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/// SwarmOps - Numeric and heuristic optimization for C#
/// Copyright (C) 2003-2011 Magnus Erik Hvass Pedersen.
/// Please see the file license.txt for license details.
/// SwarmOps on the internet: http://www.Hvass-Labs.org/
/// ------------------------------------------------------
using System.Diagnostics;
namespace SwarmOps.Problems
{
/// <summary>
/// Ackley benchmark problem.
/// </summary>
public class Ackley : Benchmark
{
#region Constructors.
/// <summary>
/// Construct the object.
/// </summary>
/// <param name="dimensionality">Dimensionality of the problem (e.g. 20)</param>
/// <param name="maxIterations">Max optimization iterations to perform.</param>
public Ackley(int dimensionality, int maxIterations)
: base(dimensionality, -30, 30, 15, 30, maxIterations)
{
}
#endregion
#region Base-class overrides.
/// <summary>
/// Name of the optimization problem.
/// </summary>
public override string Name
{
get { return "Ackley"; }
}
/// <summary>
/// Minimum possible fitness.
/// </summary>
public override double MinFitness
{
get { return 0; }
}
/// <summary>
/// Compute and return fitness for the given parameters.
/// </summary>
/// <param name="x">Candidate solution.</param>
public override double Fitness(double[] x)
{
Debug.Assert(x != null && x.Length == Dimensionality);
double fitness
= System.Math.E
+ 20
- 20 * System.Math.Exp(-0.2 * SqrtSum(x))
- CosSum(x);
// Rounding errors may cause negative fitnesses to occur even
// though the mathematical global minimum has fitness zero.
// Ensure this still works with meta-optimization which
// requires non-negative fitnesses.
if (fitness < 0)
{
fitness = 0;
}
return fitness;
}
/// <summary>
/// Return whether the gradient has been implemented.
/// </summary>
public override bool HasGradient
{
get { return true; }
}
/// <summary>
/// Compute the gradient of the fitness-function.
/// </summary>
/// <param name="x">Candidate solution.</param>
/// <param name="v">Array for holding the gradient.</param>
public override int Gradient(double[] x, ref double[] v)
{
Debug.Assert(x != null && x.Length == Dimensionality);
Debug.Assert(v != null && v.Length == Dimensionality);
double sqrtSum = SqrtSum(x);
double cosSum = CosSum(x);
double DimRec = 1.0 / Dimensionality;
for (int i = 0; i < Dimensionality; i++)
{
double elm = x[i];
v[i] = 4 * DimRec * System.Math.Exp(-0.2 * sqrtSum) * elm / sqrtSum
+ cosSum * System.Math.Sin(System.Math.PI * 2 * elm) * System.Math.PI * 2 * DimRec;
}
return 0;
}
#endregion
#region Protected methods.
/// <summary>
/// Helper-method used in both the Fitness- and Gradient-methods.
/// </summary>
protected double SqrtSum(double[] x)
{
double sum = 0;
int n = x.Length;
for (int i = 0; i < n; i++)
{
double elm = x[i];
sum += elm * elm;
}
return System.Math.Sqrt(sum / n);
}
/// <summary>
/// Helper-method used in both the Fitness- and Gradient-methods.
/// </summary>
protected double CosSum(double[] x)
{
double sum = 0;
int n = x.Length;
for (int i = 0; i < n; i++)
{
double elm = x[i];
sum += System.Math.Cos(System.Math.PI * 2 * elm);
}
return System.Math.Exp(sum / n);
}
#endregion
}
}
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