Hi. I am writing a CPLEX optimization code to generate a matrix, which takes r and n as the command line arguments, but they may be assumed 2 and 4 for now.
The condition for generating the matrix is that the sum of elements in any row or in any column should equal 10, where the elements are integers between 0 and 10. (i.e. doubly-stochastic matrix)
I turned this condition into the constraint, and generated the matrix, but it only gives a matrix with 10s and 0s.
I think it is because CPLEX always finds the "optimal" solution, but for the problem I want to solve, this is not going to help much.
I want matrices with some 6, 7, 8, 9, 10, and 0~5 for the rest.
I want to generate all possible matrices satisfying such condition (and some more condition to be added later) so that I could test all of them and exhaust the case.
How can I do that?
I am looking into this solution pool thing, and it is not easy..
Also,
cplex.out() << "number of solutions = " << cplex.getSolnPoolNsolns() << endl;
this gives 1... meaning that there is only one solution, while I know there are millions of those matrices.
If you have any ideas how to generate all the 'sub-optimal' matrices, please help me.
Thank you.
I attached my code in IPGenMat.cpp, and aa.sol was the solution it gave me.
I also copied it here below.
(In short, two questions: 1. how can I find 'less optimal' solutions? 2. how can I find all of such solutions?)
#include<ilcplex/ilocplex.h>
#include<vector>
#include<iostream>
#include<sstream>
#include<string>
using namespace std;
int main(int argc, char** argv) {
if (argc < 2) {
cerr << "Error: " << endl;
return 1;
}
else {
int r, n;
stringstream rValue(argv[1]);
stringstream nValue(argv[2]);
rValue >> r;
nValue >> n;
int N=n*r;
int ds = 10; //10 if doubly-stochastic, smaller if sub-doubly stochastic
IloEnv env;
try {
IloModel model(env);
IloArray<IloNumVarArray> m(env, N);
for (int i=0; i<N; i++) {
m[i] = IloNumVarArray(env, N, 0, 10, ILOINT);
}
IloArray<IloExpr> sumInRow(env, N);
for (int i=0; i<N; i++) {
sumInRow[i] = IloExpr(env);
}
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
sumInRow[i] += m[i][j];
}
}
IloArray<IloRange> rowEq(env, N);
for (int i=0; i<N; i++) {
rowEq[i] = IloRange(env, ds, sumInRow[i], 10); //doubly stochastic
}
IloArray<IloExpr> sumInColumn(env, N);
for (int i=0; i<N; i++) {
sumInColumn[i] = IloExpr(env);
}
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
sumInColumn[i] += m[j][i];
}
}
IloArray<IloRange> columnEq(env, N);
for (int i=0; i<N; i++) {
columnEq[i] = IloRange(env, ds, sumInColumn[i], 10); //doubly stochastic
}
for (int i=0; i<N; i++) {
model.add(rowEq[i]);
model.add(columnEq[i]);
}
IloCplex cplex(env);
cplex.extract(model);
cplex.setParam(IloCplex::SolnPoolAGap,0.0);
cplex.setParam(IloCplex::SolnPoolIntensity,4);
cplex.setParam(IloCplex::PopulateLim, 2100000000);
cplex.populate();//.solve();
cplex.out() << "solution status = " << cplex.getStatus() << endl;
cplex.out() << "number of solutions = " << cplex.getSolnPoolNsolns() << endl;
cplex.out() << endl;
cplex.writeSolutions("aa.sol");
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
cplex.out() << cplex.getValue(m[i][j]) << " | ";
}
cplex.out() << endl;
}
cplex.out() << endl;
}
catch(IloException& e) {
cerr << " ERROR: " << e << endl;
}
catch(...) {
cerr << " ERROR: " << endl;
}
env.end();
return 0;
}
}