GENMET(GEneralized Multihop Network) which is based on Wavelength-Division Multiplexsing(WDM) and can be used in order to construct the next generation lightwave network is a logical(virtual), packet-switched and multihop topology network. GENMET is a regular multihop network which is a generalization of Shuffle network and do Bruijn network As such, it has the advantage of simple routing which is critical in a high speed network Given a physical topology, different logical topologies can be derived for assigning wavelengths to the UserNodes. By appropriately assigning wavelengths, performance of the network, such as mean hop count, maximum throughput and mean packet delay can be improved. In this paper, we propose heuristic algorithms for effectively assigning a limited number of wavelengths to the given UserNodes. The Performance of proposed algorithm is compared with the random assignment and the lower bounds.