/// <summary>
/// Finds minimum of functions by transforming it to form solvable by Hooke-Jeeves algorithm.
/// </summary>
/// <param name="implicitRestrictions">List of implicit restrictions.</param>
/// <param name="function">Function used in algorithm.</param>
/// <param name="t">Parameter of transformation.</param>
/// <param name="e">Precision.</param>
/// <param name="startingPoint">Starting point of algorithm.</param>
/// <param name="epsilon">Precision used in Hooke-Jeeves method.</param>
/// <param name="deltaX">Step used for calculating new point.</param>
/// <param name="iterations">Number of iterations of algorithm.</param>
/// <returns>Minimum of function.</returns>
public static Matrica FindMinimum(List <RestrictionExpression> implicitRestrictions, Function function, double t, double e, Matrica startingPoint, Matrica epsilon, Matrica deltaX, int iterations)
{
Matrica x = new Matrica();
x.Equals(startingPoint);
int counter = 0;
while (true)
{
Matrica dx = new Matrica();
dx.Equals(deltaX);
TransformedFunction transformedFunction = new TransformedFunction(function, implicitRestrictions, t);
Matrica xs = new Matrica();
xs.Equals(x);
x = HookeJeevesMethod.FindMinimum(xs, transformedFunction, epsilon, dx, algorithmName);
t *= 10;
counter++;
if (OptimizationUtils.CheckIfPointsAreSimilar(x, xs, e) || counter > iterations)
{
break;
}
}
function.DeleteParameters();
return(x);
}
/// <summary>
/// Finds minimum of function using Box optimization method.
/// </summary>
/// <param name="function">Function used to optimize.</param>
/// <param name="implicitRestrictions">List of implicit restrictions used in Box method.</param>
/// <param name="explicitRestriction">List of explicit restrictions used in Box method.</param>
/// <param name="startingPoint">Starting point of algorithm.</param>
/// <param name="alfa">Constant alpha used in algorithm.</param>
/// <param name="iterations">Number of iterations of algorithm.</param>
/// <returns></returns>
public static Matrica FindMinimum(Function function, List <RestrictionExpression> implicitRestrictions, ExplicitRestriction explicitRestriction, Matrica startingPoint, double alfa, int iterations)
{
if (OptimizationUtils.CheckIfExplicitConstraintsAreMet(explicitRestriction, startingPoint) == false ||
OptimizationUtils.CheckIfImplicitConstraintsAreMet(implicitRestrictions, startingPoint) == false)
{
throw new ArgumentException("Starting point does not meet explicit and/or implicit conditions!");
}
int iter = 0;
function.SetParametersSize(startingPoint.NoOfRows);
Matrica centroid = new Matrica();
centroid.Equals(startingPoint);
int n = startingPoint.NoOfRows;
Random random = new Random();
double R;
List <Matrica> simplex = new List <Matrica>();
UnimodalInterval interval = explicitRestriction.GetInterval();
for (int t = 0; t < 2 * n; t++)
{
double[] point = new double[n];
for (int i = 0; i < n; i++)
{
R = random.NextDouble() * (maximumForRandom - minimumForRandom) + minimumForRandom;
point[i] = interval.Minimum + R * (interval.Maximum - interval.Minimum);
}
simplex.Insert(t, Matrica.ArrayToVector(point));
bool[] simplexPointMeetsImplicitRestrictions = new bool[implicitRestrictions.Count];
for (int i = 0; i < implicitRestrictions.Count; i++)
{
simplexPointMeetsImplicitRestrictions[i] = false;
}
while (true)
{
for (int i = 0; i < implicitRestrictions.Count; i++)
{
simplexPointMeetsImplicitRestrictions[i] = implicitRestrictions[i].CheckIfMet(simplex[t].VectorToArray());
if (simplexPointMeetsImplicitRestrictions[i] == false)
{
simplex[t].AddValue(centroid);
simplex[t].MultiplyByScalar(1.0 / 2);
break;
}
}
if (!simplexPointMeetsImplicitRestrictions.Contains(false))
{
break;
}
}
centroid = GetCentroidPoint(simplex);
}
List <double> functionValues = GetSimplexPointsFunctionValues(simplex, function);
Matrica xr = new Matrica();
do
{
int h = GetIndexOfWorstPoint(functionValues);
int h2 = GetIndexOfSecondWorstPoint(functionValues, h);
centroid = GetCentroidPoint(simplex, h);
xr = Reflection(centroid, simplex[h], alfa);
for (int i = 0; i < xr.NoOfRows; i++)
{
if (xr.LoadedMatrix[i][0] < interval.Minimum)
{
xr.LoadedMatrix[i][0] = interval.Minimum;
}
else if (xr.LoadedMatrix[i][0] > interval.Maximum)
{
xr.LoadedMatrix[i][0] = interval.Maximum;
}
}
bool[] reflectionMeetsImplicitRestrictions = new bool[implicitRestrictions.Count];
for (int i = 0; i < implicitRestrictions.Count; i++)
{
reflectionMeetsImplicitRestrictions[i] = false;
}
while (true)
{
for (int i = 0; i < implicitRestrictions.Count; i++)
{
reflectionMeetsImplicitRestrictions[i] = implicitRestrictions[i].CheckIfMet(xr.VectorToArray());
if (reflectionMeetsImplicitRestrictions[i] == false)
{
xr.AddValue(centroid);
xr.MultiplyByScalar(1.0 / 2);
break;
}
}
if (!reflectionMeetsImplicitRestrictions.Contains(false))
{
break;
}
}
double xrFunctionValue = function.CalculateValue(xr.VectorToArray());
function.IncreaseCounterValue(algorithmName);
if (xrFunctionValue > functionValues[h2])
{
xr.AddValue(centroid);
xr.MultiplyByScalar(1.0 / 2);
}
simplex[h] = xr;
functionValues[h] = xrFunctionValue;
iter++;
} while (iter < iterations);
function.DeleteParameters();
return(simplex.ElementAt(functionValues.IndexOf(functionValues.Min())));
}