Network structure plays an important role in the natural and social sciences. Optimization of network structure in achieving specified goals has been a major research focus. In this paper, we propose a definition of structural optimization in terms of minimizing the network's average path length (APL) by adding edges. We suggest a memetic algorithm to find the minimum-APL solution by adding edges. Experiments show that the proposed algorithm can solve this problem efficiently. Further, we find that APL will ultimately decrease linearly in the process of adding edges, which is affected by the network diameter.