private Iteration ExchangeBasisColumns(LpModel model, Iteration previous, int entering, int leaving)
{
int[] nxtBasis = new int[previous.BasicColumns.Length];
for (int i = 0; i < previous.BasicColumns.Length; i++)
{
if (previous.BasicColumns[i] == leaving)
{
nxtBasis[i] = entering;
}
else
{
nxtBasis[i] = previous.BasicColumns[i];
}
}
int[] nxtNonBasis = new int[previous.NonBasicColumns.Length];
for (int i = 0; i < previous.NonBasicColumns.Length; i++)
{
if (previous.NonBasicColumns[i] == entering)
{
nxtNonBasis[i] = leaving;
}
else
{
nxtNonBasis[i] = previous.NonBasicColumns[i];
}
}
return(new Iteration(nxtBasis, nxtNonBasis));
}
public void Optimize(LpModel model)
{
int m = model.A.RowCount;
int n = model.A.ColumnCount;
Iteration currentIteration = GetStartingBasis(model);
while (true)
{
Matrix <double> B = GetColumnSubset(model, currentIteration.BasicColumns);
Matrix <double> NonB = GetColumnSubset(model, currentIteration.NonBasicColumns);
Matrix <double> B_inv = B.Inverse();
Vector <double> Xb = B_inv.Multiply(model.b);
_log.Info($"Iteration 0: Xb = {Xb.ToString()}");
//reduced cost
currentIteration.BasicCostVector = GetCostVector(model, currentIteration.BasicColumns);
currentIteration.NonBasicCostVector = GetCostVector(model, currentIteration.NonBasicColumns);
currentIteration.ObjectiveValue = currentIteration.BasicCostVector.ToRowMatrix().Multiply(Xb)[0];
_log.Info($"Objective: {currentIteration.ObjectiveValue}");
Matrix <double> cbInv = currentIteration.BasicCostVector.ToRowMatrix().Multiply(B_inv);
Matrix <double> reducedCosts = cbInv.Multiply(NonB) - Matrix <double> .Build.DenseOfRowVectors(currentIteration.NonBasicCostVector);
var min = reducedCosts.Row(0).Minimum();
if (min >= 0)
{
break;
}
var minId = reducedCosts.Row(0).MinimumIndex();//entering column etc, Taha 314
int enteringColumn = currentIteration.NonBasicColumns[minId];
_log.Info($"The Entering column is: {enteringColumn}");
var bp = B_inv.Multiply(model.A.Column(enteringColumn));
//check if unbounded.. if all entries negative or zero
//ratio test to determine leaving vector
//ratio test for positive denominator only -> set rest to NaN to ignore..
bp.Map((a) =>
{
if (a <= 0)
{
return(double.NaN);
}
else
{
return(a);
}
}, bp);
var feas = Xb.PointwiseDivide(bp);
int leavingColumn = currentIteration.BasicColumns[feas.MinimumIndex()];
_log.Info($"Leaving column: {leavingColumn}");
//modify basis and continue
currentIteration = ExchangeBasisColumns(model, currentIteration, enteringColumn, leavingColumn);
_log.Info(Environment.NewLine + PrintIteration(model, currentIteration));
}
_log.Info($"Final Objective is: {Math.Round(currentIteration.ObjectiveValue, 2)}");
}
Vector <double> GetCostVector(LpModel model, int[] columns)
{
double[] c = new double[columns.Length];
for (int i = 0; i < columns.Length; i++)
{
c[i] = model.C[columns[i]];
}
return(Vector <double> .Build.DenseOfArray(c));
}
private Matrix <double> GetColumnSubset(LpModel model, int[] columns)
{
Vector <double>[] vecB = new Vector <double> [columns.Length];
for (int i = 0; i < columns.Length; i++)
{
vecB[i] = model.A.Column(columns[i]);
}
return(Matrix <double> .Build.DenseOfColumnVectors(vecB));
}
public string PrintIteration(LpModel model, Iteration iteration)
{
StringBuilder sb = new StringBuilder();
//constraint columns:
var basisInverse = GetColumnSubset(model, iteration.BasicColumns).Inverse();
var constraintColumns = basisInverse.Multiply(model.A);
var rhs = basisInverse.Multiply(model.b);
for (int i = 0; i < constraintColumns.RowCount; i++)
{
var row = constraintColumns.Row(i);
for (int j = 0; j < row.Count; j++)
{
sb.Append($" {row[j].ToString("N2")} |");
}
sb.Append($"| {rhs[i].ToString("N2")}\n");
}
return(sb.ToString());
}
private Iteration GetStartingBasis(LpModel model)
{
int m = model.A.RowCount;
int n = model.A.ColumnCount;
int[] basicColumns = new int[m];
int[] nonBasicColumns = new int[n - m];
//first base
for (int c = 0; c < n; c++)
{
if (c < (n - m))
{
nonBasicColumns[c] = c;
}
else // c >= (n-m)
{
basicColumns[c - (n - m)] = c;
}
}
return(new Iteration(basicColumns, nonBasicColumns));
}
