public void DegeneracyTest()
{
#region Arrange
var target = new Solver();
var lc1 = new LinearConstraint()
{
Coefficients = new double[3] { 1, 1, 0 },
Relationship = Relationship.LessThanOrEquals,
Value = 1
};
var lc2 = new LinearConstraint()
{
Coefficients = new double[3] { 0, -1, 1 },
Relationship = Relationship.LessThanOrEquals,
Value = 0
};
var constraints = new List<LinearConstraint>() { lc1, lc2 };
var goal = new Goal()
{
Coefficients = new double[3] { 1, 1, 1 },
ConstantTerm = 0
};
var model = new Model()
{
Constraints = constraints,
Goal = goal,
GoalKind = GoalKind.Maximize
};
var expected = new Solution()
{
Decisions = new double[3] { 0, 1, 1 },
Quality = SolutionQuality.Optimal,
AlternateSolutionsExist = false,
OptimalValue = 2
};
#endregion
//Act
var actual = target.Solve(model);
//Assert
CollectionAssert.AreEqual(expected.Decisions, actual.Decisions);
Assert.AreEqual(expected.Quality, actual.Quality);
Assert.AreEqual(expected.AlternateSolutionsExist, actual.AlternateSolutionsExist);
}
public void TwoPhaseClassTest()
{
#region Arrange
var target = new Solver();
var lc1 = new LinearConstraint()
{
Coefficients = new double[2] { 1, 1 },
Relationship = Relationship.LessThanOrEquals,
Value = 35
};
var lc2 = new LinearConstraint()
{
Coefficients = new double[2] { 1, 2 },
Relationship = Relationship.LessThanOrEquals,
Value = 38
};
var lc3 = new LinearConstraint()
{
Coefficients = new double[2] { 2, 2 },
Relationship = Relationship.LessThanOrEquals,
Value = 50
};
var constraints = new List<LinearConstraint>() { lc1, lc2, lc3 };
var goal = new Goal()
{
Coefficients = new double[2] { 350, 450 },
ConstantTerm = 0
};
var model = new Model()
{
Constraints = constraints,
Goal = goal,
GoalKind = GoalKind.Maximize
};
var expected = new Solution()
{
Decisions = new double[2] { 12, 13 },
Quality = SolutionQuality.Optimal,
AlternateSolutionsExist = false,
OptimalValue = 10050 // 12*350 + 13*450
};
var actual = target.Solve(model);
#endregion
////Act
////Assert
CollectionAssert.AreEqual(expected.Decisions, actual.Decisions);
Assert.AreEqual(expected.Quality, actual.Quality);
Assert.AreEqual(expected.AlternateSolutionsExist, actual.AlternateSolutionsExist);
}
public DenseMatrix createMatrix(Model model)
{
int numConstraints = model.Constraints.Count;
int numDecisionVars = model.Goal.Coefficients.Length;
int varCounter = numDecisionVars;
// matrix(rows, columns)
DenseMatrix coefficients = new DenseMatrix(numConstraints, numDecisionVars);
DenseMatrix artificialVars = new DenseMatrix(numConstraints, 1);
var constraintCounter = 0;
this.rhsValues = new DenseVector(numConstraints);
this.basics = new List<int>();
this.artificialRows = new List<int>();
foreach (var constraint in model.Constraints) {
rhsValues[constraintCounter] = constraint.Value;
// if the constraint RHS is negative, invert the coefficients and flip the inequality sign
if (constraint.Value < 0)
{
for (int i = 0; i< model.Goal.Coefficients.Length; i++) {
model.Goal.Coefficients[i] = model.Goal.Coefficients[i] * -1;
}
if (constraint.Relationship == Relationship.LessThanOrEquals)
{
constraint.Relationship = Relationship.GreaterThanOrEquals;
}
else if (constraint.Relationship == Relationship.GreaterThanOrEquals)
{
constraint.Relationship = Relationship.LessThanOrEquals;
}
// also flip the rhs value which we already put in the array for the simplex setup
rhsValues[constraintCounter] = rhsValues[constraintCounter] * -1;
}
coefficients.SetRow(constraintCounter, 0, constraint.Coefficients.Length, new DenseVector(constraint.Coefficients));
// if it's a less than, add a slack column to the coefs matrix
if (constraint.Relationship == Relationship.LessThanOrEquals)
{
DenseVector slack = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
slack.At(constraintCounter, 1);
coefficients = (DenseMatrix)coefficients.Append(slack.ToColumnMatrix());
this.basics.Add(varCounter);
}
else
{
// Need to add an artificial variable for >= and = constraints
DenseVector surplus = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
surplus.At(constraintCounter, -1);
coefficients = (DenseMatrix)coefficients.Append(surplus.ToColumnMatrix());
DenseVector artificial = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
artificial.At(constraintCounter, 1);
artificialVars = (DenseMatrix)artificialVars.Append(artificial.ToColumnMatrix());
// Keeps track of the rows with artificial variable, for setting w
artificialRows.Add(constraintCounter);
}
varCounter++;
constraintCounter++;
}
// put the constraints and stuff into the matrix
if (artificialVars.ColumnCount > 1)
{
artificialVars = (DenseMatrix)artificialVars.SubMatrix(0, artificialVars.RowCount, 1, artificialVars.ColumnCount - 1);
for (int i = coefficients.ColumnCount; i < coefficients.ColumnCount + artificialVars.ColumnCount; i++)
{
this.basics.Add(i);
}
coefficients = (DenseMatrix)coefficients.Append(artificialVars);
numArtificial = artificialVars.ColumnCount;
}
else
{
numArtificial = 0;
}
return coefficients;
}
public void Simple2PhaseFromPaper()
{
#region Arrange
var target = new Solver();
var lc1 = new LinearConstraint()
{
Coefficients = new double[2] { 1, 1 },
Relationship = Relationship.GreaterThanOrEquals,
Value = 4
};
var lc2 = new LinearConstraint()
{
Coefficients = new double[2] { 1, -1 },
Relationship = Relationship.GreaterThanOrEquals,
Value = 1
};
var lc3 = new LinearConstraint()
{
Coefficients = new double[2] { -1, 2 },
Relationship = Relationship.GreaterThanOrEquals,
Value = -1
};
var constraints = new List<LinearConstraint>() { lc1, lc2, lc3 };
var goal = new Goal()
{
Coefficients = new double[2] { 1, 2 },
ConstantTerm = 0
};
var model = new Model()
{
Constraints = constraints,
Goal = goal,
GoalKind = GoalKind.Minimize
};
var expected = new Solution()
{
Decisions = new double[2] { 3, 1 },
Quality = SolutionQuality.Optimal,
AlternateSolutionsExist = false,
OptimalValue = 5
};
#endregion
//Act
var actual = target.Solve(model);
//Assert
CollectionAssert.AreEqual(expected.Decisions, actual.Decisions);
Assert.AreEqual(expected.Quality, actual.Quality);
Assert.AreEqual(expected.AlternateSolutionsExist, actual.AlternateSolutionsExist);
}
public Solution Solve(Model model)
{
DenseVector testVect = DenseVector.Create(10, delegate(int s) { return s; });
DenseMatrix coefficients = createMatrix(model);
//gets the coefficients from the goal
DenseVector objFunCoeffs = new DenseVector(model.Goal.Coefficients);
//adds zeroes for the surplus/slack/artificial variables
DenseVector objFunValues = DenseVector.Create((coefficients.ColumnCount), delegate(int s) { return 0; });
objFunValues.SetSubVector(0, objFunCoeffs.Count, objFunCoeffs);
//flips the sign of everything
if (model.GoalKind == GoalKind.Maximize)
{
objFunValues = DenseVector.Create((coefficients.ColumnCount), delegate(int s) { return -objFunValues[s]; });
}
//here so I don't have to pass the model in :)
numConstraints = model.Constraints.Count;
//Maybe I could be smarter about where I put this (at the end of createMatrix?)
//take care of artificial variable stuff
if(numArtificial > 0)
{
//adds the z row to the coefficients matrix
//adds the column first
coefficients = (DenseMatrix)coefficients.Append(DenseVector.Create((coefficients.RowCount), delegate(int s) { return 0; }).ToColumnMatrix());
coefficients = (DenseMatrix)coefficients.InsertRow(coefficients.RowCount, DenseVector.Create(coefficients.ColumnCount, delegate(int s) {
if (s == coefficients.ColumnCount - 1)
return 1;
else
return -objFunValues[s];
}));
//adds a 0 to match the z row
rhsValues = DenseVector.Create(rhsValues.Count + 1, delegate(int s)
{
if (s == rhsValues.Count)
{
return model.Goal.ConstantTerm;
}
else
{
return rhsValues[s];
}
});
//changes the objFunValues to be the w thingy
objFunValues = DenseVector.Create(coefficients.ColumnCount, delegate(int s)
{
double sum = 0;
//minus 1 because we also added a column for z
if (s < coefficients.ColumnCount - numArtificial - 1)
{
//calculate each w row entry by
foreach (int index in artificialRows)
{
sum += coefficients[index, s];
}
return sum;
}
else
{
return 0;
}
});
//z is now a basic variable??
basics.Add(coefficients.ColumnCount - 1);
printMat(coefficients);
//solves it for that
optimize(coefficients, objFunValues, true);
basics.Remove(coefficients.ColumnCount - 1);
//gets rid of the last value
rhsValues = (DenseVector)rhsValues.SubVector(0, (rhsValues.Count - 1));
//chops off the z row and the artificial variables
coefficients = (DenseMatrix)coefficients.SubMatrix(0, coefficients.RowCount - 1, 0, coefficients.ColumnCount - 1 - numArtificial);
}
printMat(coefficients);
optimize(coefficients, objFunValues, false);
/*
* To find the solution:
* The first columns in the mattress (that aren't
* ssa variables) should be basic variables
* Find what the final value is by finding their indices
* in basics and then the value at that index in xprimes
* should be what you're looking for I think
* At least it's somewhere in xprimes
*/
double[] solution = new double[model.Goal.Coefficients.Length];
double op = model.Goal.ConstantTerm;
for(int i = 0; i < solution.Length; i++)
{
solution[i] = xPrime[basics.IndexOf(i), 0];
op += solution[i] * model.Goal.Coefficients[i];
}
Solution sol = new Solution()
{
Decisions = solution,
OptimalValue = op,
AlternateSolutionsExist = false,
Quality = SolutionQuality.Optimal
};
return sol;
}