In modern societies there are increasingly more often problems of various kinds, and tests are needed to solve them in experimental ways. Although, Develop a mathematical model that closely matches the reality to solve a real life problem is very complicated, since many of these models might has to contain very large number of variables (as a heuristic model that optimizes problems solving results). Furthermore, these shows as difficult problems in controlling subjective behaviours, so They are making it even more complicated than these models resemble reality (wrong solving model leads to a more complex level). The purpose of this research is the study of combinatorial optimization problems using approximate methods. In particular, this work focuses on the analysis of meta-heuristics algorithms based on history and population related to the solution of Travelling Salesman Problem (TSP) like Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Simulated Annealing (SA) and many others, as well as hybrids, which allow efficiently to solve generic problems.