The abuse of community detection algorithms posed significant risks of privacy leakage. To protect personal privacy in complex networks, community detection attack (CDA) algorithms have been proposed, which modify a small number of connections to obscure the original community structure. However, most of the existing studies focus on designing effective attack strategies while the attack budget should be given by decision makers in advance. In this article, we transform CDA into a biobjective optimization problem, where the attack effectiveness and the attack budget are optimized simultaneously. To solve this problem, an effective multiobjective evolutionary algorithm (MOEA) named CDA-MOEA is proposed, which provides the decision maker with a holistic view for assessing attack strategies. Additionally, a budget-aware population repair operator based on betweenness and permanence is suggested to enhance the diversity and quality of the nondominated solutions in CDA-MOEA. Experimental evaluations are conducted by comparing CDA-MOEA with four state-of-the-art baseline methods against five community detection algorithms on eight real-world networks. The results indicate that CDA-MOEA significantly improves attack effectiveness at the same attack cost comparing to baseline methods, confirming its superiority and practical applicability.

Multi-objective evolutionary algorithms (MOEAs) have achieved notable success in recommendation systems (RSs) by meeting diverse user needs. However, existing MOEAs lack effective methods to coordinate the challenges of cold start, low convergence of multiple objectives and lack of explainable recommendation reasons. Therefore, we propose an enhancing multi-objective optimization recommendation algorithm by integrating large language models (named as MORA-LLM). MORA-LLM uses the vast knowledge, reasoning ability and natural language generation (NLG) ability of large language models (LLMs) to compensate for the shortcomings of MOEA-based RSs in semantic understanding. Firstly, an LLM-enhancing prediction score (LEPS) strategy is proposed to alleviate the cold start problem. LEPS obtains the user embedding vector by vast knowledge of LLM and extracts interaction information of similar users to improve the accuracy of prediction scores. Secondly, an LLM-enhancing search (LES) strategy is proposed to improve the convergence of the multi-objective. LES strategy combines the reasoning ability of LLM with the competitive idea of competitive swarm optimization to achieve efficient search and balance multiple objectives. Finally, the prediction scores are further corrected based on the LLM output results and MORA-LLM offers recommendation reasons to help users better understand the recommendation results. Experimental results on real-world datasets demonstrate that MORA-LLM significantly outperforms existing algorithms in terms of recommendation accuracy and convergence.

Multi-party multi-objective optimization, which aims to find a solution set that satisfies multiple decision makers (DMs) as much as possible, has attracted the attention of researchers recently. Although multi-party multi-objective optimization is of great significance in practical applications, most existing works focus on continuous problems while paying little attention to discrete problems. To this end, we propose a multi-party multi-objective evolutionary framework named MP-HCEA for discrete problems, where a multi-party population is used to optimize all objectives of multiple DMs, and multiple single-party populations are used to respectively optimize the objectives of each DM. In MP-HCEA, a dual-phase cooperation mechanism is firstly proposed to guide the population interaction, where the weak cooperation is performed in the early phase to share offspring individuals, while the strong cooperation is performed in the later phase to share parent individuals. This dual-phase cooperation mechanism not only ensures effective information sharing between multiple populations, but also helps them to obtain high-quality solutions. In addition, a novel dual-search mechanism is proposed to guide the evolution of the multi-party population, which further enhances the convergence ability of the algorithm. Finally, we apply MP-HCEA to a real application named multi-stakeholder recommendation as a case study. Experiments on real-world multi-stakeholder recommendation datasets show that the proposed MP-HCEA outperforms several representative baselines.

Recommender systems have become immensely popular and widely used currently. Multi-objective evolutionary algorithms (MOEAs) have demonstrated successful applications in this field by taking into account both accuracy and various other performance metrics at the same time. To address the issue of high computational complexity brought about by large-scale recommendations, the concept of evolutionary multi-task (EMT) has been successfully applied. This study further presents a novel EMT-based algorithm named APEMA, which incorporates a new adaptive probabilistic operator that utilizes a variety of historical information from the population for comprehensive evaluation. By guiding the genetic operator and knowledge transfer, it can accelerate the convergence of results while simultaneously increasing the diversity of the population, thereby achieving better performance. Specifically, the APEMA algorithm uses its unique probabilistic operator to adapt to the evolving population. The effectiveness of APEMA in addressing multi-objective recommendation problems is empirically validated on the Movielens and Douban datasets. Experimental results show that it achieves superior performance compared to several state-of-the-art algorithms.

Subset selection is a fundamental problem across a wide range of applications. In this study, we explore scenarios where the variables within the original dataset are divided into distinct groups. Subsequently, we investigate an optimization problem that includes extra fairness constraints (i.e., partition matroid constraints), restricting the selection of a specified number of variables from each group, which is known as the fair subset selection (FSS) problem. First, for the case where the existing Pareto optimization algorithms do not have the ability to well handle the fairness constraints, due to they do not consider fairness constraints in the process of solutions generation. In this article, a Pareto Optimization algorithm named POFSS is proposed for FSS, by introducing a designed fairness balance flip operator. Also, we prove that POFSS has the approximation ability of$\max \{ {}[{\alpha }/{l}](1-e^{-\gamma }), {}({\gamma }/{k}), 1-e^{-r\overline {k}/k } \}$in polynomial time when$ l \lt \log _{2}{n}$and the probability of mutation is constant$c/n~(c\lt 2)$and this approximation ratio is no worse than the previous theoretical result ($\alpha $,$\gamma $represent two submodular ratios, and l is the number of disjoint groups). In addition, we apply POFSS to one typical FSS task named personalized recommendation (PR), where an acceleration strategy is designed and the acceleration ratio is strictly proved. Finally, the experimental results on the PR task show the proposed POFSS outperforms the state-of-the-art methods in addressing the FSS.

The abuse of community detection algorithms may bring the risk of privacy leakage. To protect personal privacy in complex networks, community detection attack algorithms are proposed, which can hide the true community structure of the whole network from the community detection algorithms by adding and deleting subtle edges. However, most of the existing algorithms perform attack based on a community structure so that a specific community detection method is usually adopted for obtaining the communities, which causes the algorithms to not perform well when the attacked community detection algorithm is unknown. To this end, a local structure-based community detection attack heuristic approach (LSHA) is proposed in this article, where the local structures, including several nodes with dense connections instead of the whole community structures, are considered. Unlike the whole community structures obtained by different community detection algorithms, which are usually different, the nodes in such a local structure are often assigned into the same community so that the attack is more general for different community detection algorithms. Specifically, in LSHA, a local structure selection strategy is proposed to maximize the attack effect, which selects two local structures for rewiring attack. Furthermore, two metrics, i.e., edge vulnerability and node entropy, are also suggested to select the nodes and edges for attack. In the experiments, the proposed LSHA is compared with five state-of-the-art attack algorithms. The experimental results against five representative community detection algorithms on nine real-world networks show that the proposed algorithm LSHA achieves good performance on both the attack effectiveness and the efficiency.

Multiobjective evolutionary algorithms (MOEAs) have been widely used in community detection in recent years. However, most of the existing MOEA-based ones adopted the same search strategies for all nodes and ignored the differences between the nodes. In fact, the nodes in a complex network have different structural characteristics and are of different importance during the search process of the community detection problem. To this end, in this article, a node classification-based search scheme is first proposed, where different kinds of nodes are searched in different ways. To be specific, the nodes in the network are classified into two types of nodes, candidate central (CC) nodes and noncentral (NC) nodes, by mapping the nodes into a structural similarity-based embedding space. The CC nodes are likely to be the centers of communities, and the rough structure can be searched quickly through activating the CC nodes. Then, the NC nodes are assigned to the communities with the activated central nodes. Based on the proposed scheme, a node classification-based MOEA named NCMOEA is then proposed. In NCMOEA, a mixed representation is designed to effectively encode the two different kinds of nodes. In addition, corresponding genetic operators are then suggested to search the two categories of nodes in different ways. Furthermore, an initialization strategy is also designed for initializing the population with high quality and good diversity. The experimental results on 15 real-world networks and several synthetic networks demonstrate the superiority of the proposed NCMOEA over nine representative algorithms for community detection.

Community detection plays an important role in understanding complex networks. Many traditional embedding-based community detection methods only focus on the relations between nodes in the topology space (i.e., topology graph). Besides, there are also some works that consider the feature embedding of nodes to further improve the detection performance. However, most of them ignore the relationships between nodes in the feature space (i.e., feature graph). To address this issue, in this article, we construct the feature graph from the features of nodes to capture the relations between nodes in the feature space, and incorporate it with the topology graph and the feature embedding, leading to the novel feature graph augmented network representation for community detection (FGCD) method. Specifically, FGCD extracts the embeddings of topology graph, node features, and feature graph, respectively, and ensembles them by a layerwise fusion method with an attention mechanism. Extensive experiments on 11 real-world datasets show that FGCD outperforms most existing state-of-the-art algorithms, which well demonstrates its superiority.

Subset selection that selects a limited number of variables optimizing many given criteria, is a fundamental problem with various applications such as sparse regression and unsupervised feature selection. Among the existing algorithms for subset selection, evolutionary algorithms (EAs) have achieved great performance in obtaining the subsets with high quality. However, as the selected subsets are sparse, i.e., most variables of these solutions are zero, most existing EAs for subset selection problems pose great challenges to find the optimal solutions effectively and efficiently, especially when the size of original set is large. To this end, we propose the SPESS approach which is a sparsity preserved evolutionary algorithm for subset selection. To be specific, we design two sparsity preserved operators (i.e., sparsity preserved crossover operator and sparsity preserved mutation operator), which can be used in SPESS to ensure the sparsity of the generated solutions in the process of Pareto optimization. The main advantages of the proposed sparsity preserved operators are that they can obtain high quality solutions and improve the search efficiency of the algorithm. According to the experimental results on 12 sparse regression problems and 12 unsupervised feature selection problems, the proposed SPESS is superior over the state-of-the-arts in solving subset selection tasks and the effectiveness of the proposed two sparsity preserved operators is also verified.

Critical node detection is an important task to analyze network vulnerability and measure network security. Most existing methods either focus on non-cascading scenario from the perspective of network static properties or focus on cascading scenario from the perspective of network dynamic behavior. The problem of critical node detection is unexplored in both scenarios simultaneously. To this end, we formalize the critical node detection problem into a multi-objective problem in the two scenarios at the same time. Then, a multi-objective critical node detection algorithm named MOBSCND is proposed to effectively solve the transformed problem, which can provide multiple critical node solutions for decision-makers in both cascading and non-cascading scenarios. In MOBSCND, we design an effective initialization strategy, which can produce better initial individuals while ensuring population diversity. In addition, a local search strategy is proposed to accelerate the convergence of the population and improve the quality of population individuals. The experimental results on 12 datasets show that the convergence and diversity of the solution set obtained by the proposed method are all superior to the baseline algorithms.

Influence maximization (IM) problem, which selects a subset of nodes from a social network to maximize the influence spread, appeals to numerous scholars. Since the IM problem is NP-hard, it is still an arduous task to achieve good results in terms of influence spread and running time at the same time. This article proposes a novel search space reduction strategy-based progressive evolutionary algorithm (SSR-PEA) for solving IM problems effectively and efficiently. In SSR-PEA, a novel search space reduction strategy (SSR) in the light of the power-law distribution of the social network is designed to reduce the computational overheads, which eliminates a great deal of less influential nodes in a sensible way. After that, we propose a progressive evolutionary framework based on SSR, where the$k$-element individual is optimized on the basis of the ($k$-1)-element individual to speed up the optimal solution search process. Experimental results on ten real-world networks demonstrate that the proposed algorithm SSR-PEA can achieve 98% of the influence spread achieved by cost-effective lazy forward (CELF) on average, and its running time is two or even three orders of magnitude shorter. Thus, SSR-PEA strikes a better balance between effectiveness and efficiency.

In recent years, the application of multi-objective evolutionary algorithms (MOEAs) to overlapping community detection in complex networks has been a hot research topic. However, the existing MOEAs for detecting overlapping communities show poor scalability to large-scale networks due to the fact that the encoding length of individuals is usually equal to the number of all nodes in the network. To this end, we suggest a reduced mixed representation based multi-objective evolutionary algorithm named RMR-MOEA for large-scale overlapping community detection, where the length of the individual is recursively reduced as the evolution proceeds. Specifically, a mixed representation is adopted for fast encoding and decoding the individual in the population, which consists of two parts: one represents all potential overlapping nodes and the other represents all non-overlapping nodes. Then, in each individual length reduction, two strategies are suggested to respectively shorten the length of each part in the mixed representation, with the aim to greatly reduce the search space. Finally, the experimental results on 10 real-world complex networks demonstrate the effectiveness of the proposed RMR-MOEA in terms of both detection performance and running time, especially on large-scale networks.

Earthquakes are one of the most costly natural disasters facing human beings, which happens without an explicit warning, therefore earthquake prediction becomes a very important and challenging task for humanity. Although many existing methods attempt to address this task, most of them use either seismic indicators (explicit features) designed by geologists, or feature vectors (implicit features) extracted by deep learning methods, to characterize an earthquake for earthquake prediction. The problem of combining these two kind of features to improve final earthquake prediction performance remains pretty much open. To this end, we propose a deep learning model named DLEP to effectively fuse the explicit and implicit features for accurate earthquake prediction. In DLEP, we adopt eight precursory pattern-based indicators as the explicit features, and use a convolutional neural network (CNN) to extract implicit features. Then, an attention-based strategy is suggested to fuse these two kinds of features well. In addition, a dynamic loss function is designed to deal with the category imbalance of seismic data. Finally, experimental results on eight datasets from different regions demonstrate the effectiveness of the proposed DLEP for earthquake prediction comparing to several state-of-the-art baselines.