Complex networks rely on their structural robustness for their function and performance. Considering that redundancy backup is frequently used to enhance the robustness of complex networks, we try to find better redundancy backup strategy by using optimization methods. In this paper, our contributions are twofold. First, we prove that natural connectivity is suitable for measuring network robustness. Second, a robustness optimization algorithm is proposed based on GA, while it is different from traditional GA. The method of coding, crossover and mutation operations are all improved in this research. Extensive experiments on real-world datasets demonstrate that the effectiveness of our methods is better than the classical rich-rich redundancy backup strategy.