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The paper presents an introduction to the Ant Colony Optimisation (ACO) algorithm and methods for solving the Travelling Salesman Problem (TSP). Documenting, understanding and knowledge of concepts regarding the emergent behavior and intelligence swarms optimization, easily led on solving the Travelling Salesman Problem using a computational program, such as Mathematics Wolfram via Creative Demostration Projects (*.cdf) module. The proposed application runs for a different number of ants, a different number of ants, a different number of leaders (elite ants), and a different pheromone evaporation index. As a result it can be stated that the execution time of the algorithm to solve the TSP is direct and strictly proportional to the number of ants, cities and elite ants considered, the increase of the execution time increasing significantly with the increase of the variables. Original Research Article Cioruța et al.; AJARR, 12(1): 68-77, 2020; Article no.AJARR.57673 69

Some Analytical Considerations Regarding the Traveling Salesman Problem Solved with Wolfram Mathematica Applications