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The network topology before and after optimization by MA-R cf . The size of each node is proportional to its degree.
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Research concerning cascading failures in complex networks has become a hot topic. However, most of the existing studies have focused on modelling the cascading phenomenon on networks and analysing network robustness from a theoretical point of view, which considers only the damage incurred by the failure of one or several nodes. However, such a th...
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... is useful to study the robustness of the network structures obtained MA-R cf . Thus, the network topologies of BA networks before and after optimized by MA-R cf are plotted in Fig. 3, where the size of each node is pro- portional to its degree. As shown, before optimization, low degree nodes are often connected to nodes with high degrees; consequently, the entire network is composed of numerous star networks with hub nodes. However, the optimized networks which have higher R cf , the low degree nodes are more ...
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... Cascading failures are a common interaction behaviour observed in complex systems, often manifested as continuous and dynamic state changes (Crucitti et al., 2004;Fu et al., 2020;Tang et al., 2016b). In transport systems, cascading failures typically result from dynamic load redistribution involving the transfer of cargoes or passengers and are constrained by the capacity of the hubs (i.e., stations or ports). ...
... The other category pays attention to the cascading failure among nodal members, emphasizing the catastrophic result followed by the inundation of overloaded nodes. Several models were established to simulate the dynamics of networks suffering from the cascading failure [18,19], based on which the invulnerability or robustness of networks against this type of damages has also been intensively studied [20,21]. In this way, a well-developed theoretical framework is provided to analyze the discipline and dynamics of networks under malicious attacks. ...
... With the help of these models, we can get a clearer view on the dynamics of networked systems under cascading failures, and the mitigation on this catastrophic destruction becomes possible. As in [21], a numerical measure was proposed to evaluate the robustness of networks. The load (Li) and capacity (Ci) of node i were defined based on nodal degree, as follows, ...
... The configurations of these two parameters are closely correlated with the evaluation results. As indicated in the previous studies [21,23], the initial load can be estimated by structural properties such as the degree, and α is suggested as ...
Networked systems widely exist in the modern society, and these systems are always operated in the presence of attacks and errors. The robustness of a network indicates its tolerance against potential damages, which is crucial for the network’s normal functionalities. Damage models including malicious attacks and cascading failures have been considered in previous studies. And the mitigation on these two destructive damages has attracted increasing attention, both single-objective and multiobjective optimization techniques are proposed to enhance the robustness of networks. The main weakness of these methods is that the obtained results can only handle one type of damages, either malicious attacks or cascading failures. In this way, multiple independent realizations are evitable to acquire robust candidates against different damages, which omits the inherent complementarities between the optimization of different objectives. Also, the design of networks with comprehensive robustness (CR) against both the two destructive damages is still pendent. For improving the efficiency in optimizing networks considering multiple damage models, in this article, evolutionary multitasking optimization is introduced into the optimization of network robustness. A multifactorial evolutionary algorithm (MFEA) for enhancing the CR of networks, called MFEACR, has been proposed. The algorithm is equipped with several dedicated genetic operators to find networks with robust structures against malicious attacks and cascading failures; meanwhile, the synergy between the optimization of the two objectives is exploited to improve the computational efficiency. Empirical studies demonstrate the competitive performance of
over existing methods; the efficiency enhancement is remarkable via the simultaneous optimization of multiple objectives.
... where H is the required number of attacks to achieve the attack task, for example, a significant destruction of functionality [80], [81], [82], [83], [84]. Here, H N ≤ implies that it is not always necessary to attack all nodes in order to destroy the network functions. ...
Network robustness is critical for various industrial and social networks against malicious attacks, which has various meanings in different research contexts and here it refers to the ability of a network to sustain its functionality when a fraction of the network fail to work due to attacks. The rapid development of complex networks research indicates special interest and great concern about the network robustness, which is essential for further analyzing and optimizing network structures towards engineering applications. This comprehensive survey distills the important findings and developments of network robustness research, focusing on the a posteriori structural robustness measures for single-layer IMAGE LICENSED BY INGRAM PUBLISHING Authorized licensed use limited to: OSAKA UNIVERSITY. Downloaded on May 07,2023 at 03:33:24 UTC from IEEE Xplore. Restrictions apply. FIRST QUARTER 2023 IEEE CIRCUITS AND SYSTEMS MAGAZINE 13 static networks. Specifically, the a posteriori robustness measures are reviewed from four perspectives: 1) network function-ality, including connectivity, controllability and communication ability, as well as their extensions; 2) malicious attacks, including conventional and computation-based attack strategies; 3) robust-ness estimation methods using either analytical approximation or machine learning-based prediction; 4) network robustness optimization. Based on the existing measures, a practical threshold of network destruction is introduced, with the suggestion that network robustness should be measured only before reaching the threshold of destruction. Then, a posteriori and a priori measures are compared experimentally, revealing the advantages of the a posteriori measures. Finally, prospective research directions with respect to a posteriori robustness measures are recommended.
... For example, heuristic optimization techniques [2], [7] have been shown to be effective in enhancing the robustness of networks against attacks with a low space complexity. Moreover, population-based optimization methods can achieve satisfactory results using problem-directed operators [9], [10]. ...
... The third one is to select embedding vectors of the top k high-degree nodes, with k being the number of centers used in K-means clustering. The robustness of a network is closely related to its high-degree nodes [8], [10], and the malfunctions of several hubs may cause a serious congestion in a networked system. The representations of such high-degree nodes can provide additional information to estimate the robustness of the network. ...
... Related studies [7], [11], [15] indicated that optimization methods considering multiple damage scenarios can help enhance the overall performance of network systems. Diversified solutions obtained using an MOEA can be presented to the user to handle different circumstances, and such techniques are more effective than single-objective optimization methods like in [2], [9], and [10]. With a notably reduced running time and an improved performance, the proposed algorithm is more promising to solve optimization dilemmas in real systems over existing methods. ...
The robustness of complex networks is of great significance. Great achievements have been made in robustness optimization based on single measures, however, such networks may still be vulnerable to multiple attack scenarios. Therefore, recently, multi-objective robustness optimization of networks has received increasing attention. Nevertheless, several challenges remain to be addressed, including the different computational complexities in evaluating the objectives, insufficient diversity in the obtained networks, and high computational costs of the search process. In this paper, we address the aforementioned challenges by developing a computationally efficient multi-objective optimization algorithm. Based on the unique features of complex networks, a new parallel fitness evaluation method guided by a network property parameter is designed, and embedded in a reference vector guided multi-objective evolutionary algorithm. In addition, a surrogate ensemble with heterogeneous inputs is constructed based on graph embedding information to efficiently estimate multiple robustness of networks. The proposed algorithm is validated on synthetic and real-world network data and our results show that the designed algorithm outperforms the state-of-the-art method with a marked improvement on the computational efficiency. Compared with other single-objective optimization methods, the proposed algorithm demonstrates a considerable exploitation ability.
... In order to control the failure cascading propagation, researchers prevent and recover failure cascading at node level and network level: (1) Cascading failure prevention at node level. Cascading failure are prevented by protecting the key node, such as important node load expansion [34], node immunity [35], and node load compensation [36]. ...
Industrial Internet or industrial cloud platforms based manufacturing collaboration in the form of services, namely manufacturing services collaboration (MSC), is being the new generation of networked manufacturing mode. In the process of MSC, a lot of failures would occur due to different reasons, and then propagate to cause other parts of failures. However, the classification of failures in MSC is unclear, the occurrence and propagation of failures are difficult to detect, and the control strategies for the failures and their corresponding propagation is insufficient, which lead to the lower users’ collaboration participation in the platforms. In order to solve the above problems, the failures detection, failures cascading propagation analysis and specific control strategies for the platform-based MSC are investigated in this study. Firstly, the model of manufacturing services collaboration network (MSC-Net) is established by introducing the collaborative relations aware community of complex network. Then six types of failures occurred in MSC-Net are defined, corresponding detection methods for the defined failures are presented. The specific cascading propagation characteristics of different failures are revealed. The control strategies for different failures as well as their cascading propagation in MSC-Net are proposed. Finally, a 3D Printing case is given to illustrate the feasibility of the proposed methods.
... Some populationbased search techniques have been devised for better utilizing the connection information of the original network, and promoting the search ability. Several network-specific genetic operators are proven to be effective to further improve the search performance [13], [14], [31]. Considering the fact that the topologies of some systems are of great significance or extremely hard to be modified, some protection strategies, which avoid making changes on the network structure, have also been proposed. ...
... As shown in [8], [11], [13], [14], and [31], the key for enhancing the robustness of the original network is to search for better connection types between nodes, and the basic operation is exchanging endpoints of two links. Considering the unique characteristic of graphs, the exchange is far from free but under restrictions. ...
... Some network-related evolutionary operators have been carefully designed based on existing studies in the proposed algorithm, which have been validated to be effective in searching robust networks. After generating the initial population (shown in Algorithm 2), the crossover operator is conducted to generate more candidates in the solution space; similar operations can be found in [13], [14], and [31]. The operator works as follows. ...
Robust optimization of complex networks has attracted much attention in recent years. Although existing methods have been successful in achieving promising results, the computational cost for robust optimization tasks is extremely high, which prevents them from being further applied to large-scale networks. Thus, computationally efficient robust optimization methods are in high demand. This paper proposes a low-cost method for estimating the robustness of networks with the help of graph embedding techniques and surrogate models. An evolutionary algorithm is then developed to find large-scale robust networks by combining the surrogate-assisted low-cost robustness estimator with the time-consuming real robustness measure by means of a model management strategy. Experimental results on different kinds of synthetic and real networks demonstrate the highly competitive search ability of the proposed algorithm. In addition, the algorithm is able to save up to 80% of the computation time for enhancing the robustness of large-scale networks compared with the state-of-the-art methods.
... Furthermore, the seed selection strategy is also stud-158 ied to find optimal combination of seeds. Since MAs have 159 been proven to be effective in solving different optimization 160 problems [23], [30], [31], a problem-directed MA, together 161 with several operators, is devised to find the most influen-162 tial seed sets in terms of the whole multiple network system, 163 termed MA-IM multi . The effectiveness of the proposed algo-164 rithm has been validated on both synthetic and real-world 165 network data. ...
... can be also guaranteed. The proposed measure in (2), on the 397 one hand, provides numerical measure to evaluate the influen- and enhancing networks' robustness [30], [31]. In this paper, Given a social network, the selection of seed sets with high 443 efficiency to spread influence can be solved by an optimization 444 algorithm, which has been emphasized in previous stud-445 ies [19]- [24]. ...
In order to find the nodes with better propagation ability, a large body of studies on the influence maximization problem has been conducted. Several influence spreading models and corresponding optimization algorithms have been proposed and successfully identified the infusive seeds in single isolated networks. However, as indicated by some recent studies and online materials, modern networked systems tend to have more complicated structures and multiple layers, which makes it difficult for existing seed determination techniques to deal with these networks. Thus, finding influential nodes in realistic multiplex networks remains open. Therefore, this paper aims to design an extended influence spreading model to simulate the influence diffusion process in multiplex networks, based on which a memetic algorithm is developed to find the seeds that are influential in all network layers. Experimental results on synthetic and real-world networks validate the effectiveness of the proposed algorithm. These results are helpful for identifying potential propagators in multiplex social networks, and provide solutions to analyze and gain deeper insights into networked systems.
... The robustness, describing the tolerance of a system to withstand attacks and errors, has been greatly emphasized in the study on complex networks [12][13][14][15][16][17][18][19]. With the help of several robustness measures [14,17,18], we can evaluate whether a network is reliable or not when suffering from damages. ...
... Therefore, specific operators and searching techniques that can make valid searches in network structures are needed. As shown in previous studies [13,15], memetic algorithms (MAs) with networkdirected searching operators have good performances in solving optimization problems in networks by combining the global and local genetic information of network candidates with better efficiency. Further, the implementation of individual learning procedures makes MAs capable of performing local refinements, which contributes to improve their searching ability [13,15]. ...
... As shown in previous studies [13,15], memetic algorithms (MAs) with networkdirected searching operators have good performances in solving optimization problems in networks by combining the global and local genetic information of network candidates with better efficiency. Further, the implementation of individual learning procedures makes MAs capable of performing local refinements, which contributes to improve their searching ability [13,15]. Such MAs have the potential to handle other optimization tasks in networked systems. ...
... As in [25,46] , strategies have been proposed to mitigate the damage caused by cascading failures. Moreover, for designing robust network structures and providing guidance to realistic system construction, some recent studies have used the topological rewiring method to deal with this optimization problem [4,38] and have obtained considerable results for potential practical uses. ...
... Similar to what Tang et al. did in [38] , the robustness of networks against cascading failures can be numerically evaluated through recording the change of the largest connected component in the process of losing connectivity, defined as follows: ...
... Ash et al. used an evolutionary algorithm to evolve networks with better resilience against cascading failures in [4] . Tang et al. devised a memetic algorithm to mitigate networks suffering from cascading failures and indicated that connecting nodes that have similar loads with a high probability contributes to the enhancement of robustness of networks against cascading failures [38] . ...
... Focusing on the community robustness, the enhancement methods in terms of edge-based attacks are urgent and still remained to be solved. In addition, existing community robustness enhancement techniques mainly concentrate on heuristic optimization methods [22], [24], [27]; as shown in [9], [18], and [32], these methods are proved to be of low efficiency and easy to get stuck in local optima. A powerful method to enhance community robustness is still vacant so far. ...
... Furthermore, we try to find reliable connection strategies between nodes in the given network while preserving the original community allocation information. Based on previous studies on optimization methods [9], [18], [32], a memetic algorithm MA − R com is devised to find community-robust structures. It should be noted that the optimization process keeps the degree distribution unchanged to avoid extra disturbances on the network structure. ...
... Heuristic optimization methods have been adopted in the enhancement of community robustness in previous studies [22], [24], [27]. Indicated by [9], [18], and [32], heuristic methods are easy to be trapped into local optima; meanwhile, dealing with only one candidate, these methods tend to be less efficient. Since the searching space for a robustness optimization problem is relatively large, a population-based optimization technique may provide better solutions, which has been verified in previous studies [9], [18], [32]. ...
The community structure often represents potential functionalities of systems and plays a crucial role in realistic applications. As indicated by previous studies, it is of significance to preserve the allocations of members in networks even when attacks and errors occur, and there has been much progress in studying community robustness toward nodal attacks. Meanwhile, both nodes and links are necessary to the normal function of networked systems, and the evaluation and optimization method aiming at edge-based attacks in communities is crucial as well. However, few of the existing studies have focused on such an urgent topic. Therefore, in this paper, we manage to deal with constructing robust community structures withstanding edge-based failures. A measure evaluating the community robustness against edge-based attacks is designed first, and an optimization algorithm, termed MA-R , has been devised to enhance the edge-based community robustness. The experimental results on several synthetic and real-world networks show that MA-R is effective and reliable in the optimization process; meanwhile, the original community partition information can be also preserved well. Furthermore, in order to design a comprehensively robust community structure against both node-based and edge-based attacks, the modified MA-R is designed and validated. Toward community robustness in terms of edge attacks, this paper provides a valid measure to evaluate and compare the reliability of networked systems; furthermore, the proposed optimization algorithm is effective in enhancing the performance of networks, and the obtained results are potentially valuable for solving realistic dilemmas.
