Multiplex graphs are widely used to model multi-relational complex systems and play an important role in various real-world scenarios, such as financial systems and social networks. Hence, detecting anomalous samples in multiplex graph becomes crucial to ensure cybersecurity and stability. Although existing homogeneous graph anomaly detection (GAD) methods can be applied to deal with multiplex graphs, they still face two major challenges: 1) Due to the multiplicity and complexity of relations in multiplex graphs, homogeneous GAD models fail to effectively capture anomalous behaviors that correlate with diverse relational patterns. 2) In real-world applications, malicious entities usually disguise themselves through various camouflage strategies, making it difficult to capture subtle anomalous features via single-relation analysis. To address these challenges, we propose a novel unsupervised anomaly detection method for multiplex graphs based on Similarity-constrained Fusion Graph Autoencoder (SFGA). In SFGA, we design a multiplex graph autoencoder and introduced a cross-plex attention module at the model bottleneck to achieve comprehensive modeling of cross-relation anomaly patterns. Then, a similarity balancing strategy is proposed to constrain node representations at the bottleneck from both local and global perspectives, enhancing the discriminative power against camouflaged anomalies of autoencoder and enabling more effective identification of anomalous nodes with overlapping or deceptive patterns. Extensive experiments are conducted on both synthetic and real-world datasets at varying scales, and the results demonstrate that our proposed method outperforms state-of-the-art approaches by a large margin.

In the current era of globalization, with increasing vessel cargo and limited port resources, the operational efficiency of container terminals is of paramount importance. Berth allocation and quay crane allocation problems (BACAPs) emerge as pivotal focal points, especially in large-scale container terminals. Although preventive maintenance for quay cranes is crucial for reducing equipment failures and widely implemented in real-world operations, it is often overlooked in existing studies. Lately, few methods are proposed considering maintenance activities. However, their performance are unsatisfied in terms of large-scale problems and hard to meet the requirement of efficiency. To deal with this challenge, in this paper, we present a mixed integer bi-objective optimization model and further propose a novel algorithm to address the large-scale BACAP with quay crane maintenance activities. This model aims to minimize vessel turnaround durations and the penalty of unscheduled maintenance. Meanwhile, based on NSGA-II, the model called RTAA utilizes a novel decoding method withRecurrentTemporal berthAllocation and quay craneAssignment, which can greatly reduce the probability of generating infeasible solutions in a heuristic way. Moreover, the island model is involved to improve the efficiency and parallelism of the model and enhance the diversity of the Pareto-front solutions. Compared to the existing methods in both small and large instances, the RTAA demonstrates its efficacy in discovering superior and more diverse solutions. In particular, for large-scale problems involving 100 vessels, as well as more berths and quay cranes, our model still delivers superior performance with a significant reduction in computation time. Additionally, our approach shows excellent scalability, as it can be easily adapted to scenarios that do not consider maintenance activities.

In real-world applications, spectral Graph Neural Networks (GNNs) are powerful tools for processing diverse types of graphs. However, a single GNN often struggles to handle different graph types—such as homogeneous and heterogeneous graphs—simultaneously. This challenge has led to the manual design of GNNs tailored to specific graph types, but these approaches are limited by the high cost of labor and the constraints of expert knowledge, which cannot keep up with the rapid growth of graph data. To overcome these challenges, we introduce AutoSGNN, an automated framework for discovering propagation mechanisms in spectral GNNs. AutoSGNN unifies the search space for spectral GNNs by integrating large language models with evolutionary strategies to automatically generate architectures that adapt to various graph types. Extensive experiments on nine widely-used datasets, encompassing both homophilic and heterophilic graphs, demonstrate that AutoSGNN outperforms state-of-the-art spectral GNNs and graph neural architecture search methods in both performance and efficiency.

In the field of single objective optimization algorithms, learned evolutionary algorithms have achieved success in obtaining better performance than human-designed strategies. However, these learnable evolutionary algorithms are only applicable to single-objective optimization and cannot be applied to multi-objective optimization problems. In this study, we parameterize the mutation and crossover operators using the multi-head self-attention and the selection operator using a lightweight multilayer perceptron. We utilize the evolution strategy to train their parameters across multiple multi-objective optimization problems, resulting in the development of the Meta-Learned Multi-Objective Genetic Algorithm (Meta-MOGA). We compare Meta-MOGA with other multi-objective evolutionary algorithms on various test problems and evaluate its performance on untrained MOPs. The results demonstrate that our Meta-MOGA exhibits potential and generalizability.

In real-world scenarios, most complex systems can be generally modelled as homogenous or heterogenous networks. Therefore, downstream tasks (e.g., node/graph classification, node clustering) based on these two types of graphs become ubiquitous and have drawn considerable attentions in recent years. Existing literatures on node classification mainly focuses on either homogeneous or heterogeneous graphs, while research on effectively carrying out node classification tasks on both types of graphs simultaneously still under-exploited. To fill this gap, we propose a universal Graph Neural Network architecture based on Subgraph and Subhypergraph (SS-GNN) with feature-enhanced strategy for node embedding on both homogeneous and heterogeneous graphs. Through construction of subgraph and subhypergraph with same-class nodes, our model can simultaneously deal with homogeneous and heterogeneous graphs. Graph attention modules are especially designed to embed subgraphs of same-class nodes to learn the internal topological structure and local community structure within the original graph. Additionally, to capture high-order features of graph and enhance the embedding representations of nodes, we also utilize hypergraph attention modules to embed subhypergraphs of same-class nodes. Unlike other approaches that rely on pre-defined meta-paths, our model can be readily applied to most real-world applications without requiring any domain knowledge. Finally, we conduct extensive experiments on three homogeneous and three heterogeneous real-world graphs to demonstrate the effectiveness of SS-GNN. The experimental results for node classification and clustering tasks not only show the superior performance of our proposed model compared to state-of-the-art, but also demonstrate its potentially good interpretability for graph analysis. This work may provide some enlightening insights to the study on universality of graph foundation model.

Graphs are widely used to model networks in real-world applications, with heterogeneous graph neural networks gaining increasing attention in recent years. Existing methods generally rely on first-order or high-order neighbors to capture semantic relationships, where metapath-based approaches are the most popular ones. However, existing metapath-based models not only require predefined metapaths based on prior knowledge, but also lack the consideration of metapath sequence modeling. Additionally, labeled data are scarce in massive graph data, and existing self-supervised or semisupervised models heavily rely on data enhancement strategies and complex frameworks. To address these limitations, we propose a self-supervised heterogeneous graph attention model (HGAM) based on adaptable step-size metapaths. Our model requires no prior knowledge to select the type of metapath and can adaptively capture the specific step-size metapath with high importance. The adaptable step-size metapaths module not only considers the attention weight in different step sizes, but also pays attention to the changing trend of attention, which expands the receptive field of the model and integrates global information preferably. To alleviate labeled data scarcity, our model employs a dual contrastive learning strategy. HGAM learns global representations by contrasting a high-order meta-graph against nodes, while preserving local structure through a cross-view comparison of first-order and high-order semantics. Extensive experiments on three different types of tasks, including node classification, clustering, and link prediction, are conducted on real-world datasets. Experimental results demonstrate that HGAM achieves superior performance compared to state-of-the-art methods.

Conducting functional connectivity analysis on functional magnetic resonance imaging (fMRI) data presents a significant and intricate challenge. Contemporary studies typically analyze fMRI data by constructing high-order functional connectivity networks (FCNs) due to their strong interpretability. However, these approaches often overlook temporal information, resulting in suboptimal accuracy. Temporal information plays a vital role in reflecting changes in blood oxygenation level-dependent signals. To address this shortcoming, we have devised a framework for extracting temporal dependencies from fMRI data and inferring high-order functional connectivity among regions of interest (ROIs). Our approach postulates that the current state can be determined by the FCN and the state at the previous time, effectively capturing temporal dependencies. Furthermore, we enhance FCN by incorporating high-order features through hypergraph-based manifold regularization. Our algorithm involves causal modeling of the dynamic brain system, and the obtained directed FC reveals differences in the flow of information under different patterns. We have validated the significance of integrating temporal information into FCN using four real-world fMRI datasets. On average, our framework achieves 12% higher accuracy than non-temporal hypergraph-based and low-order FCNs, all while maintaining a short processing time. Notably, our framework successfully identifies the most discriminative ROIs, aligning with previous research, and thereby facilitating cognitive and behavioral studies.

In many real-world networks, the structural connections of networks and the attributes about each node are always available. We typically call such graphs attributed networks, in which attributes always play the same important role in community detection as the topological structure. It is shown that the very existence of overlapping communities is one of the most important characteristics of various complex networks, while the majority of the existing community detection methods was designed for detecting separated communities in attributed networks. Therefore, it is quite challenging to detect meaningful overlapping structures with the combination of node attributes and topological structures. Therefore, in this article, we propose a multiobjective evolutionary algorithm based on the similarity attribute for overlapping community detection in attributed networks (MOEA-SA$_{OV}$ ). In MOEA-SA$_{OV}$ , a modified extended modularity $EQ_{OV}$ , dealing with both directed and undirected networks, is well designed as the first objective. Another objective employed is the attribute similarity $S_{A}$ . Then, a novel encoding and decoding strategy is designed to realize the goal of representing overlapping communities efficiently. MOEA-SA$_{OV}$ runs under the framework of the nondominated sorting genetic algorithm II (NSGA-II) and can automatically determine the number of communities. In the experiments, the performance of MOEA-SA$_{OV}$ is validated on both synthetic and real-world networks, and the experimental results demonstrate that our method can effectively find Pareto fronts about overlapping community structures with practical significance in both directed and undirected attributed networks.

Graph embedding methods aim to represent nodes in the network into a low-dimensional and continuous vector space while preserving the topological structure and varieties of relational information maximally. Nowadays the structural connections of networks and the attribute information about each node are more easily available than before. As a result, many community detection algorithms for attributed networks have been proposed. However, the majority of these methods cannot deal with the overlapping community detection problem, which is one of the most significant issues in the real-world complex network study. In addition, it is quite challenging to make full use of both structural and attribute information instead of only focusing on one part. To this end, in this paper we innovatively combine the graph embedding with multiobjective evolutionary algorithms (MOEAs) for overlapping community detection problems in attributed networks. As far as I am concerned, MOEA is first used to integrate with graph embedding methods for overlapping community detection. We term our method as MOEA-GEOV, which can automatically determine the number of communities without any prior knowledge and consider topological structure and vertex properties synchronously. In MOEA-GEOV, two objective functions concerning community structure and attribute similarity are carefully designed. Moreover, a heuristic initialization method is proposed to get a relatively good initial population. Then a novel encoding and decoding strategy is designed to efficiently represent the overlapping communities and corresponding embedded representation. In the experiments, the performance of MOEA-GEOVis validated on both single and multiple attribute real-world networks. The experimental results of community detection tasks demonstrate our method can effectively obtain overlapping community structures with practical significance.

The complex network is an important tool to represent relational data in nature and human society, which has been widely applied in various real-world application scenarios. A key issue for analyzing the features of networks is to represent the characteristic information in the network with rationality. Network embedding, attracting plenty of attention recently, aims to convert network information into a low-dimensional space while maintaining the structure and properties of the network maximally. Most of the existing network embedding methods intend to preserve the pairwise relationship or similarity between nodes, but the community structure, which is one of the most important features of complex networks, is largely ignored. In this article, we propose a novel network embedding method based on evolutionary algorithm (EA), termed as EA-NECommunity, which can preserve both the local proximity of nodes and the community structure of the network by optimizing a carefully designed objective function. The number of communities in the network can be automatically determined without any prior knowledge. Moreover, taking the intrinsic properties of the network embedding problems in mind, we design a local search operator based on multidirectional search which can effectively find feasible solutions. In the experiments, we first visualize the embedding representation obtained by different algorithms, and then use the problems of node clustering, node classification, and link prediction to further validate the quality of the embedding representation obtained. The experimental results show that EA-NECommunity outperforms other state-of-the-art algorithms on both the real life and synthetic networks.