有限资源下多层网络鲁棒性的优化方法

Multilayer networks exist widely in social life and many fields of science and technology. The great concerning interaction and coupling of complex systems are closely related to multilayer networks. However, multilayer networks are prone to large-scale iterative collapse which may bring huge trouble to human life. Therefore, with limited resources, how to maximize the robustness of multilayer networks is an important issue to be solved urgently. Driven by this problem, this project intends to study the optimization method for the robustness of multilayer networks with limited resources. Considering the high computational complexity of such problems, the project will first use projection mapping and tensor calculation to utilize the inline links to characterize new spectrum characteristic of multilayer networks, to reduce the computational complexity of the original problem theoretically. Then, combined with the coexistence probability and reverse percolation, we will study the set of high efficiency links in the sense of probability, to improve the robustness of multilayer networks. Particularly, for the first time, large-scale intelligent optimization algorithms and convex optimization algorithms for large-scale separable problems are combined with multilayer networks as our pioneering research. Aiming at the new problems and new features in multilayer networks, we will establish the correspondence between parameters in multilayer networks and optimization theory, designing effective algorithms with relatively low complexity and providing new ideas and new methods for improving the system robustness with limited steps. Thus, the project will provide theoretical and technical support for the safe operation of many large-scale infrastructure networks.

社会生活和科技领域广泛存在多层网络，备受关注的复杂系统的交互和耦合就与多层网络密切相关，而多层网络极易发生大规模迭代式崩溃现象，给人类正常生活带来巨大困扰。因此，如何在资源有限条件下，最大程度地提升多层网络鲁棒性是亟需解决的重大课题,受其驱动，本项目拟系统研究有限资源下提升多层网络鲁棒性的优化方法。由于相关问题的计算复杂度很高，项目将首先借助投影映射和张量计算，利用内联边刻画新的多层网络谱特征，从理论上降低原问题的计算复杂度。然后,结合共存概率与逆向渗流，研究概率意义下的高效用链路集合，用以提升多层网络鲁棒性。特别是首次将大规模智能优化算法、大规模可分问题的凸优化算法与多层网络相结合，针对多层网络中衍生的新问题新特性，建立多层网络与优化理论中参数的对应关系，设计较低复杂度的有效算法，为有限步提升多层网络鲁棒性提供新思路和新方法，为诸多大型基础网络的安全运行提供理论和技术支持。

社会生活和科技领域广泛存在多层网络，备受关注的复杂系统的交互和耦合就与多层 网络密切相关，而多层网络极易发生大规模迭代式崩溃现象，给人类正常生活带来巨大困扰。因此，如何在资源有限条件下，最大程度地提升多层网络鲁棒性是亟需解决的重大课题，受其驱动，本项目系统研究了有限资源下提升多层网络鲁棒性的优化方法。由于相关问题的计算复杂度很高，项目将首先借助多层网络中心性挖掘网络节点排序指标，从机理上降低原问题的计算复杂度。然后,结合网络划分模型，研究网络边缘节点集的发掘问题，提升多层网络保护或瓦解效率。特别是首次将大规模智能优化算法与网络结构相结合，针对资源有限的情况下，建立满足约束的单层与多层网络的瓦解算法，为有限步提升多层网络鲁棒性提供新思路和新方法，项目研究成果可为诸多大型基础网络的安全运行提供理论和技术支持。