Cplex c++ multidimensional decision variable

问题:

I'm new using cplex and I try to find some information on internet but didn't find clear stuff to help me in my problem.

I have P[k] k will be equal to 1 to 4

and I have a decision variable x[i][k] must be equal to 0 or 1 (also p[k])

the i is between 1 to 5

For now I do like this

  IloEnv env;
  IloModel model(env);
  IloNumVarArray p(env);
  p.add(IloNumVar(env, 0, 1));
  p.add(IloNumVar(env, 0, 1));
  p.add(IloNumVar(env, 0, 1));
  IloIntVar x(env, 0, 1);

  model.add(IloMaximize(env, 1000 * p[1] + 2000 * p[2] + 500 * p[3] + 1500 * p[4]));

   for(int k = 1; k <= 4; k++){
    for(int i = 1; i <= 5; i++){
      model.add(x[i][k] + x[i][k] + x[i][k] + x[i][k] + x[i][k] => 2 * p[k]; );
    }}

The loop should do something like this:

x[1][1] + x[2][1] + x[3][1] + x[4][1] + x[5][1] => 2 * p[1];

x[1][2] + x[2][2] + x[3][2] + x[4][2] + x[5][2] => 2 * p[2];

x[1][3] + x[2][3] + x[3][3] + x[4][3] + x[5][3] => 2 * p[3];

x[1][4] + x[2][4] + x[3][4] + x[4][4] + x[5][4] => 3 * p[4];

but I'm far away from this result.

Does anyone have an idea?

Thanks

回答1:

You probably want to use an IloNumExpr

for(int k = 0; k < 4; k++){
   IloNumExpr sum_over_i(env);
   for(int i = 0; i < 5; i++){
        sum_over_i += x[i][k];
   }
   model.add(sum_over_i >= 2 * p[k]; );
}

You also need to declare x as a 2-dimensional array.

IloArray x(env, 4);
for (int k = 0; k < 4; ++k)
      x[k] = IloIntVarArray(env, 5, 0, 1);

Also, in c++, array indices are from 0 to size-1, not 1 to size. Your objective should be written

model.add(IloMaximize(env, 1000 * p[0] + 2000 * p[1] + 500 * p[2] + 1500 * p[3]));

回答2:

Usertfwr already gave a good answer, but I would like to give another version of solution which might help you to code CPLEX applications in a more generic way. First, I would suggest you to use a text file to hold all the data (objective function coefficients) which will be fed into the program. In your case, you only have to copy literally the following matrix like data to notepad and name it as “coef.dat”:

[1000, 2000, 500, 1500]

Now comes the full code, let me know if have difficulties understanding any statement:

  #include <ilcplex/ilocplex.h>
  #include <fstream>
  #include <iostream>
  ILOSTLBEGIN

  int main(int argc, char **argv) {
    IloEnv env; 
    try {
        const char* inputData = "coef.dat";

        ifstream inFile(inputData);   // put your data in the same directory as your executable
        if(!inFile) {
            cerr << "Cannot open the file " << inputData << " successfully! " <<endl;
            throw(-1);
        }

        // Define parameters (coef of objective function)
        IloNumArray a(env); 

        // Read in data
        inFile >> a; 

        // Define variables 
        IloBoolVarArray p(env, a.getSize());  // note that a.getSize() = 4 
        IloArray<IloBoolVarArray> X(env, 5);  // note that you need a 5x4 X variables, not 4x5
        for(int i = 0; i < 5; i++) {
            X[i] = IloBoolVarArray(env,4);
        }

        // Build model
        IloModel model(env);

        // Add objective function 
        IloExpr  objFun (env); 
        for(int i = 0; i < a.getSize(); i++){
            objFun += a[i]*p[i];
        }

        model.add(IloMaximize(env, objFun));  

        objFun.end();  

        // Add constraints -- similar to usertfwr’s answer
        for(int i = 0; i < 4; k++){
            IloExpr sumConst (env);
            for(int j = 0; j < 5; i++){
                    sumConst += x[j][i];
            }
            // before clearing sumConst expr, add it to model
            model.add(sumConst >= 2*p[i]);
            sumConst.end(); // very important to end after having been added to the model
        }

        // Extract the model to CPLEX 
        IloCplex cplex(mod);

        // Export the LP model to a txt file to check correctness
        //cplex.exportModel("model.lp");

        // Solve model 
        cplex.solve();

    }
    catch (IloException& e) {
        cerr << "Concert exception caught: " << e << endl;
    }
    catch (...) {
           cerr << "Unknown exception caught" << endl;
    }
        env.end();
}