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The Traveling Salesman Problem (TSP) has already been solved in the semi-optimal manners using the numbers of different methods. Among them, genetic algorithms (GA) are pre-dominating. This paper presents a new approach to solve this problem using the Simplified Bi-directional Associative Memory (sBAM), a type of Artificial Neural Network. To get a comparative idea of its performance, the same problem has been solved using a genetic algorithm. In this paper, performance has been analyzed of a TSP by Genetic Algorithm (GA) and sBAM. Finally we proved that sBAM provide real time highly faster nearly optimal solutions than the genetic algorithm.