private static DifferentialEvolutionSettings GetDefaultSettings(EvaluationSettings settings, int d)
{
if (settings == null)
{
settings = new EvaluationSettings();
}
DifferentialEvolutionSettings deSettings = new DifferentialEvolutionSettings();
deSettings.Population = 8 * d + 4;
deSettings.CrossoverProbability = 1.0 - 1.0 / 8.0 - 1.0 / d;
deSettings.RelativePrecision = (settings.RelativePrecision < 0.0) ? Math.Pow(10.0, -(2.0 + 4.0 / d)) : settings.RelativePrecision;
deSettings.AbsolutePrecision = (settings.AbsolutePrecision < 0.0) ? Math.Pow(10.0, -(4.0 + 8.0 / d)) : settings.AbsolutePrecision;
deSettings.EvaluationBudget = (settings.EvaluationBudget < 0) ? 128 * d * d * d * d : settings.EvaluationBudget;
/*
* if (settings == null) {
* deSettings.RelativePrecision = Math.Pow(10.0, -(2.0 + 4.0 / d));
* deSettings.AbsolutePrecision = MoreMath.Sqr(deSettings.RelativePrecision);
* deSettings.EvaluationBudget = 128 * d * d * d * d;
* } else {
* deSettings.RelativePrecision = settings.RelativePrecision;
* deSettings.AbsolutePrecision = settings.AbsolutePrecision;
* deSettings.EvaluationBudget = settings.EvaluationBudget;
* }
*/
return(deSettings);
}
private static MultiExtremum FindGlobalExtremum(Func <IReadOnlyList <double>, double> function, IReadOnlyList <Interval> volume, MultiExtremumSettings settings, bool negate)
{
if (function == null)
{
throw new ArgumentNullException(nameof(function));
}
if (volume == null)
{
throw new ArgumentNullException(nameof(volume));
}
MultiFunctor f = new MultiFunctor(function, negate);
DifferentialEvolutionSettings deSettings = GetDefaultSettings(settings, volume.Count);
MultiExtremum extremum = FindGlobalExtremum(f, volume, deSettings);
return(extremum);
}
private static DifferentialEvolutionSettings GetDefaultSettings(MultiExtremumSettings settings, int d)
{
if (settings == null)
{
settings = new MultiExtremumSettings();
}
DifferentialEvolutionSettings deSettings = new DifferentialEvolutionSettings();
deSettings.Population = 8 * d + 4;
deSettings.CrossoverProbability = 1.0 - 1.0 / 8.0 - 1.0 / d;
deSettings.RelativePrecision = (settings.RelativePrecision < 0.0) ? Math.Pow(10.0, -(2.0 + 4.0 / d)) : settings.RelativePrecision;
deSettings.AbsolutePrecision = (settings.AbsolutePrecision < 0.0) ? Math.Pow(10.0, -(4.0 + 8.0 / d)) : settings.AbsolutePrecision;
deSettings.EvaluationBudget = (settings.EvaluationBudget < 0) ? 128 * d * d * d * d : settings.EvaluationBudget;
deSettings.Listener = settings.Listener;
return(deSettings);
}
private static DifferentialEvolutionSettings GetDefaultSettings(EvaluationSettings settings, int d)
{
DifferentialEvolutionSettings deSettings = new DifferentialEvolutionSettings();
deSettings.Population = 8 * d + 4;
deSettings.CrossoverProbability = 1.0 - 1.0 / 8.0 - 1.0 / d;
if (settings == null)
{
deSettings.RelativePrecision = Math.Pow(10.0, -(2.0 + 4.0 / d));
deSettings.AbsolutePrecision = MoreMath.Sqr(deSettings.RelativePrecision);
deSettings.EvaluationBudget = 128 * d * d * d * d;
}
else
{
deSettings.RelativePrecision = settings.RelativePrecision;
deSettings.AbsolutePrecision = settings.AbsolutePrecision;
deSettings.EvaluationBudget = settings.EvaluationBudget;
}
return(deSettings);
}
// Differential evolution is a global optimization algorithm over continuous inputs that is adapted from genetic algorithms for finite inputs.
// The idea is to maintain a population of input vectors ("agents") and to vary that population over cycles ("generations") according to rules that incorporate
// random mutation but on average tend to bring them closer to optima ("fitter").
private static MultiExtremum FindGlobalExtremum(MultiFunctor f, IReadOnlyList <Interval> volume, DifferentialEvolutionSettings settings)
{
int d = volume.Count;
// Choose a number of agents that increases with dimension and required precision.
int m = settings.Population;
Debug.WriteLine("d={0} m={1}", d, m);
Random rng = new Random(3);
// Start with random points in the allowed region.
double[][] points = new double[m][];
double[] values = new double[m];
for (int i = 0; i < m; i++)
{
points[i] = new double[d];
for (int j = 0; j < d; j++)
{
points[i][j] = volume[j].LeftEndpoint + rng.NextDouble() * volume[j].Width;
}
values[i] = f.Evaluate(points[i]);
}
while (f.EvaluationCount < settings.EvaluationBudget)
{
double[][] newPoints = new double[m][];
double[] newValues = new double[m];
for (int i = 0; i < m; i++)
{
// Mutation
// construct donor vector
int a = i; while (a == i)
{
a = rng.Next(m);
}
int b = i; while ((b == i) || (b == a))
{
b = rng.Next(m);
}
int c = i; while ((c == i) || (c == b) || (c == a))
{
c = rng.Next(m);
}
double[] donor = new double[d];
for (int j = 0; j < d; j++)
{
donor[j] = points[a][j] + mutationFactor * (points[b][j] - points[c][j]);
if (donor[j] < volume[j].LeftEndpoint)
{
donor[j] = volume[j].LeftEndpoint;
}
if (donor[j] > volume[j].RightEndpoint)
{
donor[j] = volume[j].RightEndpoint;
}
}
// Recombination
double[] trial = new double[d];
int k = rng.Next(d);
for (int j = 0; j < d; j++)
{
if ((j == k) || (rng.NextDouble() < settings.CrossoverProbability))
{
trial[j] = donor[j];
}
else
{
trial[j] = points[i][j];
}
}
// Selection
double value = f.Evaluate(trial);
if (value <= values[i])
{
newPoints[i] = trial;
newValues[i] = value;
}
else
{
newPoints[i] = points[i];
newValues[i] = values[i];
}
}
points = newPoints;
values = newValues;
// Check termination criteria
int minIndex = -1;
double minValue = Double.MaxValue;
double maxValue = Double.MinValue;
for (int i = 0; i < m; i++)
{
if (values[i] < minValue)
{
minValue = values[i];
minIndex = i;
}
if (values[i] > maxValue)
{
maxValue = values[i];
}
}
double range = maxValue - minValue;
double tol = settings.ComputePrecision(minValue);
if (range <= tol)
{
MultiExtremum result = new MultiExtremum(f.EvaluationCount, settings, points[minIndex], f.IsNegated ? -values[minIndex] : values[minIndex], Math.Max(range, 0.75 * tol), null);
return(result);
}
else if (settings.Listener != null)
{
MultiExtremum report = new MultiExtremum(f.EvaluationCount, settings, points[minIndex], f.IsNegated ? -values[minIndex] : values[minIndex], Math.Max(range, 0.75 * tol), null);
settings.Listener(report);
}
}
throw new NonconvergenceException();
}
// Differential evoluation is a global optimization algorithm over continuous inputs that is adapted from genetic algorithms for finite inputs.
// The idea is maintain a population of input vectors ("agents") and to vary that population over cycles ("generations") according to rules that incorporate
// random mutation but on average tend to bring them closer to optima ("fitter").
private static MultiExtremum FindGlobalExtremum(MultiFunctor f, IList<Interval> volume, DifferentialEvolutionSettings settings)
{
int d = volume.Count;
// Choose a number of agents that increases with dimension and required precision.
int m = settings.Population;
Debug.WriteLine("d={0} m={1}", d, m);
Random rng = new Random(3);
//Random rng = new Random(1001110000);
// Start with random points in the allowed region.
double[][] points = new double[m][];
double[] values = new double[m];
for (int i = 0; i < m; i++) {
points[i] = new double[d];
for (int j = 0; j < d; j++) {
points[i][j] = volume[j].LeftEndpoint + rng.NextDouble() * volume[j].Width;
}
values[i] = f.Evaluate(points[i]);
}
while (f.EvaluationCount < settings.EvaluationBudget) {
//double mutationFactor = 0.5 + 0.5 * rng.NextDouble();
double[][] newPoints = new double[m][];
double[] newValues = new double[m];
for (int i = 0; i < m; i++) {
// Mutation
// construct donor vector
int a = i; while (a == i) a = rng.Next(m);
int b = i; while ((b == i) || (b == a)) b = rng.Next(m);
int c = i; while ((c == i) || (c == b) || (c == a)) c = rng.Next(m);
double[] donor = new double[d];
for (int j = 0; j < d; j++) {
donor[j] = points[a][j] + mutationFactor * (points[b][j] - points[c][j]);
if (donor[j] < volume[j].LeftEndpoint) donor[j] = volume[j].LeftEndpoint;
if (donor[j] > volume[j].RightEndpoint) donor[j] = volume[j].RightEndpoint;
}
// Recombination
double[] trial = new double[d];
int k = rng.Next(d);
for (int j = 0; j < d; j++) {
if ((j == k) || (rng.NextDouble() < settings.CrossoverProbability)) {
trial[j] = donor[j];
} else {
trial[j] = points[i][j];
}
}
// Selection
double value = f.Evaluate(trial);
if (value <= values[i]) {
newPoints[i] = trial;
newValues[i] = value;
} else {
newPoints[i] = points[i];
newValues[i] = values[i];
}
}
points = newPoints;
values = newValues;
// Check termination criteria
int minIndex = -1;
double minValue = Double.MaxValue;
double maxValue = Double.MinValue;
for (int i = 0; i < m; i++) {
if (values[i] < minValue) {
minValue = values[i];
minIndex = i;
}
if (values[i] > maxValue) maxValue = values[i];
}
double range = maxValue - minValue;
double tol = settings.ComputePrecision(minValue);
if (range <= tol) {
MultiExtremum result = new MultiExtremum(f.EvaluationCount, settings, points[minIndex], f.IsNegated ? -values[minIndex] : values[minIndex], Math.Max(range, 0.75 * tol), null);
return (result);
}
//settings.OnUpdate(new MultiExtremum(points[minIndex], values[minIndex], null, f.EvaluationCount));
}
throw new NonconvergenceException();
}
private static DifferentialEvolutionSettings GetDefaultSettings(EvaluationSettings settings, int d)
{
DifferentialEvolutionSettings deSettings = new DifferentialEvolutionSettings();
deSettings.Population = 8 * d + 4;
deSettings.CrossoverProbability = 1.0 - 1.0 / 8.0 - 1.0 / d;
if (settings == null) {
deSettings.RelativePrecision = Math.Pow(10.0, -(2.0 + 4.0 / d));
deSettings.AbsolutePrecision = MoreMath.Sqr(deSettings.RelativePrecision);
deSettings.EvaluationBudget = 128 * d * d * d * d;
} else {
deSettings.RelativePrecision = settings.RelativePrecision;
deSettings.AbsolutePrecision = settings.AbsolutePrecision;
deSettings.EvaluationBudget = settings.EvaluationBudget;
}
return (deSettings);
}