Fair bandwidth allocation is an important issue in the multicast network to serve each multicast traffic at a fair rate commensurate with the receiver's capabilities and the capacity of the path of the traffic. Lexicographically fair bandwidth layer allocation problem is considered and formulated as a nonlinear integer programming problem. A nonincreasing convex function of the bandwidth layers of the virtual sessions is employed to maximize the bandwidth of each virtual session from the smallest. To solve the fairness problem a genetic algorithm (GA) is developed based on the fitness function, ranking selection and the shift crossover. Outstanding performance is obtained by the proposed GA in various multicast networks. The effectiveness of the GA becomes more powerful as the network size increases. (C) 2003 Elsevier Ltd. All rights reserved.