Particle Swarm Optimization (PSO) Standard Algorithm

The Particle Swarm Optimization (PSO) standard algorithm is a population-based optimization technique inspired by the social behavior of bird flocks or fish schools. It efficiently solves optimization problems in continuous search spaces by simulating cooperation and information sharing among individuals.

Core Algorithm Framework Particle Representation: Each particle represents a candidate solution with two key attributes - position (solution coordinates) and velocity (search direction/magnitude). Implementation typically uses arrays or matrices to store particle states. Fitness Evaluation: The objective function calculates fitness values to quantify solution quality, implemented through function handles or custom evaluation modules. Individual and Collective Experience: Particles track personal best (pBest) and global best (gBest) solutions, requiring comparison operations and global communication mechanisms. State Update: Particles iteratively update velocities and positions using mathematical formulas: Velocity Update: Combines current velocity, cognitive component (pBest influence), and social component (gBest influence) with inertia weight balancing exploration and exploitation. Position Update: Adjusts particle coordinates based on updated velocities using elementary vector addition.

Key Parameters Inertial Weight: Controls momentum preservation, typically implemented with linear/nonlinear decay schedules (e.g., from 0.9 to 0.4). Learning Factors: Cognitive (c1) and social (c2) coefficients determining individual/group influence, usually set between 1.5-2.0 via parameter tuning. Population Size: Swarm size affects computational efficiency, commonly set to 20-50 particles based on problem dimensionality.

Characteristics and Applications PSO features simple implementation (requiring only ~10-20 lines of core code), fast convergence, and suitability for continuous optimization (function optimization, neural network training). However, parameter sensitivity requires careful tuning to prevent premature convergence or local optima trapping.

Algorithm Extensions Topology Improvements: Local-best PSO using ring/k-neighbor topologies for better diversity. Adaptive Parameters: Dynamic adjustment of inertia weight or learning factors during optimization. Hybrid Approaches: Integration with genetic algorithms or other metaheuristics for enhanced global search capabilities.

Mastering standard PSO provides foundation for advanced variants including discrete PSO, multi-objective PSO, and constrained optimization adaptations.