Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which re?ects how many iteration times ACO algorithms spend in converging to the optimal solution. This study aims at using a Max-Min Ant System (MMAS), which belongs to Ants Algorithm to obtain optimal tour of the Travelling Salesman Problem of Ghacem. The study considered a twelve city node graph (major sales point of Ghacem) with the nodes representing the twelve cities, and the edges representing the major roads linking the cities. Secondary data of the inter-city driving distances was obtained from the Ghana Highway Authority. The results showed that the objective of finding the minimum tour from the Symmetric Travelling Salesman Problem (STSP) model by using Max-Min Ants System (MMAS) Algorithm was successfully achieved. The optimal route of total cost distance was found to be 1873Km. Therefore, Ghacem could minimize the cost of transportation as the Directors of Ghacem Ghana go on a tour to check on the sales performance of the twelve key Distributors in the major sales points in Ghana, starting from Tema where the company’s Head office is sited. It is very prudent for the company to rely on MMAS model to reduce fuel cost in order to maximize profit. In doing so it go along way to increase the tax revenue of the state. Keywords: Max-Min Ants System (MMAS), Ant Colony Optimization (ACO), Algorithm, Travelling Salesman (TSP), Ghace
