private Solution SolveTwoPhase()
{
Solution tmp_solution = new Solution()
{
Quality = Enums.SolutionQuality.Infeasible
};
m_RevisedModel.PrintMatrix();
//1) Solve the matrix for phase I
/*
* Steps
* 1. Modify the constraints so that the RHS of each constraint is nonnegative (This requires that each constraint with a negative RHS be multiplied by -1. Remember that if you multiply an inequality by any negative number, the direction of the inequality is reversed!). After modification, identify each constraint as a ≤, ≥ or = constraint.
* 2. Convert each inequality constraint to standard form (If constraint i is a ≤ constraint, we add a slack variable si; and if constraint i is a ≥ constraint, we subtract an excess variable ei).
* 3. Add an artificial variable ai to the constraints identified as ≥ or = constraints at the end of Step 1. Also add the sign restriction ai ≥ 0.
* 4. In the phase I, ignore the original LP’s objective function, instead solve an LP whose objective function is minimizing w = ai (sum of all the artificial variables). The act of solving the Phase I LP will force the artificial variables to be zero. 5. Since each artificial variable will be in the starting basis, all artificial variables must be eliminated from row 0 before beginning the simplex. Now solve the transformed problem by the simplex.
*/
m_ColumnSelector = ColumnSelectorFactory.GetSelector(ObjectiveType.Minumum);
tmp_solution = Solve(m_RevisedModel.PhaseNonBasisObjectiveMatrix, m_RevisedModel.PhaseBasisObjectiveMatrix, m_RevisedModel.BasisMatrix, m_RevisedModel.BasisInverseMatrix, m_RevisedModel.NonBasisMatrix, m_RevisedModel.BasisRightHandMatrix, m_RevisedModel.BasicVariables, m_RevisedModel.ObjectiveCost);
//Solving the Phase I LP will result in one of the following three cases:
//I.Case : If w = 0
//TODO test //tmp_solution.RightHandValues[tmp_solution.RightHandValues.GetLength(0) - 1, 0] = 0;
if (tmp_solution.ResultValue + m_RevisedModel.ObjectiveCost == 0)
{
m_ColumnSelector = ColumnSelectorFactory.GetSelector(m_RevisedModel.GoalType);
//transfer the phaseoneobjective function factors
RevisedSimplexModel tmp_phaseModel = m_RevisedModel;
tmp_phaseModel.TruncatePhaseResult(tmp_solution);
//II.Case : If w = 0, and no artificial variables are in the optimal Phase I basis:
// i.Drop all columns in the optimal Phase I tableau that correspond to the artificial variables.Drop Phase I row 0.
// ii.Combine the original objective function with the constraints from the optimal Phase I tableau(Phase II LP).If original objective function coefficients of BVs are nonzero row operations are done.
// iii.Solve Phase II LP using the simplex method.The optimal solution to the Phase II LP is the optimal solution to the original LP.
//tmp_phaseModel.BasisObjectiveMatrix = new Matrix(1, tmp_solution.BasicVariables.Count);
//tmp_phaseModel.BasisRightHandMatrix = new Matrix(tmp_solution.BasicVariables.Count,1);
//for (int i = 0; i < tmp_solution.BasicVariables.Count; i++)
//{
// tmp_phaseModel.BasisObjectiveMatrix[0, i] =tmp_phaseModel.ObjectiveFunction.Terms[tmp_solution.BasicVariables[i]].Factor;
// tmp_phaseModel.BasisRightHandMatrix[i,0] = tmp_phaseModel.Subjects[i].RightHandValue;
//}
tmp_solution = Solve(tmp_phaseModel.BasisNonObjectiveMatrix, tmp_phaseModel.BasisObjectiveMatrix, tmp_phaseModel.BasisMatrix, tmp_phaseModel.BasisInverseMatrix, tmp_phaseModel.NonBasisMatrix, tmp_phaseModel.BasisRightHandMatrix, tmp_phaseModel.BasicVariables, tmp_phaseModel.ObjectiveCost);
//tmp_solution = Solve(tmp_phaseModel.PhaseNonOneBasisObjectiveMatrix, tmp_phaseModel.BasisObjectiveMatrix, tmp_phaseModel.PhaseOneBasisMatrix, tmp_phaseModel.BasisMatrix, tmp_phaseModel.PhaseOneNonBasisMatrix, tmp_phaseModel.BasisRightHandMatrix, tmp_solution.BasicVariables, tmp_phaseModel.ObjectiveCost);
System.Diagnostics.Debug.WriteLine("Solution " + tmp_solution.Quality.ToString());
//if ( )
//III.Case : If w = 0, and at least one artificial variable is in the optimal Phase I basis:
// i.Drop all columns in the optimal Phase I tableau that correspond to the nonbasic artificial variables and any variable from the original problem that has a negative coefficient in row 0 of the optimal Phase I tableau. Drop Phase I row 0.
// ii.Combine the original objective function with the constraints from the optimal Phase I tableau(Phase II LP).If original objective function coefficients of BVs are nonzero row operations are done.
// iii.Solve Phase II LP using the simplex method.The optimal solution to the Phase II LP is the optimal solution to the original LP.
//if ( )
}
//II.Case : If w > 0 then the original LP has no feasible solution(stop here).
else
{
tmp_solution.Quality = SolutionQuality.Infeasible;
}
//assign the actual value to the result terms
return(tmp_solution);
}
Solution ISolutionBuilder.getResult()
{
Solution tmp_solution = new Solution()
{
Quality = Enums.SolutionQuality.Infeasible
};
if (m_RevisedModel.IsTwoPhase)
{
tmp_solution = SolveTwoPhase();
}
else
{
m_ColumnSelector = ColumnSelectorFactory.GetSelector(m_RevisedModel.GoalType);
tmp_solution = Solve(m_RevisedModel.BasisNonObjectiveMatrix, m_RevisedModel.BasisObjectiveMatrix, m_RevisedModel.BasisMatrix, m_RevisedModel.BasisMatrix.Invert(), m_RevisedModel.NonBasisMatrix, m_RevisedModel.BasisRightHandMatrix, m_RevisedModel.BasicVariables, m_RevisedModel.ObjectiveCost);
}
//for feaseble solution, all of rhs values must be positive or zero and Z must be zero after all iteration
PrepareSolutionResult(m_RevisedModel.NonBasisMatrix, WorkingRightHandValues, m_RevisedModel.ObjectiveFunction.Terms, tmp_solution);
return(tmp_solution);
}