Research on mechanisms for optimizing the risk resistance capability of hypernetworks.

The research on hypernetworks robustness focuses on improving their ability to resist various risks such as attacks and disasters. In the face of deliberate attacks, there is a huge risk of failure in Barabási-Albert (BA) hypernetworks. However, the methods to improve the risk resistant capacity of BA hypernetwork are lack. In this paper, two optimization mechanisms are proposed based on structural characteristics and connectivity. They are the self-optimization mechanism of random recombination for hyperedges(RRH) and the self-optimization mechanism of low degree preference recombination for hyperedges(LDPRH). The best improvement performance (BIP) is used as the evaluation metric, and a comparative analysis is conducted to assess the effectiveness of these mechanisms in enhancing the robustness of BA hypernetworks through simulation experiments. The research results indicate that both mechanisms effectively improve the hypernetwork's risk resistance, but the optimization effects differ. When the number of recombined hyperedges is 0.2*M (where M is the total number of hyperedges in the hypernetwork), the BIP of the random recombination mechanism stabilize at 25%, while the BIP of the low preference recombination mechanism ultimately reaches about 65%. To further validate the effectiveness of these optimization mechanisms, they were applied to Newman-Watts (NW) hypernetworks and Barabási-Albert (BA) ordinary networks, the latter based on binary relationships. The results showed that these optimization mechanisms also improved the risk resistance of NW hypernetworks and BA ordinary networks, especially in the BA ordinary network, where the BIP could reach up to 73%. Additionally, a significant correlation is observed between BIP, the number of hyperedge reshuffling operations, and the uniformity of the hypernetwork. Moreover, these optimization mechanisms are further validated in the context of China's high-speed railway hypernetwork, highlighting their practical application potential.