In this paper, an Evolutionary approach for optimization of cyclic Gas Transmission Network (GTN) is presented. The GTNs comprise of nodes, links, compressor stations and valves where the last one is a main component of GTNs which generally not considered in similar works. In this approach, at first a reduced network will be generated from the original GTN and the cycles of the reduced network will be identified. Then an iterative approach will be used to find the cycles flows which optimize the objective function. This approach calculates the pressure variables at fixed flow rates using dynamic programming (DP) and updates the gas flow rates to improve the objective function in every iteration. The objective function is a weighted summation of total number of running compressor stations and their total fuel consumption. The flow rates will be updated using Genetic Algorithm (GA) which is modified to speed up its convergence. The main modifications are related to decomposing of chromosomes to subchromosomes and finding the upper and lower limits for crossover and mutation. A number of real examples of Iranian GTN are exploited to support the proposed approach.