/// <summary>
/// metóda pre získanie zadania úlohy lineárneho programovania z okna
/// </summary>
/// <param name="variablesCount">počet premenných</param>
/// <returns>zadanie úlohy lineárneho programovania</returns>
public LPTreeBody GetTaskInput(int variablesCount)
{
LinearTaskInputWindow dlg = new LinearTaskInputWindow(variablesCount);
bool? result = dlg.ShowDialog();
if (result == true)
{
myTaskType = dlg.TaskType;
myTaskFunction = (Equation)dlg.CriterialFunction.Clone();
myTaskConditions = (EquationsCollection)dlg.ConditionFunctions;
LPTreeBody tree = new LPTreeBody(dlg.CriterialFunction, dlg.ConditionFunctions, dlg.TaskType);
return tree;
}
return null;
}
/// <summary>
/// metóda pre pridanie rovnice - ohraničenia
/// </summary>
/// <param name="theEquation">ohraničenie</param>
public void InsertEquation(Equation theEquation)
{
myConditions.Add(theEquation);
}
private int myVariablesCount = 0; //pocet premennych
#endregion Fields
#region Constructors
/// <summary>
/// konštruktor
/// </summary>
/// <param name="theType">typ úlohy</param>
/// <param name="theFunction">kriteriálna funkcia</param>
public Simplex(LinearTypes theType, Equation theFunction)
{
myFunction = theFunction;
myVariablesCount = myFunction.LeftSide.Count;
myType = theType;
}
/// <summary>
/// metóda pre transformáciu problému do kanonického tvaru
/// </summary>
public void TransformToCanonicalForm()
{
// Zmena problemu na maximalizacny.
if (myType == LinearTypes.Minimalization)
{
myType = LinearTypes.Maximalization;
myFunction.Multiply(-1);
}
// Zmena nerovnosti na rovnosti.
myConditions.RemoveInequality();
myTempFunction = myConditions.HelpFunction;
// Zmena koeficientov na pravej strane na nezaporne.
foreach (Equation item in myConditions)
{
if (item.RightSide < 0)
{
item.Multiply(-1);
}
}
// Doplnenie 0 do kriteriálnej funkcie
for (int i = 0; i < myConditions[0].LeftSide.Count - myVariablesCount; i++)
{
myFunction.AddVariable(0);
}
}
/// <summary>
/// metóda pre riešenie úlohy simplexovou metódou
/// </summary>
/// <returns>riešenie</returns>
public Solution Solve()
{
TransformToCanonicalForm();
myFunction.Multiply(-1); //transformacia krit. fcie do tvaru z-ax-...=0
myTempFunction = myConditions.HelpFunction;
if (myTempFunction.LeftSide.Count > 0)
{
if (IsSolveWithHelpFunction() == false)
{
return null;
}
}
while (!IsOptimal()) //test optimality
{
int minIndex = FindIndexOfMinimalCoefInFunction(); //vyhladanie min prvku v spodnom riadku
PivotResult pivotResult = FindPivot(minIndex); //urcenie pivota + jeho polohy
if (pivotResult == null)
{
return null;
}
Equation pivotEq = myConditions[pivotResult.Index]; //vyber ohranicenia, v ktorom je pivot
foreach (Equation item in myConditions) //prenasobenie ohraniceni - eliminacia na 0
{
if (item != pivotEq)
{
item.Combine(pivotEq, -item.LeftSide[minIndex] / pivotResult.Pivot);
}
}
myFunction.Combine(pivotEq, -myFunction.LeftSide[minIndex] / pivotResult.Pivot); //prenasobenie kf - eliminacia na 0
pivotEq.Multiply((double)1 / pivotResult.Pivot); //prenasobenie ohranicenia, v ktorom je pivot jeho prvratenou hodnotou - eliminacia na 1
}
Solution solution = RetrieveSolution(myVariablesCount);
return solution;
}
/// <summary>
/// konštruktor
/// </summary>
/// <param name="function">kriteriálna funkcia</param>
/// <param name="conditions">ohraničenia</param>
/// <param name="type">typ úlohy lineárneho programovania</param>
public LPTreeBody(Equation function, EquationsCollection conditions, LinearTypes type)
{
myRoot = new LPTreeItem(function, type, conditions);
myUnprocessedItems.Add(myRoot);
}
/// <summary>
/// metóda pre vytvorenie kópie objektu
/// </summary>
/// <returns>kópia objektu</returns>
public object Clone()
{
Equation eq = new Equation(new double[] { }, myType.Clone().ToString(), myRightSide);
foreach (double item in myLeftSide)
{
eq.AddVariable(item);
}
return eq;
}
/// <summary>
/// metóda pre súčet dvoch rovníc
/// </summary>
/// <param name="theEquation">rovnica, ktorá má byť pripočítaná k pôvodnej rovnici</param>
/// <param name="theFactor">koeficient, ktorým je potrebné pripočítavanú rovnicu vynásobiť</param>
public void Combine(Equation theEquation, double theFactor)
{
//premenná pre uloženie počtu premenných na ľavej strane
int leftSideLength = theEquation.LeftSide.Count > this.LeftSide.Count ? theEquation.LeftSide.Count : this.LeftSide.Count;
for (int i = 0; i < leftSideLength; i++)
{
double secondValue = 0;
if (i < theEquation.LeftSide.Count)
{
secondValue = theEquation.LeftSide[i] * theFactor;
}
if (i < this.LeftSide.Count)
{
this.LeftSide[i] += secondValue;
}
}
this.myRightSide += theFactor * theEquation.RightSide;
}
/// <summary>
/// konštuktor
/// </summary>
/// <param name="function">kriteriálna funkcia</param>
/// <param name="type">typ úlohy lineárneho programovaina</param>
/// <param name="conditions">ohraničenia</param>
public LPTreeItem(Equation function, LinearTypes type, EquationsCollection conditions)
{
myConditions = conditions;
myFunction = function;
myType = type;
myFunctionBackup = (Equation)function.Clone();
foreach (Equation item in conditions)
{
myConditionsBackup.Add((Equation)item.Clone());
}
Simplex simplex = new Simplex(myType, myFunction);
simplex.InsertEquations(myConditions);
Solution solution = simplex.Solve();
myNodeSolution = solution;
if (solution != null)
{
myHasSolution = true;
double val = double.MinValue;
int index = -1;
for (int i = 0; i < solution.Count; i++)
{
if (Math.Abs(Math.Round(solution[i]) - solution[i]) > 0.000005)
{
val = solution[i];
index = i;
break;
}
}
// Ak nie je nájdené riešenie celočíselné:
if (val > double.MinValue + 0.000005)
{
int left = (int)Math.Floor(val);
int right = (int)Math.Ceiling(val);
// príprava ľavej strany ohraničenia
List<double> leftSide = new List<double>();
for (int i = 0; i < myFunctionBackup.LeftSide.Count; i++)
{
if (i == index)
{
leftSide.Add(1);
}
else
{
leftSide.Add(0);
}
}
// príprava ohraničenia pre ľavého syna
EquationsCollection leftConditions = (EquationsCollection)myConditionsBackup.Clone();
leftConditions.Add(new Equation(leftSide, "<=", left));
// príprava ohraničenia pre pravého syna
EquationsCollection rightConditions = (EquationsCollection)myConditionsBackup.Clone();
rightConditions.Add(new Equation(leftSide, ">=", right));
// vytvorenie potomkov
myLeftChild = new LPTreeItem((Equation)myFunctionBackup.Clone(), myType, (EquationsCollection)leftConditions.Clone());
myRightChild = new LPTreeItem((Equation)myFunctionBackup.Clone(), myType, (EquationsCollection)rightConditions.Clone());
myUpperBound = myFunction.RightSide;
}
else
{
// Ak je nájdené riešenie celočíselné:
myLowerBound = (int)myFunction.RightSide;
myUpperBound = (int)myFunction.RightSide;
myIsFinalNode = true;
}
}
}
/// <summary>
/// metóda pre výpočet dolnej medze
/// </summary>
/// <param name="function">kriteriálna funkcia</param>
/// <param name="solution">riešenie bez zaokrúhlenia</param>
/// <returns>dolná medza daného uzla</returns>
public double CountLowerBound(Equation function, Solution solution)
{
double lowerBoundFromRounding = 0;
Solution roundedSolution = new Solution();
foreach (double i in solution)
{
roundedSolution.Add(Math.Round(i));
}
foreach (double i in solution)
{
foreach (double j in function.LeftSide)
{
if (solution.IndexOf(i)==function.LeftSide.IndexOf(j))
{
lowerBoundFromRounding += j * i;
}
}
}
return lowerBoundFromRounding;
}