/// <summary>
/// Calculates the objective based on Ackley's function.
/// </summary>
/// <param name="c"></param>
/// <returns></returns>
/// <remarks>
/// Ackley's function is given by:
///
/// F(x) = 20 + e
/// - 20*exp(-0.2*sqrt((1/n)*Sum(i=1,n) {x_i^2}))
/// - exp((1/n)*Sum(i=1,n){cos(2*pi*x_i)})
/// </remarks>
public static double AckleyMinimizationObjective(Chromosome c)
{
int n = c.Genes.Length;
DoubleGene[] x = new DoubleGene[c.Genes.Length];
Array.Copy(c.Genes, x,c.Genes.Length); // performs type casting for each element
double f;
double objective;
// Split the equation into three parts:
// F(x) =
// (a) 20 + e
// (b) - 20*exp(-0.2*sqrt((1/n)*Sum(i=1,n) {x_i^2}))
// (c) - exp((1/n)*Sum(i=1,n){cos(2*pi*x_i)})
//
// Calculate the (c) part.
//
double f_c = 0;
for(int i=0;i<n;i++)
{
f_c += Math.Cos(2*Math.PI*x[i].Value);
}
f_c *= ( 1.0/n );
f_c = -Math.Exp( f_c );
//
// Calculate the (b) part
//
double f_b = 0;
for(int i=0;i<n;i++)
{
double sum;
sum = (x[i].Value * x[i].Value)/n;
f_b += sum;
}
f_b = Math.Sqrt( f_b );
f_b *= -0.2;
f_b = Math.Exp( f_b );
f_b *= -20.0;
//
// Calculate the (a) part
//
double f_a = 0;
f_a = 20.0 + Math.E;
//
// Calculate the total as (a) + (b) + (c)
//
f = f_a + f_b + f_c;
objective = Math.Abs(f);
return objective;
}
/// <summary>
/// Returns a random allele based on the constraints.
/// </summary>
override public Gene GetRandomAllele()
{
DoubleGene gene = new DoubleGene(this);
double newDouble;
newDouble = genX.Utils.Rand.NextDouble();
newDouble *= (MaxValue - MinValue);
newDouble += MinValue;
gene.Value = newDouble;
return gene;
}
/// <summary>
/// Returns a random allele based on the constraints.
/// </summary>
override public Gene GetRandomAllele()
{
DoubleGene gene = new DoubleGene(this);
double newDouble;
newDouble = genX.Utils.Rand.NextDouble();
newDouble *= (MaxValue - MinValue);
newDouble += MinValue;
gene.Value = newDouble;
return(gene);
}