/**
* @param basicMatrixIn the coefficient matrix of constraints
* @return Array[2][m+1]
* First row is just reduced cost
* Second row is dual cost vector
*/
private static double[][] calLP(double[][] basicMatrixIn, double[] orderNumVec)
{
double[][] basicMatrix = cloneMatrix(basicMatrixIn); // LP solve modifies our input array
int nVar = basicMatrix.Length;
IntPtr solver = Lpsolve.make_lp(0, nVar);
Lpsolve.set_verbose(solver, 1);
// add constraints
for (int r = 0; r < nVar; r++)
{
Lpsolve.add_constraint(solver, basicMatrix[r], Lpsolve.lpsolve_constr_types.EQ, orderNumVec[r + 1]);
}
// set objective function
double[] minCoef = new double[nVar + 1]; // coefficients
for (int i = 0; i < minCoef.Length; i++)
{
minCoef[i] = 1;
}
minCoef[0] = nVar;
Lpsolve.set_obj_fn(solver, minCoef);
Lpsolve.set_minim(solver);
// solve the problem
int solFlag = (int)Lpsolve.solve(solver);
// solution
double[] rhs = new double[Lpsolve.get_Ncolumns(solver)];
Lpsolve.get_variables(solver, rhs);
double[] duals = new double[Lpsolve.get_Ncolumns(solver) + Lpsolve.get_Nrows(solver) + 1];
Lpsolve.get_dual_solution(solver, duals);
// delete the problem and free memory
Lpsolve.delete_lp(solver);
// Prepare result
double[][] rst = new double[3][];
rst[0] = new double[nVar + 1];
rst[0][0] = solFlag;
rst[1] = new double[nVar + 1];
rst[1][0] = nVar;
rhs.CopyTo(rst[1], 1);
rst[2] = new double[nVar + 1];
rst[2][0] = nVar;
Array.Copy(duals, 1, rst[2], 1, nVar);
return(rst);
}
/**
* Calculate which column index should be replaced
*
* @return index of the column that will leave the pattern matrix
*/
private static int[] calLeavingColumn(double[][] basicMatrixIn, double[] newPattern, double[] rhs)
{
double[][] basicMatrix = cloneMatrix(basicMatrixIn); // LP solve modifies our input array
int nVar = basicMatrix.Length;
IntPtr solver = Lpsolve.make_lp(0, nVar);
Lpsolve.set_verbose(solver, 1);
// add constraints
for (int r = 0; r < nVar; r++)
{
Lpsolve.add_constraint(solver, basicMatrix[r], Lpsolve.lpsolve_constr_types.EQ, newPattern[r]);
}
// set objective function
double[] minCoef = new double[nVar + 1];
for (int i = 0; i < minCoef.Length; i++)
{
minCoef[i] = 1;
}
minCoef[0] = nVar;
Lpsolve.set_obj_fn(solver, minCoef);
Lpsolve.set_minim(solver);
// solve the problem
int solFlag = (int)Lpsolve.solve(solver);
// solution
double[] var = new double[Lpsolve.get_Ncolumns(solver)];
Lpsolve.get_variables(solver, var);
// leaving column
int minIndex = -1;
double minVal = double.MaxValue;
for (int i = 0; i < var.Length; i++)
{
if (var[i] > 0 && (rhs[i + 1] / var[i]) < minVal)
{
minIndex = i;
minVal = rhs[i + 1] / var[i];
}
}
// delete the problem and free memory
Lpsolve.delete_lp(solver);
return(new int[] { solFlag, minIndex + 1 });
}
private static double[][] calKnapsackWithLpSolve(double stockLen, double[] orderNumVec, double[] orderLenVec)
{
int nVar = orderNumVec.Length - 1;
IntPtr solver = Lpsolve.make_lp(0, nVar);
Lpsolve.set_verbose(solver, 1);
// add constraints
Lpsolve.add_constraint(solver, orderLenVec, Lpsolve.lpsolve_constr_types.LE, stockLen);
// objArr.length is equal to nCol + 1
for (int c = 1; c <= nVar; c++)
{
Lpsolve.set_int(solver, c, 1);
double[] constraintVec = new double[nVar + 1];
constraintVec[0] = nVar;
for (int cIndex = 1; cIndex <= nVar; cIndex++)
{
constraintVec[cIndex] = cIndex == c ? 1 : 0;
}
Lpsolve.add_constraint(solver, constraintVec, Lpsolve.lpsolve_constr_types.LE, orderNumVec[c]);
}
// set objective function
Lpsolve.set_obj_fn(solver, orderLenVec);
Lpsolve.set_maxim(solver);
// solve the problem
int solFlag = (int)Lpsolve.solve(solver);
// solution
double reducedCost = Lpsolve.get_objective(solver);
double[] var = new double[Lpsolve.get_Ncolumns(solver)];
Lpsolve.get_variables(solver, var);
// delete the problem and free memory
Lpsolve.delete_lp(solver);
// Prepare result
double[][] rst = new double[2][];
rst[0] = new double[] { reducedCost };
rst[1] = var;
return(rst);
}