public void FindMinimumGoldsteinPriceFunction_AnalyticResult(MultiDimOptimizerConstraintProvider constraintTransformation)
{
var randomNumberStream = CreateStubRandomNumberStream();
var optimizer = new PraxisOptimizer(randomNumberStream, PraxisOptimizer.StandardAbortCondition, constraintTransformation);
var constraint = optimizer.Constraint.Create(MultiDimRegion.Interval.Create(2, new[] { -2.0, -2.0 }, new[] { 2.0, 2.0 }));
var optimizerAlgorithm = optimizer.Create(constraint);
optimizerAlgorithm.Function = optimizer.Function.Create(2, z =>
{
var x = z[0];
var y = z[1];
return((1.0 + Math.Pow(x + y + 1.0, 2) * (19.0 - 14.0 * x + 3 * x * x - 14.0 * y + 6.0 * x * y + 3.0 * y * y)) * (30.0 + Math.Pow(2.0 * x - 3.0 * y, 2) * (18.0 - 32.0 * x + 12.0 * x * x + 48.0 * y - 36 * x * y + 27 * y * y)));
});
/* take an initial guess which is not extremly fare away from the argMin: */
var actualArgMin = new double[2];
actualArgMin[0] = 0.35;
actualArgMin[1] = -0.45; // Box-Constraint Transformation: sometimes one gets quite high arguments -/+ 3.13E19 arguments which yields to f(x) =\infinity and the algorithm fails
double actualMinimum;
var state = optimizerAlgorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedMinimum = 3.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-2), "Minimum");
var expectedArgMin = new[] { 0.0, -1.0 };
Assert.That(actualArgMin, Is.EqualTo(expectedArgMin).AsCollection.Within(1E-1));
}
public void FindMinimumGoldsteinPriceFunction_AnalyticResult(MultiDimOptimizerConstraintProvider constraintTransformation)
{
var optimizer = new PowellOptimizer(PowellOptimizer.StandardAbortCondition, PowellOptimizer.StandardLineSearchOptimizer, constraintTransformation);
var constraint = optimizer.Constraint.Create(MultiDimRegion.Interval.Create(2, new[] { -2.0, -2.0 }, new[] { 2.0, 2.0 }));
var optimizerAlgorithm = optimizer.Create(constraint);
optimizerAlgorithm.Function = optimizer.Function.Create(2, z =>
{
var x = z[0];
var y = z[1];
return((1.0 + Math.Pow(x + y + 1.0, 2) * (19.0 - 14.0 * x + 3 * x * x - 14.0 * y + 6.0 * x * y + 3.0 * y * y)) * (30.0 + Math.Pow(2.0 * x - 3.0 * y, 2) * (18.0 - 32.0 * x + 12.0 * x * x + 48.0 * y - 36 * x * y + 27 * y * y)));
});
/* take an initial guess which is not extremly fare away from the expected argMin: */
var actualArgMin = new double[2];
actualArgMin[0] = -0.1;
actualArgMin[1] = -0.75;
double actualMinimum;
var state = optimizerAlgorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedMinimum = 3.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-2), "Minimum");
var expectedArgMin = new[] { 0.0, -1.0 };
Assert.That(actualArgMin, Is.EqualTo(expectedArgMin).AsCollection.Within(1E-1));
}
/// <summary>Initializes a new instance of the <see cref="PowellOptimizer"/> class.
/// </summary>
/// <param name="abortCondition">The abort (stopping) condition for the Simulated Annealing optimizer.</param>
/// <param name="lineSearchOptimizer">The line search optimizer to take into account.</param>
/// <param name="constraintProvider">The constraint provider, i.e. transformation etc. for the support of specific constraints (the original algorithm does not support any constraints).</param>
public PowellOptimizer(PowellOptimizerAbortCondition abortCondition, OneDimOptimizer lineSearchOptimizer, MultiDimOptimizerConstraintProvider constraintProvider)
{
AbortCondition = abortCondition ?? throw new ArgumentNullException(nameof(abortCondition));
LineSearchOptimizer = lineSearchOptimizer ?? throw new ArgumentNullException(nameof(lineSearchOptimizer));
m_ConstraintProvider = constraintProvider ?? throw new ArgumentNullException(nameof(constraintProvider));
m_Name = new IdentifierString("Powell optimizer");
m_FunctionDescriptor = new OrdinaryMultiDimOptimizerFunctionFactory();
m_ConstraintDescriptor = new MultiDimOptimizerConstraintFactory(constraintProvider.SupportedConstraints);
}
/// <summary>Initializes a new instance of the <see cref="NelderMeadOptimizer"/> class.
/// </summary>
/// <param name="abortCondition">The abort (stopping) condition for the Nelder-Mead optimizer.</param>
/// <param name="constraintProvider">The constraint provider, i.e. transformation etc. for the support of specific constraints (the original algorithm does not support any constraints).</param>
/// <param name="initialScaleFactor">A scaling factor which is used to create from a specific initial guess the N + 1 points (in \R^N) of the start simplex.</param>
public NelderMeadOptimizer(NelderMeadOptimizerAbortCondition abortCondition, MultiDimOptimizerConstraintProvider constraintProvider, double initialScaleFactor = 1.0)
{
AbortCondition = abortCondition ?? throw new ArgumentNullException(nameof(abortCondition));
m_ConstraintProvider = constraintProvider ?? throw new ArgumentNullException(nameof(constraintProvider));
m_Name = new IdentifierString("Nelder-Mead-Simplex search optimizer");
m_FunctionDescriptor = new OrdinaryMultiDimOptimizerFunctionFactory();
m_ConstraintDescriptor = new MultiDimOptimizerConstraintFactory(constraintProvider.SupportedConstraints);
InitialScaleFactor = initialScaleFactor;
}
/// <summary>Initializes a new instance of the <see cref="PraxisOptimizer"/> class.
/// </summary>
/// <param name="randomNumberStream">The random number stream.</param>
/// <param name="abortCondition">The abort (stopping) condition for the Simulated Annealing optimizer.</param>
/// <param name="constraintProvider">The constraint provider, i.e. transformation etc. for the support of specific constraints (the original algorithm does not support any constraints).</param>
/// <param name="scalingFactor">A scaling parameter. If the scales for the different parameters are very different this value should be/ set to a value of about 10.0.</param>
/// <param name="expectedDistanceToSolution">A step length parameter which should be set equal to the expected distance from the solution.</param>
public PraxisOptimizer(IRandomNumberStream randomNumberStream, PraxisOptimizerAbortCondition abortCondition, MultiDimOptimizerConstraintProvider constraintProvider, double scalingFactor = 1.0, double expectedDistanceToSolution = 1.0)
{
if (randomNumberStream == null)
{
throw new ArgumentNullException(nameof(randomNumberStream));
}
m_SingleRandomNumberStream = new SingleRandomNumberStream(randomNumberStream, 250);
AbortCondition = abortCondition ?? throw new ArgumentNullException(nameof(abortCondition));
m_ConstraintProvider = constraintProvider ?? throw new ArgumentNullException(nameof(constraintProvider));
ScalingFactor = scalingFactor;
ExpectedDistanceToSolution = expectedDistanceToSolution;
m_Name = new IdentifierString("PRAXIS optimizer");
m_FunctionDescriptor = new OrdinaryMultiDimOptimizerFunctionFactory();
m_ConstraintDescriptor = new MultiDimOptimizerConstraintFactory(constraintProvider.SupportedConstraints);
}
/// <summary>Initializes the <see cref="PowellOptimizer" /> class.
/// </summary>
static PowellOptimizer()
{
StandardAbortCondition = PowellOptimizerAbortCondition.Create();
StandardLineSearchOptimizer = new BrentOptimizer();
StandardConstraintProvider = MultiDimOptimizerConstraintProvider.BoxTransformation;
}
/// <summary>Initializes the <see cref="PraxisOptimizer" /> class.
/// </summary>
static PraxisOptimizer()
{
StandardAbortCondition = PraxisOptimizerAbortCondition.Create();
StandardConstraintProvider = MultiDimOptimizerConstraintProvider.BoxTransformation;
}
/// <summary>Initializes the <see cref="MultiDimOptimizerConstraintProvider" /> class.
/// </summary>
static MultiDimOptimizerConstraintProvider()
{
BoxTransformation = new BoxTransformationFactory();
QuadraticPenalty = new QuadraticPenaltyConstraintProvider();
}