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.

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.

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, multiobjective 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 article, we address the aforementioned challenges by developing a computationally efficient multiobjective 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 multiobjective 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.

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 MFEA textsubscript CR, 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 ${\mathrm{ MFEA}}_{\mathrm{ CR}}$ over existing methods; the efficiency enhancement is remarkable via the simultaneous optimization of multiple objectives.

The directedness of links is of significance in complex networks, and much attention has been paid to study the dynamics of directed networks recently.In networked systems, where the emergence of cooperation and robustness are two hot issues in recent decades. Previous studies have indicated that the structures for promoting these two properties are opposite, which also reveals the great impact of structures on the functionalities of networks. Moreover, several realistic problems also reflect the importance of simultaneously promoting the robustness and cooperation maintaining ability on directed networks, however, few studies have focused on solving this urgent problem. Therefore, in this paper, concentrating on optimizing the cooperation maintaining ability together with controllable robustness on directed networks, we first model this issue as a multi-objective optimization problem, and then a multi-objective evolutionary algorithm, labeled as MOEA-Netcc, has been devised to solve this problem. In the experiments, the performance of MOEA-Netcc is validated on both synthetic and real networks, and the results show that MOEA-Netcc can not only achieve balanced optimal results without changing degree distribution of networks; but also create diverse Pareto fronts, which provide various potential candidates for decision makers to deal with social and economic dilemmas.