Particle Swarm Optimization Algorithm for Finding Shortest Paths in Obstacle-Embedded Path Graphs

This MATLAB program implements Particle Swarm Optimization (PSO) to find shortest paths in path graphs containing obstacles. PSO is a computational optimization method that mimics collective behaviors observed in bird flocking to discover optimal solutions. The algorithm initializes multiple candidate paths (particles) that navigate through the graph while adapting their trajectories based on both individual best positions and swarm-best solutions. Key implementation components include obstacle collision detection mechanisms and fitness functions that penalize infeasible paths crossing restricted areas. The program employs velocity update equations incorporating inertia weights and acceleration coefficients to balance exploration and exploitation phases. Each particle's position represents a potential path solution encoded using graph node sequences or coordinate waypoints. Through this implementation, users can observe how PSO dynamically refines path candidates by evaluating distance metrics while avoiding obstacles. The solution demonstrates practical applications of swarm intelligence in solving complex path planning problems with constrained environments, providing insights into parameter tuning strategies and convergence behavior analysis for robotic navigation and autonomous systems.