//Compute SolverIteration from preceding iteration
private static SolverIteration ComputeIteration(SolverIteration previous)
{
SolverIteration iteration = previous.Copy();
var column = IncomingVariable(iteration.DecisionVariables);
var row = LeavingVariable(GetColumn(iteration.InputGrid, column),
iteration.BaseVariables);
var variable = iteration.InputGrid[row][column];
var rowArray = iteration.InputGrid[row];
for (int i = 0; i < rowArray.Length; i++)
{
rowArray[i] /= variable;
}
iteration.BaseVariables[row] /= variable;
for (int i = 0; i < iteration.InputGrid.Length; i++)
{
if (i == row)
{
continue;
}
var value = iteration.InputGrid[i][column];
for (int j = 0; j < iteration.InputGrid[i].Length; j++)
{
iteration.InputGrid[i][j] -= value * iteration.InputGrid[row][j];
}
iteration.BaseVariables[i] -= value * iteration.BaseVariables[row];
}
var val = iteration.DecisionVariables[column];
for (int i = 0; i < iteration.DecisionVariables.Length; i++)
{
iteration.DecisionVariables[i] -=
val * iteration.InputGrid[row][i];
}
iteration.Bases[row] = iteration.Variables[column];
iteration.Z = 0;
for (var i = 0; i < iteration.Bases.Length; i++)
{
var baseVar = iteration.Bases[i];
iteration.Z += GetVariableObjective(baseVar, iteration) * iteration.BaseVariables[i];
}
previous.SelectedGridPositions = (row, column);
return(iteration);
}
//Remove artificial variable indexes after two-phases finishes
public static SolverIteration RemoveIndexes(SolverIteration iteration, int cutoffIndex)
{
var cutIteration = iteration.Copy();
var variables = iteration.Variables.Take(cutoffIndex).ToArray();
var objectiveVariables = iteration.ObjectiveVariables.Take(cutoffIndex)
.ToArray();
var decisionVariables = iteration.DecisionVariables.Take(cutoffIndex)
.ToArray();
var inputGrid = new List <BigRational[]>();
for (int i = 0; i < iteration.InputGrid.Length; i++)
{
inputGrid.Add(iteration.InputGrid[i].Take(cutoffIndex).ToArray());
}
cutIteration.Variables = variables;
cutIteration.ObjectiveVariables = objectiveVariables;
cutIteration.DecisionVariables = decisionVariables;
cutIteration.InputGrid = inputGrid.ToArray();
return(cutIteration);
}
//Run two-phases simplex algorithm starting from an initial SolverIteration
public static SolvedModel TwoPhases(SolverIteration initialIteration, List <Constraint> constraints)
{
var twoPhasesInitialIteration = initialIteration.Copy();
int artificialCutoff = -1;
for (int i = 0; i < initialIteration.Variables.Length; i++)
{
if (initialIteration.Variables[i].Type == VariableType.Artificial)
{
artificialCutoff = i;
break;
}
}
if (artificialCutoff == -1)
{
throw new ArgumentException();
}
var twoPhasesObjective = Enumerable.Repeat <BigRational>(
BigRational.One, twoPhasesInitialIteration.Variables.Length).ToArray();
for (int i = 0; i < artificialCutoff; i++)
{
twoPhasesObjective[i] = 0;
}
twoPhasesInitialIteration.ObjectiveVariables = twoPhasesObjective;
var twoPhaseBases = twoPhasesInitialIteration
.Variables.Skip(
twoPhasesInitialIteration.Variables.Length - twoPhasesInitialIteration.Bases.Length)
.ToArray();
twoPhasesInitialIteration.Bases = twoPhaseBases;
for (int i = 0; i < twoPhasesInitialIteration.Variables.Length; i++)
{
BigRational Zj = BigRational.Zero;
for (int j = 0; j < twoPhasesInitialIteration.Bases.Length; j++)
{
var rowVariable = twoPhasesInitialIteration.Bases[j];
var rowObjectiveIndex = Array.IndexOf(twoPhasesInitialIteration.Variables, rowVariable);
var rowObjective = twoPhasesInitialIteration.ObjectiveVariables[rowObjectiveIndex];
Zj += twoPhasesInitialIteration.InputGrid[j][i] * rowObjective;
}
twoPhasesInitialIteration.DecisionVariables[i] = twoPhasesInitialIteration.ObjectiveVariables[i] - Zj;
}
twoPhasesInitialIteration.Z = 0;
for (var i = 0; i < twoPhasesInitialIteration.Bases.Length; i++)
{
var baseVar = twoPhasesInitialIteration.Bases[i];
var columnIndex = Array.IndexOf(twoPhasesInitialIteration.Variables, baseVar);
twoPhasesInitialIteration.Z += twoPhasesInitialIteration.BaseVariables[i] * twoPhasesInitialIteration.ObjectiveVariables[columnIndex];
}
var solvedTwoPhases = Simplex(twoPhasesInitialIteration, constraints);
solvedTwoPhases.TwoPhasesIterations = solvedTwoPhases.SimplexIterations;
solvedTwoPhases.SimplexIterations = new List <SolverIteration>();
if (solvedTwoPhases.Result != SolvedResult.Optimized)
{
return(solvedTwoPhases);
}
if (solvedTwoPhases.Z != 0)
{
solvedTwoPhases.Result = SolvedResult.Unbounded;
return(solvedTwoPhases);
}
var finalIteration = solvedTwoPhases.TwoPhasesIterations.Last();
for (int i = 0; i < finalIteration.Bases.Length; i++)
{
if (finalIteration.Bases[i].Type == VariableType.Artificial &&
finalIteration.BaseVariables[i] > 0)
{
solvedTwoPhases.Result = SolvedResult.Infeasible;
return(solvedTwoPhases);
}
}
finalIteration = RemoveIndexes(
finalIteration.Copy(), artificialCutoff);
finalIteration.ObjectiveVariables = initialIteration.ObjectiveVariables.Take(artificialCutoff).ToArray();
finalIteration.Z = 0;
for (var i = 0; i < finalIteration.Bases.Length; i++)
{
var baseVar = finalIteration.Bases[i];
var columnIndex = Array.IndexOf(finalIteration.Variables, baseVar);
if (columnIndex == -1)
{
finalIteration.Z += 0;
}
else
{
finalIteration.Z += finalIteration.BaseVariables[i] * finalIteration.ObjectiveVariables[columnIndex];
}
}
for (int i = 0; i < finalIteration.Variables.Length; i++)
{
var zj = -GetColumn(finalIteration.InputGrid, i).Sum();
var cj = finalIteration.ObjectiveVariables[i];
finalIteration.DecisionVariables[i] =
-GetColumn(finalIteration.InputGrid, i).Sum() - finalIteration.ObjectiveVariables[i];
}
var simplexResult = Simplex(finalIteration, constraints);
simplexResult.TwoPhasesIterations = solvedTwoPhases.TwoPhasesIterations;
return(simplexResult);
}