint 10: both spoons are picked up at same time at dropoff: Td2a,1 == Td2a,2
model.add(varHelp[j][1][5] == varHelp[j][0][5]);
}
model.add(obj);
}
void CPLEXSolver::add_in_constraint(LinearConstraint *con, double coef){
DBG("Creating a Gurobi representation of a constriant %s\n", "");
IloNumArray weights(*env, (IloInt)con->_coefficients.size());
IloNumVarArray vars(*env, (IloInt)con->_variables.size());
for(unsigned int i = 0; i < con->_variables.size(); ++i){
DBG("\tAdding variable to CPLEX\n%s", "");
IloNumVar var_ptr;
if(con->_variables[i]->_var == NULL){
IloNumVar::Type type;
if(con->_variables[i]->_continuous) type = IloNumVar::Float;
// else if(con->_lower == 0 && con->_upper == 1) type = IloNumVar::Bool;
else type = IloNumVar::Int;
var_ptr = IloNumVar(getEnv(),
con->_variables[i]->_lower, // LB
con->_variables[i]->_upper, // UB
type);
int *var_id = new int;
*var_id = variables->getSize();
variables->add(var_ptr);
con->_variables[i]->_var = (void*) var_id;
DBG("Created new variable with id %d. type:%c lb:%f ub:%f coef:%f\n", *var_id, type, con->_variables[i]->_lower, con->_variables[i]->_upper, coef);
} else {
var_ptr = (*variables)[*(int*)(con->_variables[i]->_var)];
}
vars[i] = (*variables)[*(int*)(con->_variables[i]->_var)];
weights[i] = con->_coefficients[i];
}
IloNumExprArg lin_expr = IloScalProd(weights, vars);
if(coef < -0.1){
model->add(IloMinimize(*env, lin_expr));
} else if(coef > 0.1){
model->add(IloMaximize(*env, lin_expr));
} else {
if(con->_lhs > -INFINITY && con->_rhs < INFINITY){
if(con->_lhs == con->_rhs) {
model->add(lin_expr == con->_lhs);
} else {
model->add(IloRange(*env, con->_lhs, lin_expr, con->_rhs));
}
} else if(con->_lhs > -INFINITY) model->add(lin_expr >= con->_lhs);
else if(con->_rhs < INFINITY) model->add(lin_expr <= con->_rhs);
}
}
bool MIQPSolver::createModel()
{
try
{
model.add(IloMaximize(environment, g - h - p + s));
model.add(constraints);
cplex = IloCplex(model);
}
catch (...)
{
return false;
}
return true;
}
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
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
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
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
void BNC::buildModelCF(){
env = new IloEnv;
model = new IloModel(*env);
variables = new IloNumVarArray(*env);
constraints = new IloRangeArray(*env);
list< list<int> > cliques;
int count_chose = 0;
bool chose_edge[n][n];
for( int i = 0; i < n; ++i )
for( int j = 0; j < n; ++j )
chose_edge[i][j] = false;
while( count_chose < m ){
list<int> current_clique;
//choose a initial node
for( int i = 0; i < n; ++i ){
for( int j = 0; j < n; ++j ){
if( graph[i][j] ){
if( !chose_edge[i][j] ){
chose_edge[i][j] = chose_edge[j][i] = true;
++count_chose;
current_clique.push_back(i);
current_clique.push_back(j);
goto done;
}
}
}
}
done:
//build a clique
int i = current_clique.front();
for( int j = 0; j < n; ++j ){
if( graph[i][j] ){
if( !chose_edge[i][j] ){
bool add_node = true;
list<int>::iterator it = current_clique.begin();
while( it != current_clique.end() ){
if( !graph[*it][j] ){
add_node = false;
break;
}
++it;
}
if( add_node ){
{
list<int>::iterator it = current_clique.begin();
while( it != current_clique.end() ){
if( !chose_edge[*it][j] )
++count_chose;
chose_edge[*it][j] = chose_edge[j][*it] = true;
++it;
}
}
current_clique.push_back(j);
}
}
}
}
cliques.push_back( current_clique );
}
//create variables
for( int i = 0; i < n; ++i ){
variables->add( IloIntVar( *env, 0, 1 ) );
variables->add( IloIntVar( *env, 0, 1 ) );
}
list< list<int> >::iterator it1 = cliques.begin();
while( it1 != cliques.end() ){
list<int>::iterator it2 = it1->begin();
IloRange newconstraintA( *env, 0, 1 );
IloRange newconstraintB( *env, 0, 1 );
while( it2 != it1->end() ){
newconstraintA.setLinearCoef( (*variables)[*it2], 1 );
newconstraintB.setLinearCoef( (*variables)[n+*it2], 1 );
++it2;
}
constraints->add( newconstraintA );
constraints->add( newconstraintB );
++it1;
}
for( int i = 0; i < n; ++i ){
IloRange newconstraintAB( *env, 0, 1 );
newconstraintAB.setLinearCoef( (*variables)[i], 1 );
newconstraintAB.setLinearCoef( (*variables)[n+i], 1 );
constraints->add( newconstraintAB );
}
//objective function
IloObjective obj = IloMaximize(*env);
//objective
for( int i = 0 ; i < n; i++ ){
obj.setLinearCoef((*variables)[i], 1 );
obj.setLinearCoef((*variables)[n+i], 1 );
}
model->add( *constraints );
model->add( obj );
cplex = new IloCplex(*model);
configureCPLEX();
//write model in file cplexmodel.lp
cplex->exportModel("cplexmodel.lp");
}
//on the reduced problem
void solveIP(double time_limit, int ite, double gap){
IloEnv env;
IloModel model(env);
IloIntVarArray x(env, n_var, 0, 1);
IloRangeArray con(env);
IloExpr obj(env);
int i,j,k;
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
obj+=group[i].profit[j]*x[sum_n_item[i]+j];
}
}
model.add(IloMaximize(env, obj));
obj.end();
for(k=0;k<m;k++){
IloExpr expr(env);
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
expr+=group[i].consume[j][k]*x[sum_n_item[i]+j];
}
}
con.add(expr<=Gb[k]);
expr.end();
}
for(i=0;i<n;i++){
IloExpr expr(env);
for(j=0;j<group[i].nItem;j++){
expr+=x[sum_n_item[i]+j];
}
con.add(expr==1);
expr.end();
}
/*
int *tempFix=new int[n_var];
memset(tempFix, 0, n_var*sizeof(int));
for(i=0;i<rp.len;i++){
tempFix[rp.posi[i]]=1;
}
//force those not appeared in rp to 0
for(i=0;i<n;i++){
IloExpr expr(env);
for(j=0;j<group[i].nItem;j++){
if(tempFix[sum_n_item[i]+j]==0){
expr+=x[sum_n_item[i]+j];
}
}
con.add(expr==0);
expr.end();
}
delete []tempFix;
*/
//add constrains from the last iteration
if(ite>0){
for(k=0;k<ite;k++){
IloExpr expr(env);
for(i=0;i<len_v1[k];i++){
expr+=x[pre_v1[k][i]];
}
for(i=0;i<len_v0[k];i++){
expr-=x[pre_v0[k][i]];
}
con.add(expr<=sum_pre_v1[k]-1);
expr.end();
}
}
if(0&&len_rdCost0>0&&len_rdCost1>0){
IloExpr expr(env);
for(i=0;i<len_rdCost1;i++){
expr+=(1-x[rdCost_sort1[i].posi])*rdCost_sort1[i].value;
}
for(i=0;i<len_rdCost0;i++){
expr+=x[rdCost_sort[i].posi]*rdCost_sort[i].value;
}
con.add(expr<=gap);
expr.end();
}
if(len_rdCost0>0){
printf("0 rdCostSort_len:%d. \n",len_rdCost0);
k=1;
int start=0, end;
int cnt=0;
//for(i=0;i<len_rdCost0;i++) printf("%lf, ", rdCost_sort[i].value);
while(start<len_rdCost0){
double sum=0;
for(i=start;i<len_rdCost0-k;i++){
sum=0;
for(int ii=i;ii<i+k;ii++){
sum+=rdCost_sort[ii].value;
}
if(sum<gap) break;
}
if(i>=len_rdCost0-k && sum<gap) break;
//printf("cut %d, start=%d, end=%d\n",k-1, start, i+k);
end=i+k;
IloExpr expr1(env);
for(i=start;i<end;i++){
expr1+=x[rdCost_sort[i].posi];
}
con.add(expr1<=k-1);
expr1.end();
for(i=start;i<end;i++){
pre_v0[ite][cnt++]=rdCost_sort[i].posi;
}
start=end;
k++;
}
len_v0[ite]=cnt;
}
if(len_rdCost1>0){
printf("1 rdCost_sort length:%d. \n",len_rdCost1);
k=1;
int start=0, end;
int cnt=0;
sum_pre_v1[ite]=0;
//for(i=0;i<len_rdCost1;i++) printf("%lf, ", rdCost_sort1[i].value);
while(start<len_rdCost1){
double sum=0;
for(i=start;i<len_rdCost1-k;i++){
sum=0;
for(int ii=i;ii<i+k;ii++){
sum+=rdCost_sort1[ii].value;
}
if(sum<gap) break;
}
if(i>=len_rdCost1-k && sum<gap) break;
//printf("cut %d, start=%d, end=%d\n",k-1, start, i+k);
end=i+k;
IloExpr expr1(env);
for(i=start;i<end;i++){
expr1+=x[rdCost_sort1[i].posi];
}
int cnt1=(end-start)-(k-1);
con.add(expr1>=cnt1);
expr1.end();
for(i=start;i<end;i++){
pre_v1[ite][cnt++]=rdCost_sort1[i].posi;
}
sum_pre_v1[ite]=sum_pre_v1[ite]+(end-start);
start=end;
k++;
}
len_v1[ite]=cnt;
}
model.add(con);
IloCplex cplex(model);
cplex.setParam(IloCplex::TiLim, time_limit);
cplex.setParam(IloCplex::Threads, 1);
cplex.setParam(IloCplex::NodeFileInd,2);
//cplex.setOut(env.getNullStream());
if(LB>0){
printf("\t add start point\n");
IloNumVarArray start_var(env);
IloNumArray start_val(env);
int k=0;
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
if(bestSolVec[i]==j){
start_val.add(1);
} else start_val.add(0);
start_var.add(x[k]);
k++;
}
}
cplex.addMIPStart(start_var, start_val);
start_var.end();
start_val.end();
}
if(!cplex.solve()){
std::cout<<"not solved IP."<<std::endl;
} else {
std::cout<<"solution status "<<cplex.getStatus()<<std::endl;
std::cout<<"solution value "<<cplex.getObjValue()<<std::endl;
if((double)cplex.getObjValue()>LB){
LB=(double)cplex.getObjValue();
IloNumArray vals(env);
cplex.getValues(vals, x);
printf("new best solution vector is: ");
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
if(cplex.getValue(x[sum_n_item[i]+j])>1-EPSILON){
printf("%d ", j);
bestSolVec[i]=j;
}
}
}
printf("\n\n");
}
}
env.end();
}
void solveLP(){
IloEnv env;
IloModel model(env);
IloNumVarArray x(env, n_var, 0,1);
IloRangeArray con(env);
IloExpr obj(env);
int i,j,k;
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
obj+=group[i].profit[j]*x[sum_n_item[i]+j];
}
}
model.add(IloMaximize(env,obj));
obj.end();
for(k=0;k<m;k++){
IloExpr expr(env);
for(i=0;i<n;i++){
for(j=0;j<group[i].nItem;j++){
expr+=group[i].consume[j][k]*x[sum_n_item[i]+j];
}
}
con.add(expr<=Gb[k]);
expr.end();
}
for(i=0;i<n;i++){
IloExpr expr(env);
for(j=0;j<group[i].nItem;j++){
expr+=x[sum_n_item[i]+j];
}
con.add(expr==1);
expr.end();
}
model.add(con);
IloCplex cplex(model);
cplex.setOut(env.getNullStream());
cplex.setParam(IloCplex::Threads,1);
if(cplex.solve()){
printf("LP solved with new value: %lf \n\n", cplex.getObjValue());
UB=cplex.getObjValue();
len_rdCost0=len_rdCost1=0;
for(i=0;i<n_var;i++) {
primal_sol[i]=(double)cplex.getValue(x[i]);
rdCosts[i]=FABS((double)cplex.getReducedCost(x[i]));
if(primal_sol[i]<EPSILON && rdCosts[i]>EPSILON){// non-basic variables at 0
rdCost_sort[len_rdCost0].value=rdCosts[i];
rdCost_sort[len_rdCost0++].posi=i;
} else if(primal_sol[i]>1-EPSILON && rdCosts[i]>EPSILON){// non-basic variables at 1
rdCost_sort1[len_rdCost1].value=rdCosts[i];
rdCost_sort1[len_rdCost1++].posi=i;
}
}
qsort(rdCost_sort, len_rdCost0,sizeof(ValuePosi), cmp);
qsort(rdCost_sort1, len_rdCost1, sizeof(ValuePosi), cmp);
len_v1=new int[maxIte];
len_v0=new int[maxIte];
pre_v0=new int*[maxIte];
pre_v1=new int*[maxIte];
for(i=0;i<maxIte;i++){
pre_v1[i]=new int[len_rdCost1];
pre_v0[i]=new int[len_rdCost0];
}
sum_pre_v1=new int[maxIte];
memset(len_v0, 0,maxIte*sizeof(int));
memset(len_v1, 0, maxIte*sizeof(int));
memset(sum_pre_v1, 0, maxIte*sizeof(int));
} else{
printf("LP not solved\n");
}
}
int main(int argc, char **argv) {
clock_t t1, t2;
t1 = clock();
IloEnv env;
IloModel model(env);
IloCplex cplex(model);
/************************** Defining the parameters ************************************/
IloInt N; //No. of nodes
IloInt M; //No. of calls
Num2DMatrix links(env); //Defines the topology of the network
IloNumArray call_demand(env); //link bandwidth requirement of each call
IloNumArray call_revenue(env); //revenue generated from the call
IloNumArray call_origin(env); //origin node index of each call
IloNumArray call_destination(env); //destination node index of each call
Num2DMatrix Q(env); //Bandwidth capacity of each link
Num2DMatrix sigma(env); //Standard deviation of service times on link (i,j)
Num2DMatrix cv(env); //coefficient of variation of service times on the link (i,j)
IloNum C; //Unit queueing delay cost per unit time
IloNumArray R_approx_init(env);
ifstream fin;
const char* filename = "BPP_data_sample - Copy.txt";
if (argc > 1)
filename = argv[1];
fin.open(filename);
//fin.open("BPP_10node_navneet.txt");
fin >> links >> call_origin >> call_destination >> call_demand >>
call_revenue >> Q >> cv >> R_approx_init >> C ;
cout << "Reading Data from the file - "<<filename<<endl;
N = links.getSize();
M = call_origin.getSize();
IloInt H = R_approx_init.getSize();
Num3DMatrix R_approx(env, N); //The tangential linear function approximation to R.
for (IloInt i=0; i<N; i++) {
R_approx[i] = Num2DMatrix(env, N);
for (IloInt j=0; j<N; j++) {
R_approx[i][j] = IloNumArray(env, H);
for (IloInt h=0; h<H; h++)
R_approx[i][j][h] = R_approx_init[h];
}
}
/************************** Defining the parameters ENDS ************************************/
/************* Defining the variables defined in the model formulation **********************/
IloNumVarArray Y(env, M, 0, 1, ILOINT); //Variable to define whether a call m is routed or not
IloNumArray Y_sol(env, M); //Solution values
NumVar3DMatrix X(env, N); //Variable to define whether a call m is routed along path i-j
Num3DMatrix X_sol(env, N);
for (IloInt i=0; i<N; i++) {
X[i] = NumVar2DMatrix(env, N);
X_sol[i] = Num2DMatrix(env, N);
for (IloInt j=0; j<N; j++) {
X[i][j] = IloNumVarArray(env, M, 0, 1, ILOINT);
X_sol[i][j] = IloNumArray(env, M);
}
}
NumVar3DMatrix W(env, N); //Variable to define whether a call m is routed along path i-j
for (IloInt i=0; i<N; i++) {
W[i] = NumVar2DMatrix(env, N);
for (IloInt j=0; j<N; j++)
W[i][j] = IloNumVarArray(env, M, 0, 1, ILOINT);
}
NumVar2DMatrix R(env, (IloInt)N); //The linearization Variable
for (IloInt i=0; i<N; i++)
R[i] = IloNumVarArray(env, (IloInt)N, 0, IloInfinity, ILOFLOAT);
/************* Defining the variables defined in the model formulation ENDS *****************/
/**************************** Defining the Constraints *******************************/
// Constraint #1 : Flow Conservation Constraint
for (IloInt m=0; m<M; m++) {
for (IloInt i=0; i<N; i++) {
IloExpr constraint1(env);
for (IloInt j=0; j<N; j++) {
if (links[i][j] == 1)
constraint1 += W[i][j][m];
}
for (IloInt j=0; j<N; j++) {
if (links[j][i] == 1)
constraint1 += -W[j][i][m];
}
if (i == call_origin[m])
model.add(constraint1 == Y[m]);
else if (i == call_destination[m])
model.add(constraint1 == -Y[m]);
else
model.add(constraint1 == 0);
constraint1.end();
}
}
// Constraint #2 :
for (IloInt m=0; m<M; m++) {
for (IloInt i=0; i<N; i++) {
for (IloInt j=0; j<N; j++) {
if (links[i][j] == 1)
model.add(W[i][j][m] + W[j][i][m] <= X[i][j][m]);
}
}
}
// Constraint #3 : Link Capacity Constraint
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
IloExpr constraint3(env);
for (IloInt m=0; m<M; m++)
constraint3 += call_demand[m]*X[i][j][m];
model.add(constraint3 <= Q[i][j]);
constraint3.end();
}
}
}
// Constraint #4 : Defining the constraint for initial values of R_approx,
// Cuts must be added during the iterations whenever the values are updated
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
for (IloInt h=0; h<H; h++) {
IloExpr constraint4_lhs(env);
IloNum constraint4_rhs = 0;
for (IloInt m=0; m<M; m++)
constraint4_lhs += call_demand[m]*X[i][j][m];
constraint4_lhs -= (Q[i][j]/((1+R_approx[i][j][h])*(1+R_approx[i][j][h])))*R[i][j];
constraint4_rhs = Q[i][j]*((R_approx[i][j][h]/(1+R_approx[i][j][h])) *
(R_approx[i][j][h]/(1+R_approx[i][j][h])));
model.add(constraint4_lhs <= constraint4_rhs);
constraint4_lhs.end();
}
}
}
}
/************************** Defining the Constraints ENDS ****************************/
/************************ Defining the Objective Function ****************************/
IloExpr Objective(env);
IloExpr Obj_expr1(env);
IloExpr Obj_expr2(env);
for (IloInt m=0; m<M; m++)
Obj_expr1 += call_revenue[m]*Y[m];
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
Obj_expr2 += (1+cv[i][j] * cv[i][j])*R[i][j];
for (IloInt m=0; m<M; m++)
Obj_expr2 += ((1-cv[i][j] * cv[i][j])/Q[i][j])*call_demand[m]*X[i][j][m];
}
}
}
Objective += Obj_expr1 - 0.5*C*Obj_expr2;
model.add(IloMaximize(env, Objective));
//model.add(IloMinimize(env, -Objective));
Objective.end();
Obj_expr1.end();
Obj_expr2.end();
/********************** Defining the Objective Function ENDS **************************/
IloNum eps = cplex.getParam(IloCplex::EpInt);
IloNum UB = IloInfinity;
IloNum LB = -IloInfinity;
/***************** Solve ***********************/
do {
cplex.setParam(IloCplex::MIPInterval, 5);
cplex.setParam(IloCplex::NodeFileInd ,2);
cplex.setOut(env.getNullStream());
cplex.exportModel("BPP_model.lp");
if(!cplex.solve()) {
cout << "Infeasible"<<endl;
system("pause");
}
else {
for (IloInt m=0; m<M; m++) {
if (cplex.getValue(Y[m]) > eps) {
cout << "Call(m) = "<<m+1<<" : "<<call_origin[m]+1<<" --> "<<call_destination[m]+1
<<"; demand = "<<call_demand[m]<<endl;
cout << "Path : ";
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
if (cplex.getValue(X[i][j][m]) > eps) {
X_sol[i][j][m] = 1;
cout <<i+1<<"-"<<j+1<<"; ";
}
}
}
}
cout << endl << endl;
}
}
//system("pause");
}
UB = min(UB, cplex.getObjValue());
IloNum lbound = 0;
for (IloInt m=0; m<M; m++)
if(cplex.getValue(Y[m]) > eps)
lbound += call_revenue[m];
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
IloNum lbound_temp1 = 0;
IloNum lbound_temp2 = 0;
for (IloInt m=0; m<M; m++)
lbound_temp1 += call_demand[m]*X_sol[i][j][m];
lbound_temp2 = 0.5*(1+cv[i][j]*cv[i][j]) * (lbound_temp1*lbound_temp1) / (Q[i][j]*(Q[i][j]-lbound_temp1));
lbound_temp2 += lbound_temp1 / Q[i][j];
lbound -= C*lbound_temp2;
}
}
}
LB = max(LB, lbound);
Num2DMatrix R_approx_new(env, N);
for (IloInt i=0; i<N; i++)
R_approx_new[i] = IloNumArray(env, N);
for (IloInt i=0; i<N; i++) {
for (IloInt j=i+1; j<N; j++) {
if (links[i][j] == 1) {
IloExpr cut_lhs(env);
IloNum cut_rhs = 0;
IloNum cut_temp = 0;
for (IloInt m=0; m<M; m++) {
cut_temp += call_demand[m]*X_sol[i][j][m];
}
R_approx_new[i][j] = cut_temp / (Q[i][j] - cut_temp);
//cout << "R_approx_new = "<<R_approx_new<<endl;
for (IloInt m=0; m<M; m++)
cut_lhs += call_demand[m]*X[i][j][m];
cut_lhs -= (Q[i][j]/((1+R_approx_new[i][j])*(1+R_approx_new[i][j])))*R[i][j];
cut_rhs = Q[i][j]*((R_approx_new[i][j]/(1+R_approx_new[i][j])) *
(R_approx_new[i][j]/(1+R_approx_new[i][j])));
model.add(cut_lhs <= cut_rhs);
cut_lhs.end();
}
}
}
cout << "UB = "<<UB<<endl;
cout << "LB = "<<LB<<endl;
cout << "Gap (%) = "<<(UB-LB)*100/LB<<endl;
//system("pause");
}while ((UB-LB)/UB > eps);
t2 = clock();
float secs = (float)t2 - (float)t1;
secs = secs / CLOCKS_PER_SEC;
cout << "CPUTIME = "<<secs <<endl<<endl;
}
void ScenarioProblem::addSimProblem(IloModel mod){
mod.add(_simSP.getP());
mod.add(_simSP.getD());
mod.add(_simSP.getTheta());
if(_pd->getGeneratorSwitch()){
mod.add(_simSP.getY());
}
if(_pd->getEnergyStorage()){
mod.add(_simSP.getE());
mod.add(_simSP.getEDeltaPlus());
mod.add(_simSP.getEDeltaMinus());
mod.add(_simSP.getEnergyStorage());
}
// if(_pd->getReDispatch()&&index>0){
// mod.add(_simSP.getPDelta());
// mod.add(_simSP.getGenReDispatch());
// }
if(_pd->getReserve()){
mod.add(_simSP.getR());
mod.add(_simSP.getReserveMargin());
// if(index>0) mod.add(_simSP.getRampingCapacity());
}
mod.add(_simSP.getF());
mod.add(_simSP.getX());
if(_pd->getLineSwitch()){
mod.add(_simSP.getZ());
mod.add(_simSP.getW());
}
mod.add(_simSP.getEnergyConservation());
mod.add(_simSP.getPhaseAngleUp());
mod.add(_simSP.getPhaseAngleDown());
mod.add(_simSP.getLineLimitsUp());
mod.add(_simSP.getLineLimitsDown());
if(_pd->getCapacity()){
mod.add(_simSP.getLineLimitsUpM());
mod.add(_simSP.getLineLimitsDownM());
}
if(_pd->getLineSwitch()){
mod.add(_simSP.getLineSwitch());
mod.add(_simSP.getLineBurnt());
}
mod.add(_simSP.getGenLimitsUp());
mod.add(_simSP.getGenLimitsDown());
if(_pd->getEnergyStorage()){
mod.add( IloMaximize( _pd->getEnv(), _simSP.getSumD()
-.1*( IloSum(_simSP.getEDeltaPlus()) + IloSum(_simSP.getEDeltaMinus()) )
));
}
else{
mod.add( IloMaximize( _pd->getEnv(), _simSP.getSumD() ));
}
}
void Instance::VerifySolution() {
IloEnv env;
IloInt i, j;
IloModel model(env);
IloInt nbImpressions = num_impressions_;
IloInt nbAdvertisers = num_advertisers_;
NumVarMatrix x(env, nbImpressions);
// NumVarMatrix y(env, nbImpressions);
for(i = 0; i < nbImpressions; i++) {
x[i] = IloNumVarArray(env, nbAdvertisers, 0.0, 1.0, ILOFLOAT);
// y[i] = IloNumVarArray(env, nbAdvertisers, 0.0, 1.0, ILOFLOAT);
}
// Add impression constraints.
for(i = 0; i < nbImpressions; i++) {
model.add(IloSum(x[i]) <= 1.0);
}
// Add weighted contraint.
IloExpr weighted_constraint(env);
for(j = 0; j < nbImpressions; j++) { // demand must meet supply
for(i = 0; i < nbAdvertisers; i++) {
weighted_constraint += ((double) transpose_bids_matrix_[j][i]) * ((double) weights_[i]) * x[j][i];
}
}
model.add(weighted_constraint <= ((double) global_problem_.budget_));
weighted_constraint.end();
IloExpr obj_exp(env);
for(i = 0; i < nbImpressions; i++) {
for(j = 0; j < nbAdvertisers; j++) {
obj_exp += ((double) transpose_bids_matrix_[i][j]) * x[i][j];
}
}
model.add(IloMaximize(env, obj_exp));
obj_exp.end();
IloCplex cplex(env);
cplex.setOut(env.getNullStream());
cplex.extract(model);
// Optimize the problem and obtain solution.
if ( !cplex.solve() ) {
env.error() << "Failed to optimize LP" << endl;
throw(-1);
}
IloNumArray vals(env);
long double sum_b = 0;
for (int a = 0; a < num_advertisers_; ++a) {
//slacks_[a] = 0;
for (i = 0; i < nbImpressions; i++) {
if (cplex.getValue(x[i][a]) > 0) {
//slacks_[a] = slacks_[a] + cplex.getValue(x[i][a]) * bids_matrix_[a].find(i)->second;
sum_b += cplex.getValue(x[i][a]) * bids_matrix_[a].find(i)->second * weights_[a];
}
}
}
cout << "Cplex buget allocation is = ";
cout << sum_b;
cout << "\n";
if (cplex.getObjValue() == CalculateGlobalMWProblemOpt()) {
cout << "Solution checks \n";
} else {
cout << "Solution does not check, Cplex opt is ";
cout << cplex.getObjValue();
cout << "\n";
}
env.end();
}
void fagoc::Modelo_solver::impl::solve()
{
/*******************************************************
* INICIALIZAÇÃO DE VARIÁVEIS E REFERÊNCIAS *
******************************************************/
const auto& disciplinas = parent.curso().disciplinas();
const auto& horario = parent.horario();
const auto& ofertadas = parent.curso().ofertadas();
const auto num_disciplinas = parent.curso().num_disciplinas();
const auto num_horas = parent.horario().size();
// Variáveis do aluno
const auto& aprovacoes = parent.aluno().aprovacoes();
const auto& cursadas = parent.aluno().cursadas();
const auto& periodo_aluno = parent.aluno().periodo();
const auto& turma_aluno = parent.aluno().turma();
auto periodo_alu_num = split_curso_string(periodo_aluno).first;
// Preferências do aluno (mesma turma/período)
std::vector<char> pref(num_disciplinas, 0);
for (auto d = 0u; d < num_disciplinas; d++) {
if (disciplinas[d].periodo == periodo_aluno
&& disciplinas[d].turma == turma_aluno) {
pref[d] = 1;
}
}
/******************************************************
* ELABORAÇÃO DO MODELO *
******************************************************/
IloModel mod{env};
// Variáveis de decisão
IloBoolVarArray y(env, num_disciplinas);
// Carga horária
IloExpr carga{env};
for (auto d = 0u; d < num_disciplinas; d++) {
carga += disciplinas[d].credito * y[d];
}
// Preferências
IloExpr mesma_turma{env};
for (auto d = 0u; d < num_disciplinas; d++) {
mesma_turma += pref[d] * y[d];
}
IloExpr obj{env};
// Função objetivo
obj += carga + 0.1 * mesma_turma;
mod.add(IloMaximize(env, obj));
obj.end();
/*****************************************************
* RESTRIÇÕES *
*****************************************************/
// Período mínimo
for (auto d = 0u; d < num_disciplinas; d++) {
auto periodo_disc_num = split_curso_string(disciplinas[d].periodo_minimo).first;
mod.add(y[d] * periodo_disc_num <= periodo_alu_num);
}
// Pré-requisitos
for (auto d = 0u; d < num_disciplinas; d++) {
auto num_prereq = 0;
auto prereq_aprov = 0;
for (auto p = 0u; p < num_disciplinas; p++) {
if (!disciplinas[d].prerequisitos[p]) {
continue;
}
num_prereq++;
if (aprovacoes[p]) {
prereq_aprov++;
}
/*
for (auto i = 0u; i < num_disciplinas; i++) {
if (disciplinas[p].equivalentes[i] && aprovacoes[i]) {
prereq_aprov++;
break;
}
}
*/
}
mod.add(num_prereq * y[d] <= prereq_aprov);
}
// Co-requisitos
for (auto d = 0u; d < num_disciplinas; d++) {
for (auto c = 0u; c < num_disciplinas; c++) {
if (disciplinas[d].corequisitos[c]) {
/*
auto coreq_cumprido = 0;
for (auto i = 0u; i < num_disciplinas; i++) {
if (disciplinas[c].equivalentes[i] && cursadas[i]) {
coreq_cumprido = 1;
break;
}
}
*/
auto coreq_cumprido = cursadas[c];
mod.add(y[d] <= y[c] + coreq_cumprido);
}
}
}
// Disciplinas equivalentes
/*
for (auto d = 0u; d < num_disciplinas; d++) {
IloExpr disc_equiv(env);
for (auto e = 0u; e < num_disciplinas; e++) {
disc_equiv += disciplinas[d].equivalentes[e] * y[e];
}
mod.add(disc_equiv <= 1);
disc_equiv.end();
}
*/
// Cria as restrições dos horários
for (auto h = 0u; h < num_horas; h++) {
IloExpr disc_concorrente(env);
for (auto d = 0u; d < num_disciplinas; d++) {
disc_concorrente += horario[h][d] * y[d];
}
mod.add(disc_concorrente <= 1);
disc_concorrente.end();
}
// Disciplinas já aprovadas
for (auto d = 0u; d < num_disciplinas; d++) {
/*
auto aprovacao_equivalente = 0;
for (auto i = 0u; i < num_disciplinas; i++) {
if (disciplinas[d].equivalentes[i] && aprovacoes[i]) {
aprovacao_equivalente = 1;
break;
}
}
*/
auto aprovacao_equivalente = aprovacoes[d];
mod.add(y[d] <= 1 - aprovacao_equivalente);
}
// Disciplinas ofertadas
for (auto d = 0u; d < num_disciplinas; d++) {
mod.add(y[d] <= ofertadas[d]);
}
/********************************************************
* RESOLUÇÃO DO MODELO *
********************************************************/
// Se o número de disciplinas for menor que 30, utiliza
// o CPLEX. Se for maior, a versão community não resolve, então
// utiliza-se o CP Optimizer
IloNumArray solucao_cplex(env);
double funcao_objetivo;
if (num_disciplinas <= 30) {
IloCplex cplex{mod};
// Se o tempo limite foi configurado, aplicá-lo ao CPLEX
if (tempo_limite != 0) {
cplex.setParam(IloCplex::Param::TimeLimit, tempo_limite);
}
cplex.setOut(env.getNullStream());
cplex.solve();
funcao_objetivo = cplex.getObjValue();
cplex.getValues(solucao_cplex, y);
} else {
IloCP cp{mod};
// Se o tempo limite foi configurado, aplicá-lo ao CPLEX
if (tempo_limite != 0) {
cp.setParameter(IloCP::TimeLimit, tempo_limite);
}
cp.setOut(env.getNullStream());
cp.solve();
funcao_objetivo = cp.getObjValue();
cp.getValues(y, solucao_cplex);
}
solucao = Solucao{num_disciplinas, funcao_objetivo, parent.aluno().nome()};
// Atribui resposta às variáveis membro
for (auto d = 0u; d < num_disciplinas; d++) {
if (solucao_cplex[d]) {
solucao.solucao_bool[d] = 1;
solucao.nomes_disciplinas.push_back(disciplinas[d].id);
}
}
}
int
main()
{
IloEnv env;
try {
NumMatrix cost(env, nbMonths);
cost[0]=IloNumArray(env, nbProducts, 110.0, 120.0, 130.0, 110.0, 115.0);
cost[1]=IloNumArray(env, nbProducts, 130.0, 130.0, 110.0, 90.0, 115.0);
cost[2]=IloNumArray(env, nbProducts, 110.0, 140.0, 130.0, 100.0, 95.0);
cost[3]=IloNumArray(env, nbProducts, 120.0, 110.0, 120.0, 120.0, 125.0);
cost[4]=IloNumArray(env, nbProducts, 100.0, 120.0, 150.0, 110.0, 105.0);
cost[5]=IloNumArray(env, nbProducts, 90.0, 100.0, 140.0, 80.0, 135.0);
// Variable definitions
IloNumVarArray produce(env, nbMonths, 0, IloInfinity);
NumVarMatrix use(env, nbMonths);
NumVarMatrix buy(env, nbMonths);
NumVarMatrix store(env, nbMonths);
IloInt i, p;
for (i = 0; i < nbMonths; i++) {
use[i] = IloNumVarArray(env, nbProducts, 0, IloInfinity);
buy[i] = IloNumVarArray(env, nbProducts, 0, IloInfinity);
store[i] = IloNumVarArray(env, nbProducts, 0, 1000);
}
IloExpr profit(env);
IloModel model(env);
// For each type of raw oil we must have 500 tons at the end
for (p = 0; p < nbProducts; p++) {
store[nbMonths-1][p].setBounds(500, 500);
}
// Constraints on each month
for (i = 0; i < nbMonths; i++) {
// Not more than 200 tons of vegetable oil can be refined
model.add(use[i][v1] + use[i][v2] <= 200);
// Not more than 250 tons of non-vegetable oil can be refined
model.add(use[i][o1] + use[i][o2] + use[i][o3] <= 250);
// Constraints on food composition
model.add(3 * produce[i] <=
8.8 * use[i][v1] + 6.1 * use[i][v2] +
2 * use[i][o1] + 4.2 * use[i][o2] + 5 * use[i][o3]);
model.add(8.8 * use[i][v1] + 6.1 * use[i][v2] +
2 * use[i][o1] + 4.2 * use[i][o2] + 5 * use[i][o3]
<= 6 * produce[i]);
model.add(produce[i] == IloSum(use[i]));
// Raw oil can be stored for later use
if (i == 0) {
for (IloInt p = 0; p < nbProducts; p++)
model.add(500 + buy[i][p] == use[i][p] + store[i][p]);
}
else {
for (IloInt p = 0; p < nbProducts; p++)
model.add(store[i-1][p] + buy[i][p] == use[i][p] + store[i][p]);
}
// Logical constraints
// The food cannot use more than 3 oils
// (or at least two oils must not be used)
model.add((use[i][v1] == 0) + (use[i][v2] == 0) + (use[i][o1] == 0) +
(use[i][o2] == 0) + (use[i][o3] == 0) >= 2);
// When an oil is used, the quantity must be at least 20 tons
for (p = 0; p < nbProducts; p++)
model.add((use[i][p] == 0) || (use[i][p] >= 20));
// If products v1 or v2 are used, then product o3 is also used
model.add(IloIfThen(env, (use[i][v1] >= 20) || (use[i][v2] >= 20),
use[i][o3] >= 20));
// Objective function
profit += 150 * produce[i] - IloScalProd(cost[i], buy[i]) -
5 * IloSum(store[i]);
}
// Objective function
model.add(IloMaximize(env, profit));
IloCplex cplex(model);
if (cplex.solve()) {
cout << "Solution status: " << cplex.getStatus() << endl;
cout << " Maximum profit = " << cplex.getObjValue() << endl;
for (IloInt i = 0; i < nbMonths; i++) {
IloInt p;
cout << " Month " << i << " " << endl;
cout << " . buy ";
for (p = 0; p < nbProducts; p++) {
cout << cplex.getValue(buy[i][p]) << "\t ";
}
cout << endl;
cout << " . use ";
for (p = 0; p < nbProducts; p++) {
cout << cplex.getValue(use[i][p]) << "\t ";
}
cout << endl;
cout << " . store ";
for (p = 0; p < nbProducts; p++) {
cout << cplex.getValue(store[i][p]) << "\t ";
}
cout << endl;
}
}
else {
cout << " No solution found" << endl;
}
}
catch (IloException& ex) {
cerr << "Error: " << ex << endl;
}
catch (...) {
cerr << "Error" << endl;
}
env.end();
return 0;
}
