Particle Swarm Optimization (PSO) is a commonly used optimization to solve many problems. The PSO, which is developed for continuous optimization, is updated to solve discrete problems and Discrete PSO (DPSO) is obtained in this study. With DPSO, the Traveling Salesman Problem (TSP), which is well-known in the literature as a discrete problem, is solved. In order to improve the results, the swap method, the shift method, and the symmetry method are added to DPSO. The symmetry method is a new and successful method. The variations of the DPSO occurred according to the selected method type (DPSO1 (swap method), DPSO2 (shift method), DPSO3 (swap and shift methods), DPSO4 (symmetry method), DPSO5 (swap, shift, and symmetry methods), DPSO6 (swap, shift, symmetry, and 2-opt methods)). The effect of each method on the performance of the DPSO has been studied in detail. To demonstrate the success of the variations of the DPSO, the results are additionally compared with many well-known and new discrete algorithms in the literature. The results showed that the performance of DPSO has improved with the symmetry method and it has achieved better results than the discrete heuristic algorithms recently proposed in the literature.