Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 543573.doi: 10.23919/JSEE.2023.000080
• COMPLEX SYSTEMS THEORY AND PRACTICE •
Kewei YANG(), Jichao LI(), Maidi LIU(), Tianyang LEI, Xueming XU(), Hongqian WU(), Jiaping CAO(), Gaoxin QI()
Received:
20221123
Online:
20230615
Published:
20230630
Contact:
Kewei YANG
Email:kayyang27@nudt.edu.cn;ljcnudt@hotmail.com;lmdnudt@hotmail.com;xueming_x2m@163.com;wuhongqian19@nudt.edu.cn;jiapingcao@126.com;qi198@foxmail.com
About author:
Cofirst author
Supported by:
Kewei YANG, Jichao LI, Maidi LIU, Tianyang LEI, Xueming XU, Hongqian WU, Jiaping CAO, Gaoxin QI. Complex systems and network science: a survey[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 543573.
Table 1
Measurement of network invulnerability in three theories"
Category  Indicator  Review 
Graph theory  Connectivity Toughness Integrity Tenacity Scattering number Coefficient of expansion Algebraic connectivity  Graph theorybased network invulnerability usually has high computational complexity. It is unrealistic and unscientific to measure the invulnerability of complex networks with huge scales and uncertain connection relationships. 
Statistical physics  Network invulnerability of different attack strategies Seepage problems in generalized stochastic networks Network invulnerability with the repair mechanism Network invulnerability considering degree correlation condition Network invulnerability of the local world evolution model  While adapting to the current situation of the huge scale of network complexity, it also greatly expands the vision of the research on the resistance of complex networks, and relevant achievements are concentrated in the research fields of network learning, network propagation, network synchronization, etc. 
Characteristic spectrum  Natural connectivity Helmholtz free energy of network Physical implications of natural connectivity  It contains a lot of network topology information. Derivation and analysis of the network characteristic spectrum are helpful to deepen our understanding of some properties and behaviors of the network. 
Table 2
Cascading failure model"
Cascading failure model  Brief introduction 
Load capacity model  When encountering some accidental failure or intentional damage, a node in the network will exceed the limit capacity and cause failure, which will then lead to the overload increase of other nodes or connections and cause failure until the entire network is restabilized [ 
Sandpile model  Assume that for sand in the sand pile, the sand surface gradually becomes steeper with the gradual increase of sand and the probability of a large area collapse of the sand pile increases [ 
OPA model  This model is based on the power grid with increasing energy demand. It can summarize the dynamic evolution process of the power grid, the engineering response process of system failures, and the continuous updating process of generation capacity. At the same time, it defines two types of cascading failure types, each with different dynamic characteristics [ 
CASCADE model  The model has two assumptions: for the nodes, the initial load is given randomly, and each node fails according to random probability; when the load of a node exceeds the limit capacity, it causes the node to redistribute its load so that other nodes in the network can obtain an equal amount of load [ 
Table 3
Typical research on three kinds of optimization methods"
Optimization method  Typical research  
Constructing the optimal network by analytical method  Valente et al. [  
Paul et al. [  
Tanizawa et al. [  
Optimizing destruction by edge enhancement  Beygelzimer et al. [  
Zhao et al. [  
Cao et al. [  
Optimizing destruction by edge reconnection  Nonguaranteed reconnection optimization  Liu et al. [ 
Netotea et al. [  
Priester et al. [  
Guaranteed reconnection optimization  Peixoto et al. [  
Herrmann et al. [ 
Table 4
Classification of network disintegration problems"
Perspective  Type  Related work 
Target object of disintegration  Nodebased  [ 
Edgebased  [  
Type of disintegration network  For homogeneous networks  [ 
For heterogeneous networks  [  
For multilayer networks  [  
Constraints of disintegration  Under the homogeneous cost constraint  [ 
Under the heterogeneous cost constraint  [ 
Table 5
Classification of network disintegration methods and their typical methods"
Classification  Typical method  Advantages and disadvantages 
Methods based on mathematical programming  Branch and bound method Mixed iterative rounding method Univariate decomposition Dynamic programming  The optimal network disintegration scheme can be obtained. It has high requirements for the objective function and constraint conditions and is not applicable to largescale networks. 
Methods based on the centrality index  Degree centrality kcore centrality Intermediate centrality Proximity centrality  Simple and easy to implement, but the important node set under a single index is not necessarily the optimal node removal set. 
Methods based on heuristic algorithms  Tabu search algorithm Genetic algorithm Simulated annealing algorithm Random greedy adaptive search algorithm  A good network disintegration scheme can be obtained that has high robustness and wide applicability. The time complexity is high. 
Methods based on reinforcement learning  Qlearning Deep Qnetwork (DQN)  It has nothing to do with specific knowledge and rules and is applicable to all kinds of problems; it is not interpretable. 
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