public void Vardim()
{
// This function is described by Powell in his NEWOUA paper as one that caused problems for the simplest formulation of that minimizer.
Func<IList<double>, double> f = (IList<double> x) => {
double s1 = 0.0;
double s2 = 0.0;
for (int i = 0; i < x.Count; i++) {
s1 += i * (x[i] - 1.0);
s2 += MoreMath.Sqr(x[i] - 1.0);
}
return (s2 + s1 * s1 + s1 * s1 * s1 * s1);
};
for (int n = 2; n < 8; n++) {
Console.WriteLine("n = {0}", n);
ColumnVector start = new ColumnVector(n);
ColumnVector solution = new ColumnVector(n);
solution.Fill((i, j) => 1.0);
MultiExtremum min = MultiFunctionMath.FindLocalMinimum(f, start);
Console.WriteLine(min.EvaluationCount);
Console.WriteLine("{0} ({1}) ?= 0.0", min.Value, min.Precision);
Assert.IsTrue(min.Dimension == n);
Assert.IsTrue(TestUtilities.IsNearlyEqual(min.Value, 0.0, new EvaluationSettings() { AbsolutePrecision = 4.0 * min.Precision }));
Assert.IsTrue(TestUtilities.IsNearlyEqual(min.Location, solution, new EvaluationSettings() { RelativePrecision = Math.Sqrt(4.0 * min.Precision) }));
}
}
public void Schwefel()
{
// Test over [-500,500], minimum at (420.969,...) -> -418.983*d, many local minima
Func<IList<double>, double> function = (IList<double> x) => {
double s = 0.0;
for (int i = 0; i < x.Count; i++) {
s += x[i] * Math.Sin(Math.Sqrt(Math.Abs(x[i])));
}
return (-s);
};
for (int n = 2; n < 32; n = (int) Math.Round(AdvancedMath.GoldenRatio * n)) {
Console.WriteLine("n={0}", n);
Interval[] box = new Interval[n];
for (int i = 0; i < box.Length; i++) box[i] = Interval.FromEndpoints(-500.0, 500.0);
MultiExtremum minimum = MultiFunctionMath.FindGlobalMinimum(function, box);
Assert.IsTrue(minimum.Dimension == n);
Console.WriteLine(minimum.EvaluationCount);
Console.WriteLine("{0} ({1}) ?= {2}", minimum.Value, minimum.Precision, -418.983 * n);
Assert.IsTrue(TestUtilities.IsNearlyEqual(minimum.Value, -418.983 * n, new EvaluationSettings() { AbsolutePrecision = minimum.Precision }));
foreach (double coordinate in minimum.Location) Console.WriteLine(coordinate);
ColumnVector solution = new ColumnVector(n);
solution.Fill((int i, int j) => 420.969);
Assert.IsTrue(TestUtilities.IsNearlyEqual(minimum.Location, solution, new EvaluationSettings() { RelativePrecision = 2.0 * Math.Sqrt(Math.Abs(minimum.Precision / minimum.Value)) }));
}
}