private Solution SolveTwoPhase(StandartSimplexModel simplexModel)
{
Solution tmp_solution = new Solution()
{
Quality = Enums.SolutionQuality.Infeasible
};
simplexModel.CurrentPhase = 1;
simplexModel.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.
*/
VariableType tmp_inclusive = VariableType.Original | VariableType.Slack | VariableType.Excess;
m_ColumnSelector = ColumnSelectorFactory.GetSelector(ObjectiveType.Minumum);
tmp_solution = Solve(simplexModel.VarTypes, tmp_inclusive, simplexModel.ArtificialObjectiveMatrix, simplexModel.ConstarintMatrix, simplexModel.RightHandMatrix, simplexModel.BasicVariables, simplexModel.ObjectiveCost, true);
//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_epsilon)
{
simplexModel.CurrentPhase = 2;
//transfer the phaseoneobjective function factors
simplexModel.TruncatePhaseResult(tmp_solution);
simplexModel.PrintMatrix();
//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.
//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 ( )
tmp_solution = Solve(simplexModel.VarTypes, tmp_inclusive, simplexModel.ObjectiveMatrix, simplexModel.ConstarintMatrix, simplexModel.RightHandMatrix, simplexModel.BasicVariables, simplexModel.ObjectiveCost, simplexModel.GoalType == ObjectiveType.Minumum);
System.Diagnostics.Debug.WriteLine("Solution " + tmp_solution.Quality.ToString());
}
//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
PrepareSolutionResult(simplexModel.ConstarintMatrix, simplexModel.RightHandMatrix, simplexModel.ObjectiveFunction.Terms, tmp_solution);
return(tmp_solution);
}
private Solution SolveStandart(StandartSimplexModel simplexModel)
{
//simplexModel.ConvertStandardModel();
simplexModel.PrintMatrix();
//simplexModel.CreateMatrixSet();
VariableType tmp_inclusive = VariableType.Original | VariableType.Slack;
Solution tmp_solution = Solve(simplexModel.VarTypes, tmp_inclusive, simplexModel.ObjectiveMatrix, simplexModel.ConstarintMatrix, simplexModel.RightHandMatrix, simplexModel.BasicVariables, simplexModel.ObjectiveCost, simplexModel.GoalType == ObjectiveType.Minumum);
PrepareSolutionResult(simplexModel.ConstarintMatrix, simplexModel.RightHandMatrix, simplexModel.ObjectiveFunction.Terms, tmp_solution);
return(tmp_solution);
}
internal static void PhaseOnePrintMatrix(this StandartSimplexModel model)
{
model.PrintMatrix();
string tmp_sign = string.Empty;
System.Diagnostics.Debug.WriteLine("Goal :" + model.GoalType.ToString());
System.Diagnostics.Debug.Write("New Objective Function - " + model.GoalType.ToString() + ": ");
foreach (Term item in model.PhaseObjectiveFunction.Terms)
{
tmp_sign = string.Empty;
if (Math.Sign(item.Factor) > -1)
{
tmp_sign = "+";
}
System.Diagnostics.Debug.Write(tmp_sign + item.Factor + "*" + item.Vector + " ");
}
System.Diagnostics.Debug.Write(" = ");
System.Diagnostics.Debug.WriteLine(model.PhaseObjectiveFunction.RightHandValue);
System.Diagnostics.Debug.WriteLine("*********************************");
}