Multi-Objective Evolutionary Algorithms implemented in .NET
Install-Package cs-moea -Version 1.0.2The following MOEAs are supported:
- MOEAD
- NSGA-II
- GDE-3
- HAP-MOEA
- Hybrid-Game
The library supports both multi-objective and multi-constraints optimization problem in which the solutions are continuous vectors.
Please refer to the sample codes in the cs-moea-samples project for how to use the library to solve various optimization problems.
The cs-moea-samples-gui-winforms project shows the demo of the multi-objective optimization using these algorithm with a GUI that shows the pareto front of the MOEA results. A number of benchmarks are included for comparing various MOEA implementations:
- NDND
- NGPD
- TNK
- OKA2
- SYMPART
The details these implementations can be found in MOEA.Benchmarks namespace of the cs-moea project.
The section below provides some details on how to do this using various MOEAs.
The following sample codes show how to use NSGA-II to solve the NDND multi-objective optimization problem:
NSGAII<ContinuousVector> algorithm = new NSGAII<ContinuousVector>(new NDNDProblem());
algorithm.PopulationSize = 100;
algorithm.Initialize();
while (!algorithm.IsTerminated)
{
algorithm.Evolve();
Console.WriteLine("Current Generation: {0}", algorithm.CurrentGeneration);
Console.WriteLine("Size of Archive: {0}", algorithm.NondominatedArchiveSize);
}
ContinuousVector finalSolution = algorithm.GlobalBestSolution;
NondominatedPopulation<ContinuousVector> paretoFront = algorithm.NondominatedArchive;Where the NDNDProblem class is defined as below:
public class NDNDProblem: IMOOProblem
{
public int GetObjectiveCount()
{
return 2;
}
public int GetDimensionCount()
{
return 2;
}
public bool IsFeasible(MOOSolution s)
{
return true;
}
public bool IsMaximizing()
{
return false;
}
public double CalcObjective(MOOSolution s, int objective_index)
{
ContinuousVector x = (ContinuousVector)s;
double f1 = 1 - System.Math.Exp((-4) * x[0]) * System.Math.Pow(System.Math.Sin(5 * System.Math.PI * x[0]), 4);
if (objective_index == 0)
{
return f1;
}
else
{
double f2, g, h;
if (x[1] > 0 && x[1] < 0.4)
g = 4 - 3 * System.Math.Exp(-2500 * (x[1] - 0.2) * (x[1] - 0.2));
else
g = 4 - 3 * System.Math.Exp(-25 * (x[1] - 0.7) * (x[1] - 0.7));
double a = 4;
if (f1 < g)
h = 1 - System.Math.Pow(f1 / g, a);
else
h = 0;
f2 = g * h;
return f2;
}
}
public double GetUpperBound(int dimension_index)
{
return 1;
}
public double GetLowerBound(int dimension_index)
{
return 0;
}
}The following sample codes show how to use GDE-3 to solve the NDND multi-objective optimization problem:
GDE3<ContinuousVector> algorithm = new GDE3<ContinuousVector>(new TNKProblem());
algorithm.PopulationSize = 100;
algorithm.Initialize();
while (!algorithm.IsTerminated)
{
algorithm.Evolve();
Console.WriteLine("Current Generation: {0}", algorithm.CurrentGeneration);
Console.WriteLine("Size of Archive: {0}", algorithm.NondominatedArchiveSize);
}
ContinuousVector finalSolution = algorithm.GlobalBestSolution;
NondominatedPopulation<ContinuousVector> paretoFront = algorithm.NondominatedArchive;The following sample codes show how to use HAP-MOEA to solve the NDND multi-objective optimization problem:
HAPMOEA<ContinuousVector> algorithm = new HAPMOEA<ContinuousVector>(new NDNDProblem());
algorithm.Config.PopulationSize = 100;
algorithm.Initialize();
while (!algorithm.IsTerminated)
{
algorithm.Evolve();
Console.WriteLine("Current Generation: {0}", algorithm.CurrentGeneration);
Console.WriteLine("Size of Archive: {0}", algorithm.NondominatedArchiveSize);
}
NondominatedPopulation<ContinuousVector> paretoFront = algorithm.NondominatedArchive;The following sample codes show how to use Hybrid-Game to solve the NDND multi-objective optimization problem:
HybridGame<ContinuousVector> algorithm = new HybridGame<ContinuousVector>(new NDNDProblem());
algorithm.Config.PopulationSize = 100;
algorithm.Initialize();
while (!algorithm.IsTerminated)
{
algorithm.Evolve();
Console.WriteLine("Current Generation: {0}", algorithm.CurrentGeneration);
Console.WriteLine("Size of Archive: {0}", algorithm.NondominatedArchiveSize);
}
NondominatedPopulation<ContinuousVector> paretoFront = algorithm.NondominatedArchive;