Particle Swarm Optimization Implementation for Traveling Salesman Problem

This program implements Particle Swarm Optimization (PSO) for solving the Traveling Salesman Problem (TSP). The TSP represents a classic combinatorial optimization challenge where the objective is to find the shortest possible route that visits each given city exactly once and returns to the starting city. The Particle Swarm Optimization algorithm is a population-based heuristic approach that simulates the social behavior of bird flocking to search for optimal solutions. The implementation includes position and velocity updates for each particle, where particles represent potential TSP solutions encoded as city permutations. Key algorithmic components include: inertia weight adjustment for convergence control, personal best (pBest) and global best (gBest) tracking, and 2-opt local search integration for solution refinement. The program outputs the optimal route sequence, total distance calculation using Euclidean distance metrics, and convergence progress visualization through iterative fitness evaluation.