MATLAB Source Code for Standard Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) is a population-based intelligent optimization algorithm primarily used for solving continuous optimization problems. This algorithm simulates the social behavior of bird flocks or fish schools, where individuals collaborate and share information to find optimal solutions through collective intelligence.

The core concepts of the standard PSO algorithm include the following components:

Particle Swarm Initialization: Randomly generate a population of particles, where each particle represents a potential solution in the search space with assigned initial velocity and position. In MATLAB implementation, this typically involves using rand() or randn() functions to create position and velocity matrices. Fitness Evaluation: Calculate the fitness value for each particle based on the objective function to measure solution quality. This requires defining a fitness function that can be vectorized for efficient computation across all particles. Personal and Global Best Update: Each particle maintains its historical best solution (personal best), while the entire swarm tracks the global best solution. This is implemented through comparison operations and matrix updates in MATLAB. Velocity and Position Update: Particles dynamically adjust their velocity and position based on their personal best and the global best, continuously moving toward better solutions. The update equations involve inertia weight, acceleration coefficients, and random factors. Convergence Criteria: The algorithm terminates when reaching maximum iterations or meeting convergence conditions; otherwise, it continues iterative optimization. Common implementations use while or for loops with break conditions.

When implementing the standard PSO algorithm in MATLAB, key parameters typically require configuration: Swarm Size: Affects search scope and convergence speed, generally recommended between 20-50 particles. Larger populations provide better exploration but increase computational cost. Inertia Weight: Balances global exploration and local exploitation capabilities. Higher weights favor global search, while lower weights emphasize local refinement. Common implementations use linear decreasing inertia weights. Acceleration Coefficients (Cognitive and Social Factors): Typically set around 2, controlling how particles move toward personal best and global best positions. These parameters influence the algorithm's exploration-exploitation balance. Maximum Iterations: Determines algorithm runtime, should be set appropriately based on problem complexity. Can be implemented using iteration counters and termination conditions.

The standard PSO algorithm is easy to implement with high computational efficiency, suitable for various continuous optimization problems such as function optimization and neural network training. However, when dealing with complex multimodal optimization problems, improved strategies (such as adaptive weights, hybrid algorithms) may be necessary to enhance performance. MATLAB implementations benefit from vectorized operations for efficient swarm management and fitness evaluation.