Particle Swarm Optimization (PSO) Algorithm Source Code with Implementation Details

Particle Swarm Optimization (PSO) is a population-based intelligent optimization algorithm that simulates the social behavior of bird flocks or fish schools. It efficiently searches for optimal solutions in the solution space through information sharing and collaboration among individuals (particles).

Core Algorithm Concept Each particle represents a potential solution with position and velocity attributes. During iterations, particles update their states based on two critical factors: Personal Best (pBest): The best position experienced by the particle itself Global Best (gBest): The best position found by the entire population

Particles adjust their velocity vectors (inertia component + cognitive component + social component) to move toward these reference points, eventually converging near the global optimum.

Typical Implementation Workflow Initialize particle swarm with random positions and velocities Calculate fitness values for each particle (i.e., objective function values) Update personal best and global best records Adjust particle movement direction using velocity update formula Repeat iterations until termination conditions are met

Function Optimization Applications In test function optimization (such as Rastrigin, Rosenbrock, etc.), PSO enhances performance through these strategies: Introducing inertia weight to balance global exploration and local exploitation Using constriction factor to control convergence speed Combining neighborhood topology (global version/local version) to prevent premature convergence

Parameter Selection Recommendations Population size typically ranges from 20-50 particles Inertia weight decreases linearly (e.g., from 0.9 to 0.4) Learning factors c1/c2 are usually set around 2.0

The algorithm is widely applied in neural network training, engineering design optimization, and other scenarios requiring global search capabilities. Its advantages include simple implementation, fast convergence speed, and no requirement for gradient information.

Code Implementation Highlights: - Velocity update: v = w*v + c1*rand()*(pBest-x) + c2*rand()*(gBest-x) - Position update: x = x + v - Boundary handling mechanisms for constrained optimization - Fitness evaluation function customization for different problems