MATLAB Implementation of PSO (Particle Swarm Optimization) Algorithm

PSO (Particle Swarm Optimization) is a population-based intelligent optimization algorithm that simulates the collective behavior of biological groups such as bird flocks or fish schools to find optimal solutions. This algorithm searches for optimal solutions in the solution space through cooperation and information sharing among particles, characterized by simple implementation and fast convergence speed.

Implementing the PSO algorithm in MATLAB typically involves the following key steps:

Particle Swarm Initialization First, determine parameters such as particle count, dimensionality, and maximum iteration number, then randomly initialize each particle's position and velocity. Typically, particles' initial positions and velocities are randomly distributed within predefined bounds to ensure search diversity. In MATLAB code, this can be implemented using rand() or randn() functions with scaling factors to define search boundaries.

Fitness Value Calculation Each particle's position corresponds to a fitness value (i.e., objective function value) that measures solution quality. For function optimization, the fitness can be the function's value at the current particle position. The MATLAB implementation requires defining a fitness function handle that accepts particle positions as input and returns scalar fitness values.

Update Personal Best and Global Best Each particle records its historical best position (personal best), while the entire swarm tracks the global best position. During each iteration, if a particle finds a better position than its historical record, it updates its personal best; if the global best position is surpassed, the global best is updated. This is typically implemented using comparison operations and value reassignment in MATLAB.

Velocity and Position Update According to PSO's core formulas, particles adjust their velocities and positions based on personal best and global best positions. The velocity update formula typically incorporates inertia weight, cognitive learning factor, and social learning factor to balance exploration of new areas and convergence to optimal solutions. The MATLAB code implementation involves vectorized operations for efficient computation of velocity and position updates across all particles.

Termination Condition Check The algorithm terminates when reaching the maximum iteration count or when fitness values meet specified precision requirements. The final global best position represents the solution to the optimization problem. This can be implemented using while or for loops with break conditions in MATLAB.

This MATLAB program implements PSO algorithm optimization for a simple function, making it suitable for beginners to understand PSO's fundamental workflow. To optimize other functions, users need only modify the fitness function section. PSO's flexibility enables wide applications in engineering optimization, machine learning parameter tuning, and other domains. The code structure includes clear function segmentation with commented sections for easy modification and extension.