void ISolutionBuilder.setStandartModel(SimplexModel model)
{
m_BaseModel = model;
m_StandartModel = new StandartSimplexModel(model);
m_RevisedModel = new RevisedSimplexModel(m_StandartModel);
m_RevisedModel.ConvertStandardModel();
}
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);
}
internal static void TruncatePhaseResult(this StandartSimplexModel model, Solution solution)
{
//transfer the phaseoneobjective function factors
List <int> tmp_RemoveArtficialIndex = new List <int>();
List <int> tmp_RemoveOtherIndex = new List <int>();
List <int> tmp_totalRemoveIndex = new List <int>();
bool tmp_retainArtficialFound = false; //if retain and remove count are eqauls as aritmetich operation
for (int i = 0; i < model.ArtificialObjectiveMatrix.ColumnCount; i++)
{
if (model.VarTypes[i] == VariableType.Artificial)
{
if (model.ArtificialObjectiveMatrix[0, i] < 0)
{
tmp_RemoveArtficialIndex.Add(i);
}
else
{
tmp_retainArtficialFound = true;
}
}
else
{
if (model.ArtificialObjectiveMatrix[0, i] < 0)
{
tmp_RemoveOtherIndex.Add(i);
}
}
}
//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 (!tmp_retainArtficialFound)
{
tmp_totalRemoveIndex = tmp_RemoveArtficialIndex;
}
//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.
else
{
//merge and sort removed artificial and removed other variables
tmp_totalRemoveIndex.AddRange(tmp_RemoveArtficialIndex);
tmp_totalRemoveIndex.AddRange(tmp_RemoveOtherIndex);
}
tmp_totalRemoveIndex.Sort();
TruncatePhaseColumns(model, tmp_totalRemoveIndex, model.BasicVariables);
}
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("*********************************");
}
private static void TruncatePhaseColumns(StandartSimplexModel model, List <int> removeList, List <int> basicVariables)
{
//declare new matrix for replace Phase I result
int tmp_rowCount = model.ConstarintMatrix.RowCount;
int tmp_oldColumnCount = model.ObjectiveMatrix.ColumnCount;
int tmp_removeCount = removeList.Count;
//int[] tmp_basic = new int[tmp_oldColumnCount - tmp_removeCount];
double[] tmp_objectiveMatrix = new double[tmp_oldColumnCount - tmp_removeCount];
VariableType[] tmp_types = new VariableType[tmp_oldColumnCount - tmp_removeCount];
double[,] tmp_constarintMatrix = new double[tmp_rowCount, tmp_oldColumnCount - tmp_removeCount];
//transfer the basic flag to teh temprory array
for (int i = removeList.Count - 1; i > -1; i--)
{
for (int j = 0; j < basicVariables.Count; j++)
{
if (basicVariables[j] > removeList[i])
{
basicVariables[j] = basicVariables[j] - 1;
}
}
}
Dictionary <Term, Subject> tmp_RemovePairList = new Dictionary <Term, Subject>();
int tmp_newIndex = 0;
for (int i = 0; i < model.ArtificialObjectiveMatrix.ColumnCount; i++)
{
if (removeList.Contains(i))
{
tmp_RemovePairList.Add(model.ObjectiveFunction.Terms[i], model.ObjectiveFunction);
for (int j = 0; j < model.ConstarintMatrix.RowCount; j++)
{
tmp_RemovePairList.Add(model.Subjects[j].Terms[i], model.Subjects[j]);
}
}
else
{
//narrow the types
tmp_types[tmp_newIndex] = model.VarTypes[i];
//narrow the basic matrix value
tmp_objectiveMatrix[tmp_newIndex] = model.ObjectiveMatrix[0, i];
for (int j = 0; j < model.ConstarintMatrix.RowCount; j++)
{
tmp_constarintMatrix[j, tmp_newIndex] = Math.Round(model.ConstarintMatrix[j, i], 5);
}
tmp_newIndex++;
}
}
foreach (KeyValuePair <Term, Subject> item in tmp_RemovePairList)
{
item.Value.Terms.Remove(item.Key);
}
//Update the objective function original variable with cosntraint value;
double[] tmp_objectiveMatrixUpdated = new double[tmp_objectiveMatrix.Length];
tmp_objectiveMatrix.CopyTo(tmp_objectiveMatrixUpdated, 0);
//VariableType tmp_inclusive = (VariableType.Original | VariableType.Slack | VariableType.Excess);
double tmp_pivotValue = 0;
for (int i = 0; i < tmp_objectiveMatrix.Length; i++)
{
//is variable inclusion group
//if (tmp_objectiveMatrix[i] != 0 && tmp_types[i] == (tmp_types[i] & tmp_inclusive))
if (tmp_objectiveMatrix[i] != 0 && basicVariables.Contains(i) && tmp_constarintMatrix[basicVariables.IndexOf(i), i] == 1)
{
tmp_pivotValue = tmp_objectiveMatrix[i];
//Find the related cosntraint row
for (int j = 0; j < tmp_constarintMatrix.GetLength(0); j++)
{
//pivot cell must be addresset by unit matrix
if (tmp_constarintMatrix[j, i] != 1)
{
continue;
}
//5)Calculate new objective Row (Rn') by multiple contraint factor.RO'=RO-xRn'
for (int k = 0; k < tmp_objectiveMatrix.Length; k++)
{
tmp_objectiveMatrixUpdated[k] = Math.Round(tmp_objectiveMatrixUpdated[k] - tmp_pivotValue * tmp_constarintMatrix[j, k], 5);
}
//in addition set the left value
model.ObjectiveCost = Math.Round(model.ObjectiveCost - tmp_pivotValue * model.RightHandMatrix[j, 0], 5);
}
}
}
model.VarTypes = tmp_types;
model.ObjectiveMatrix = new Matrix(tmp_objectiveMatrixUpdated);
model.ConstarintMatrix = new Matrix(tmp_constarintMatrix);
model.BasicVariables = basicVariables;
model.ObjectiveCost = 0;
}
internal static void CreateMatrixSet(this StandartSimplexModel model)
{
int rowCount = model.Subjects.Count;
int columnCount = model.ObjectiveFunction.Terms.Count;
double[] tmp_objectiveMatrix = new double[columnCount];
//miz w= a1 + a2 + a3 + .. +an
double[] tmp_phaseObjectiveMatrix = new double[columnCount];
VariableType[] tmp_types = new VariableType[columnCount];
double[,] tmp_constarintMatrix = new double[rowCount, columnCount];
double[,] tmp_RightHandMatrix = new double[rowCount, 1]; // +1 is for objective function, second dimension is for ratio
List <int> tmp_basicVariables = new List <int>();
int tmp_colIndex = -1;
//set the basic variable flag as -1
for (int i = 0; i < rowCount; i++)
{
tmp_basicVariables.Add(-1);
}
for (int j = 0; j < columnCount; j++)
{
tmp_objectiveMatrix[j] = model.ObjectiveFunction.Terms[j].Factor;
tmp_types[j] = model.ObjectiveFunction.Terms[j].VarType;
}
for (int i = 0; i < rowCount; i++)
{
tmp_colIndex = 0;
for (int j = 0; j < columnCount; j++)
{
//we add absolutely column element to the constarint matrix.
tmp_constarintMatrix[i, j] = model.Subjects[i].Terms[j].Factor;
//if term is basic, let us calculate the constarint matrix
if (model.ObjectiveFunction.Terms[j].Basic)// && model.Subjects[i].Terms[j].Factor==1)
{
//basic variable flag
if (tmp_constarintMatrix[i, j] == 1)// && tmp_rowIndex == tmp_colIndex)
{
tmp_basicVariables[i] = j;
}
tmp_colIndex++;
}
}
tmp_RightHandMatrix[i, 0] = model.Subjects[i].RightHandValue;
}
if (model.IsTwoPhase)
{
for (int j = 0; j < columnCount; j++)
{
tmp_phaseObjectiveMatrix[j] = (-1) * model.PhaseObjectiveFunction.Terms[j].Factor;
}
model.ObjectiveCost = (-1) * model.PhaseObjectiveFunction.RightHandValue;
}
model.ObjectiveMatrix = new Matrix(tmp_objectiveMatrix);
model.ArtificialObjectiveMatrix = new Matrix(tmp_phaseObjectiveMatrix);
model.RightHandMatrix = new Matrix(tmp_RightHandMatrix);
model.ConstarintMatrix = new Matrix(tmp_constarintMatrix);
model.VarTypes = tmp_types;
model.BasicVariables = tmp_basicVariables;
}
