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This paper focuses on incentive-based offline inter-AS traffic engineering with end-to-end quality of service (QoS) guarantees. We investigate a key inter-AS traffic engineering problem, the "egress router selection problem". The objective is to select an egress router for each expected aggregate inter-AS traffic flow so that the required end-to-end QoS is provided and the capacity constraint of each inter-AS link is met while minimizing the total inter-AS transit cost. The problem is NP-hard and we propose a genetic algorithm to solve it. Simulation results show that our proposed approach performs better than conventional greedy-based approaches.