Particle Swarm Optimization-Based Algorithms for Traveling Salesman Problem

Particle Swarm Optimization (PSO) is an optimization technique grounded in swarm intelligence, drawing inspiration from how bird flocks or fish schools coordinate their movements. In this work, we propose a novel discrete PSO (DPSO) method tailored for the Traveling Salesman Problem (TSP), a well-known NP-hard challenge that seeks the shortest route visiting each city exactly once before returning to the start. Because TSP is inherently discrete, we adapt PSO to handle city-sequence permutations effectively. To reduce unnecessary elongations of the travel path, our approach introduces a specialized crossover deletion mechanism that eliminates disadvantageous route crossovers. In an experimental study using a 50-city TSP, comparative results demonstrate that the proposed DPSO not only delivers high-quality solutions but also accelerates convergence and enhances solution accuracy.