void binmap(int *rule, // 1 or 2, just like for approx()
double *beamAngle, double *pitch, double *roll, // all of length 1
int *n, // length of distance, z1-z4, and y1-y4
double *distance, // like "x"
double *y1, double *y2, double *y3, double *y4, // like a set of "y" values
// below are storage
double *buffer, // do not allocate locally, for speed
double *z1, double *z2, double *z3, double *z4, // calculated here; just supply space
double *Y1, double *Y2, double *Y3, double *Y4) // calculated here; just supply space
{
int i;
// distance, y, y1-y4 are of length *n
// beamAngle, pitch, and roll are of length 1
const double RPD = atan2(1.0, 1.0) / 45.0; // radians/degree
#if 0
Rprintf("n %d\n", *n);
Rprintf("beamAngle %f pitch %f roll %f\n", *beamAngle, *pitch, *roll);
#endif
double cr = cos((*roll) * RPD);
double sr = sin((*roll) * RPD);
double cp = cos((*pitch) * RPD);
double sp = sin((*pitch) * RPD);
double tt = tan((*beamAngle) * RPD);
#if 0
Rprintf("C : r %.6f p %.6f cr %.6f sr %.6f cp %.6f sp %.6f tt %.6f\n", *roll, *pitch, cr, sr, cp, sp, tt);
#endif
for (i=0; i < *n; i++) {
z1[i] = distance[i] * (cr - tt * sr) * cp;
z2[i] = distance[i] * (cr + tt * sr) * cp;
z3[i] = distance[i] * (cp + tt * sp) * cr;
z4[i] = distance[i] * (cp - tt * sp) * cr;
}
#if 0
Rprintf("C : z1 ");
for (i = 0; i < 8; i++)
Rprintf("%11.6f ", i, z1[i]);
Rprintf("\n");
#endif
// y <- .C(C_R_approx, as.double(x), as.double(y), as.integer(nx),
// xout = as.double(xout), as.integer(length(xout)), as.integer(method),
// as.double(yleft), as.double(yright), as.double(f), NAOK = TRUE,
// PACKAGE = "stats")$xout
double f = 0.0; // unused, since we set method=1; see docs on approx()
double left, right;
// void R_approx(double *x, double *y, int *nxy, double *xout, int *nout,
// int *method, double *yleft, double *yright, double *f)
// NOTE: replaces xout with the interpolated value!
int method = 1; // "linear" for approx()
if (*rule == 1) { left = NA_REAL; right = NA_REAL; } else { left = y1[0]; right = y1[*n]; }
for (i = 0; i < *n; i++) {
buffer[i] = distance[i];
}
R_approx(z1, y1, n, buffer, n, &method, &left, &right, &f);
for (i = 0; i < *n; i++) {
Y1[i] = buffer[i];
buffer[i] = distance[i];
}
if (*rule == 1) { left = NA_REAL; right = NA_REAL; } else { left = y2[0]; right = y2[*n]; }
R_approx(z2, y2, n, buffer, n, &method, &left, &right, &f);
for (i = 0; i < *n; i++) {
Y2[i] = buffer[i];
buffer[i] = distance[i];
}
if (*rule == 1) { left = NA_REAL; right = NA_REAL; } else { left = y3[0]; right = y3[*n]; }
R_approx(z3, y3, n, buffer, n, &method, &left, &right, &f);
for (i = 0; i < *n; i++) {
Y3[i] = buffer[i];
buffer[i] = distance[i];
}
if (*rule == 1) { left = NA_REAL; right = NA_REAL; } else { left = y4[0]; right = y4[*n]; }
R_approx(z4, y4, n, buffer, n, &method, &left, &right, &f);
for (i = 0; i < *n; i++) {
Y4[i] = buffer[i];
}
}
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;
}
