The self-optimization of network resource utilization is one of the important goals for Internet Traffic Engineering. To achieve this goal, many label switched path selection solutions are proposed. However, there are two drawbacks in these solutions. First, they are computationally expensive because they identify the critical links based on the maxflow algorithm. Second, they do not consider the self-demand of the current request when trying to avoid the interference. In this paper, we propose a novel Autonomic Interference Avoidance (AIA) algorithm, which autonomically selects the path with the least interference with the future requests, to overcome these shortcomings. First, AIA identifies the critical links in the shortest paths found by the Shortest Path First (SPF) algorithm, instead of the computationally expensive maxflow algorithm. Second, we introduce the competitive principle to take into account the self-demand of the current request as well as the network status. Therefore, AIA achieves both high resource efficiency and low computation complexity.