Assignment 3 Large Scale Optimisaton Kavitha C Didugu Question 1: /************************************************************************************ * This is the cplex code to solve iteration by iteration iteration the example presnted by Kelley (1960): The cutting-plane method for solving convex programs. * Minimize x1 - x2 * s.t.: * -2 <= x1 <= 2 * -2 <= x2 <= 2 * 3x1^2 -2x1x2 + x2^2 - <= 0 ***********************************************************************************/ #include
#include #include #include #include #include #include #include #include #include #include #include #include #include #include //#include #include #include //for //for vectors #include //#include #include //#include //#include #include using namespace namespace std; std; ILOSTLBEGIN //typedef IloArray TwoDMatrix; int main(int int main( int argc, argc, char char **argv) **argv) { IloEnv env; try { IloNumVar t(env, 0, IloInfinity, ILOFLOAT); IloNum tv; IloNumVarArray X(env, 2, -2, 2, ILOFLOAT); IloNumArray X_val(env, 2); IloModel model(env); IloExpr Obj(env); Obj = X[0] - X[1]; //model.add(-16*X[0] + 8*X[1] <= 25);
problems
model.add(IloMinimize(env,Obj)); // IloMinimize is used for minimization
//Alternatively, model.add(IloMinimize(env,Obj)); can be replaced by the following three lines. //This is useful while iterating in Decomposition Techniques where the objective function is redefined at each iteration //IloObjective Objective = IloMinimize(env); //model.add(Objective); //Objective.setExpr(Obj); Obj.end(); // Optimize IloCplex cplex(model); //cplex.setOut(env.getNullStream()); // This is to supress the output of Branch & Bound Tree on screen //cplex.setWarning(env.getNullStream()); //This is to supress warning messages on screen cplex.solve(); //solving the MODEL if (cplex.getStatus() == IloAlgorithm::Infeasible) // if the problem is infeasible { env.out() << "Problem Infeasible" << endl; } X_val[0] = cplex.getValue(X[0]); X_val[1] = cplex.getValue(X[1]); // Print results ofstream fout; fout.open("A3Q1 output.txt");
cout<< "Objective Value = " << cplex.getObjValue() << endl; cout<<"X1 = "<
catch(IloException &e) { env.out() << "ERROR: " << e << endl; } catch(...) { env.out() << "Unknown exception" << endl; } env.end(); return 0; }
OUTPUT Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -4 X1 = -2 X2 = 2 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.75 X1 = -0.75 X2 = 2 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.75 X1 = -1.375 X2 = 1.375 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.46591 X1 = -0.920455 X2 = 1.54545
Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.46591 X1 = -1.10899 X2 = 1.35692 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.46591 X1 = -1.25235 X2 = 1.21356 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.45149 X1 = -1.17346 X2 = 1.27803 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.45035 X1 = -1.20915 X2 = 1.2412 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.44977 X1 = -1.22749 X2 = 1.22228 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.44952 X1 = -1.21805 X2 = 1.23148 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.4495 X1 = -1.2227 X2 = 1.22681 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.44949 X1 = -1.22502 X2 = 1.22447 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.44949 X1 = -1.22386 X2 = 1.22563 Iteration:IloNumVar(0)[0 .. 1.#INF] Objective Value = -2.44949
X1 = -1.22444 X2 = 1.22505 Question 2: (a) Cutting Plane Algorithm: #include #include #include #include #include #include #include #include #include //#include #include #include //for vectors #include //#include #include //#include //#include #include using namespace std; ILOSTLBEGIN //typedef IloArray TwoDMatrix;
int main(int argc, char **argv) { IloEnv env; int N=500; int C=100; float SR=0 ; float P=0; int i=0; IloNumVar M(env, 0, IloInfinity, ILOFLOAT); IloNum MV; float LB=0; float UB= 99999; float check = 0; IloNumVar R(env, 0, IloInfinity, ILOFLOAT); IloNum RV; //IloNumVarArray AR(env, N, 0, IloInfinity, ILOFLOAT); IloNumArray ARV(env,N); //IloNumVarArray P(env, N, 0, IloInfinity, ILOFLOAT); IloNumArray PV(env,N); //IloNumVar SR(env, 0, IloInfinity, ILOFLOAT); IloNumVarArray x(env, N, 0, 1, ILOINT); IloIntArray xv(env, N); try { const char* data_filename = "Data_NLKnapsack_500node.dat" ; if (argc > 1) { data_filename = argv[1]; } fstream datafile;
datafile.open(data_filename,ios::in);
if (!datafile) { cerr << "ERROR: could not open file " << data_filename << " for reading" << endl; cerr << "usage: " << argv[0] << " " << endl; throw(-1); } datafile >> ARV >> PV >> SR; //N = ARV.getSize(); datafile.close(); cout<=0.01); // Optimize IloCplex cplex(model); cplex.solve(); //cplex.setWarning(env.getNullStream()); //This is to supress warning messages on screen float j=0; ofstream fout; fout.open("A3Q2-cut.txt" );
//int num = 150;
while(j==0) { RV=cplex.getValue(R); MV=cplex.getValue(M); IloExpr cut_lhs(env);
float MV1; MV1 = RV*SR/(1+RV); cut_lhs = ((M-MV1)-(R-RV)*SR/((1+RV)*(1+RV))); model.add(cut_lhs <= 0); cut_lhs.end(); cplex.solve(); //solving the MODEL if (cplex.getStatus() == IloAlgorithm::Infeasible) // if the problem is infeasible { env.out() << "Problem Infeasible" << endl; } //cout<< "Objective Value = " << cplex.getObjValue() << endl; RV=cplex.getValue(R); MV=cplex.getValue(M); for(int i=0;iLB){LB=check;} fout<<"LB is "<
if(MV-SR*RV/(1+RV) < 0.001) { if(MV-SR*RV/(1+RV) > (-1)*0.001) { j=1; } } //j=j+0.01; }
for(int i=0; i<500; i++) { if(xv[i]==1) { fout<<"xv "<< i+1 << " "<
env.end(); return 0;
}
OUTPUT: 1)LB is 12955.9 check is 12955.9 UB is 22621 2) LB is 12955.9 check is 12955.9 UB is 22522 3)LB is 12955.9 check is 12955.9 UB is 22327.1 4)LB is 12955.9 check is 12955.9 UB is 21949.1 5)LB is 12955.9 check is 12955.9 UB is 21238.2 6)LB is 20826 check is 20826 UB is 20833.4 7)LB is 20826 check is 20826 UB is 20826.1 8)LB is 20826 check is 20826 UB is 20826 Nodes Served (1 denotes their selection) Node 7 1 Node 52 1 Node 59 1 Node 86 1 Node 93 1 Node 119 1 Node 134 1 Node 136 1 Node 152 1
Node Node Node Node Node Node Node Node Node Node Node Node
197 199 203 226 288 362 368 382 388 426 471 478
1 1 1 1 1 1 1 1 1 1 1 1
(b) Finite constraint linearization: #include #include #include #include #include #include #include #include #include //#include #include #include //for vectors #include //#include #include //#include //#include #include using namespace std; ILOSTLBEGIN //typedef IloArray TwoDMatrix;
int main(int argc, char **argv) { IloEnv env; int N=500; int C=100; float SR=0 ; float P=0; int i=0; //IloNumVar M(env, 0, IloInfinity, ILOFLOAT); float MV; float LB=0; float UB= 99999; float check = 0; IloNumVar R(env, 0, IloInfinity, ILOFLOAT); IloNum RV; int D= 9999; //IloNumVarArray AR(env, N, 0, IloInfinity, ILOFLOAT); IloNumArray ARV(env,N); //IloNumVarArray P(env, N, 0, IloInfinity, ILOFLOAT);
IloNumArray PV(env,N); //IloNumVar SR(env, 0, IloInfinity, ILOFLOAT); IloBoolVarArray x(env, N); IloNumArray xv(env, N); IloNumVarArray y(env, N, 0, IloInfinity, ILOFLOAT); IloNumArray yv(env, N); IloNumVar M(env, 0, IloInfinity, ILOFLOAT); try { const char* data_filename = "Data_NLKnapsack_500node.dat" ; if (argc > 1) { data_filename = argv[1]; } fstream datafile; datafile.open(data_filename,ios::in); if (!datafile) { cerr << "ERROR: could not open file " << data_filename << " for reading" << endl; cerr << "usage: " << argv[0] << " " << endl; throw(-1); } datafile >> ARV >> PV >> SR; //N = ARV.getSize(); datafile.close(); cout<=(R*SR - M));
for(int i=0; i=R-D*(1-x[i])); //cout<=0.01); // Optimize IloCplex cplex(model); //cplex.setWarning(env.getNullStream()); //This is to supress warning messages on screen float j=0; ofstream fout; fout.open("A3Q2-2.txt"); cplex.solve(); //solving the MODEL if (cplex.getStatus() == IloAlgorithm::Infeasible) // if the problem is infeasible { env.out() << "Problem Infeasible" << endl; } //cout<< "Objective Value = " << cplex.getObjValue() << endl; RV=cplex.getValue(R); MV=cplex.getValue(M); float Q= 0; Q = cplex.getValue(Nowitisright); cout<
for(int i=0;i
OUTPUT xv 7 xv 52 xv 59 xv 86 xv 93 xv 119 xv 134 xv 136 xv 152 xv 197 xv 199 xv 203 xv 226 xv 288 xv 362 xv 368 xv 382 xv 388
xv 426 xv 471 xv 478 Optimal value= 20826
VERDICT: Finite constraint linearization takes much more time compared to the cutting plane algorithm. The cutting plane algorithm , as we can see, has run a small number o f iterations before the upper and lower bound converged to the optimal value. But the finite constraint linearistaion method only marginally improves the optimality gap for each iteration and hence it is more time taking.
