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Routing problems in networks are the problems related to sequencing and, of late, they have been receiving increased attention. Such problems usually occur in the areas of transportation and communication. A network problem involves the determination of a route from city i (origin) to city i (destination) for which there exist a number of alternative paths at various stages of the journey. The cost of journey, which may be function of distance, time or money, is different for different routes and the problem is to find the minimum cost route. Theoretically, the procedure involves determination of the cost of all the possible routes and selecting the one with minimum cost. However, in actual practice the number of such feasible alternatives is too large to be tried one by one. For instance, with 6 alternative paths, the number of possibilities is 51 = 120, with 9 paths the number becomes 8! = 40,320, while for 21 paths it increases to 2.4329 x 1018 This proves the necessity of a more efficient method to find the optimal path. There are many problems associated with networks, out of which the following two are important 1. The travelling salesman problem