ParticleSwarmOptimizer Class

public class ParticleSwarmOptimizer : PopulationBasedOptimizer<ParticleSwarmOptimizer.ParticleSwarm, ParticleSwarmOptimizer.Particle>

Public Class ParticleSwarmOptimizer
	Inherits PopulationBasedOptimizer(Of ParticleSwarmOptimizer.ParticleSwarm, ParticleSwarmOptimizer.Particle)

public ref class ParticleSwarmOptimizer : public PopulationBasedOptimizer<ParticleSwarmOptimizer.ParticleSwarm^, ParticleSwarmOptimizer.Particle>

type ParticleSwarmOptimizer = 
    class
        inherit PopulationBasedOptimizer<ParticleSwarmOptimizer.ParticleSwarm, ParticleSwarmOptimizer.Particle>
    end

Inheritance

Object  →  ManagedIterativeAlgorithm<Vector<Double>, Double, OptimizationSolutionReport<Vector<Double>>>  →  MultidimensionalOptimizer<Vector<Double>, OptimizationSolutionReport<Vector<Double>>>  →  PopulationBasedOptimizer<Vector<Double>, ParticleSwarmOptimizer.ParticleSwarm, ParticleSwarmOptimizer.Particle>  →  PopulationBasedOptimizer<ParticleSwarmOptimizer.ParticleSwarm, ParticleSwarmOptimizer.Particle>  →  ParticleSwarmOptimizer

Particle Swarm Optimization (PSO) is a population-based stochastic optimization technique inspired by the social behavior of bird flocking or fish schooling. Each particle in the swarm represents a candidate solution and moves through the search space according to its own experience and the experience of neighboring particles.

Before running the algorithm, you must set the LowerBounds and UpperBounds properties to specify the search space constraints. The ExtremumType property specifies whether a minimum or a maximum of the objective function is desired.

The PSO algorithm maintains a population of particles, each representing a potential solution. Particles adjust their positions based on their own best-known positions and the best-known positions of their neighbors, guided by cognitive and social coefficients.

The optimizer supports various topologies, such as global, ring, random, and Von Neumann, which define the neighborhood relationships between particles. Different topologies can significantly affect the performance of the optimization process.

Key parameters include the constriction factor, cognitive coefficient, social coefficient, and maximum velocity, which control the dynamics of particle movement. The population size is determined by the number of dimensions and a population multiplier.

The optimizer also includes mechanisms to handle stagnation and population diversity, ensuring robust convergence to optimal solutions.

The following example demonstrates how to use the ParticleSwarmOptimizer to find a minimum of the Rastrigin function.

// Define the Rastrigin function
Func<Vector<double>, double> rastrigin = (x) =>
{
    int n = x.Length;
    double A = 10;
    double sum = A * n;
    for (int i = 0; i < n; i++)
    {
        sum += x[i] * x[i] - A * Math.Cos(2 * Math.PI * x[i]);
    }
    return sum;
};

// Define the lower and upper bounds
Vector<double> lowerBounds = Vector.Create<double>(2, -5.12);
Vector<double> upperBounds = Vector.Create<double>(2, 5.12);

// Create the optimizer
var optimizer = new ParticleSwarmOptimizer(
    objectiveFunction: rastrigin,
    lowerBounds: lowerBounds,
    upperBounds: upperBounds
);

// Run the optimization
optimizer.FindMinimum();

// Get the result
Vector<double> solution = optimizer.Extremum;
double value = optimizer.ValueAtExtremum;

Reference