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Rapid advances in the world of high-speed optical network and high-speed electronic routing has led to consideration of advanced models such as genetic algorithms (GAs). GAs have proved to be a practical and robust optimization and search tool for network design. However, a GA is not generally employed in traffic grooming over mesh networks. In this paper, we propose a new GA model to handle the traffic grooming problem in an all-optical WDM mesh network. The new model extends classical GAs with heuristic approach to support network cost optimization for combining multiple traffic streams into a single lightpath. In addition, to support our new GA model, we have developed a set of new investigation including position-based bit matrix encoding, genetic heuristic operators, and fitness evaluation function using the clustering method. The experimental results show that our GA model is superior to traditional heuristic approaches for the 5, 6 and 14-node benchmark networks.