Complex Network Optimization Research Articles

Synergistic Integration of Local and Global Information for Critical Edge Identification

Identifying critical edges in complex networks is a fundamental challenge in the study of complex networks. Traditional approaches tend to rely solely on either global information or local information. However, this dependence on a single information source fails to capture the multi-layered complexity of critical edges, often resulting in incomplete or inaccurate identification. Therefore, it is essential to develop a method that integrates multiple sources of information to enhance critical edge identification and provide a deeper understanding and optimization of the structure and function of complex networks. In this paper, we introduce a Global–Local Hybrid Centrality method which integrates a second-order neighborhood index, a first-order neighborhood index, and an edge betweenness index, thus combining both local and global perspectives. We further employ the edge percolation process to evaluate the significance of edges in maintaining network connectivity. Experimental results on various real-world complex network datasets demonstrate that the proposed method significantly improves the accuracy of critical edge identification, providing theoretical and methodological support for the analysis and optimization of complex networks.

Enhancing network robustness with structural prior and evolutionary techniques

Robustness optimization in complex networks is a critical research area due to its implications for the reliability and stability of various systems. However, existing algorithms encounter two key challenges: the lack of integration of prior network knowledge, leading to suboptimal solutions, and high computational costs, which hinder their practical application. To address these challenges, this paper introduces Eff-R-Net, an efficient evolutionary algorithm framework aimed at enhancing the robustness of complex networks through accelerated evolution. Eff-R-Net leverages global and local network information, featuring a novel three-part composite crossover operator. Prior network knowledge is incorporated in mutation and local search operators to expedite the construction of networks with superior robustness. Additionally, a simplified method for calculating robustness enhances efficiency, while adaptive hyper-parameters dynamically adjust operators execution probabilities for optimal evolution. Extensive evaluations on both synthetic (Scale-Free, Erdös-Rényi, and Small-World) and three infrastructure real-world networks demonstrate the superiority of Eff-R-Net. The algorithm improves robustness by 12.8% and reduces computational time by 25.4% compared to state-of-the-art algorithm in real-world network experiments. These findings underscore Eff-R-Net's versatility and potential in enhancing network robustness across different domains.

Enhancing Bicycle Trajectory Planning in Urban Environments through Complex Network Optimization

Enhancing Bicycle Trajectory Planning in Urban Environments through Complex Network Optimization

Vital Nodes Identification via Evolutionary Algorithm With Percolation Optimization in Complex Networks

Vital Nodes Identification via Evolutionary Algorithm With Percolation Optimization in Complex Networks

Complex Network Optimization for Fixed-Time Continuous Action Iteration Dilemma by Using Reinforcement Learning

Complex Network Optimization for Fixed-Time Continuous Action Iteration Dilemma by Using Reinforcement Learning

A Review of Community Detection Based on Modularity Optimization in Complex Networks

A Review of Community Detection Based on Modularity Optimization in Complex Networks

Scalability and Performance Optimization Strategies in Large-Scale System Architectures

This paper aims to break away from traditional thinking paradigms by introducing theories and methods from complexity science to provide innovative and effective solutions for scalability and performance optimization of large-scale system architectures. The paper first constructs a complex network model for large-scale system architecture, which includes nodes (services), edges (interactions), and global attributes, along with dynamic models reflecting key metrics such as system performance and scalability, providing a theoretical foundation for subsequent research. Subsequently, from a complexity perspective, it innovatively proposes scalability strategies, including adaptive scalability strategies for complex network optimization, data-driven complex system regulation, and elastic computing and service orchestration mechanisms. In terms of performance optimization, it applies tools such as complex systems observation theory and network flow theory to explore insights and breakthroughs in complexity related to full-link performance monitoring and diagnostics, asynchronous communication, task scheduling, and software-hardware collaborative optimization. Finally, the paper summarizes the research findings, distilling the core concepts and methodological innovations of scalability and performance optimization strategies from a complexity perspective. It also looks ahead to the prospects of further integrating complexity science and information technology in the future, along with potential research topics in new scenarios and challenges.

Graph Representation Learning for Wireless Communications

Wireless networks are inherently graph-structured, in which, graph representation learning can be utilized to solve complex network optimization problems. In graph representation learning, feature vectors for each entity in the network are calculated such that they could capture spatial and temporal dependencies in their local and global neighborhoods. Specifically, graph neural networks (GNNs) are powerful tools to solve these complex problems because of their expressive representation and reasoning power. In this paper, the potential of graph representation learning and GNNs in wireless networks is presented. An overview of graph representation learning is provided which covers the fundamentals and concepts such as feature design over graphs, GNNs, and their design principles. The potential of graph representation learning in wireless networks is presented via a few exemplary use cases and some initial results on the GNNbased access point selection for cell-free massive Multiple-Input Multiple-Output (MIMO) systems.

Conflicting evidence fusion using a correlation coefficient-based approach in complex network

Dempster–Shafer evidence theory (D–S theory) can effectively deal with uncertain information and it is one of the effective data fusion methods. However, Dempster’s combination rule of D–S theory often produces counter-intuitive fusion results when the handled body of evidence (BOE) is highly conflicting with each other. Therefore, many new methods have been gradually proposed to optimize BOE to avoid the counter-intuitive fusion results. In this work, inspired by the complex network, a body of evidence is compared to a node, therefore multiple nodes composed of the BOEs constitute a complex network structure, and a correlation coefficient is adopted to measure the degree of correlation between two BOEs. The direct and indirect interaction weights of each node are determined through the direct and indirect interactions among the nodes to reflect their importance in the complex network. After that, the total weight of each BOE is calculated through using the direct and indirect weights. Finally, after modifying the original BOE with weight factor, the final result is obtained after information fusion by using Dempster’s combination rule. This work analyses a practical application case based on the proposed evidential-weighting complex networks in D–S theory. The experiment result shows that the complex network optimization algorithm proposed in this work possesses a good convergence and has significantly improved the counter-intuitive fusion results brought about by the highly conflicting evidence with Dempster’s combination rule.

4G/5G Cell-level multi-indicator forecasting based on dense-MLP

With the development of 4G/5G, the rapid growth of traffic has caused a large number of cell indicators to exceed the warning threshold, and network quality has deteriorated. It is necessary for operators to solve the congestion in advance and effectively to guarantee the quality of user experience. Cell-level multi-indicator forecasting is the foundation task for proactive complex network optimization. In this paper, we propose the 4G/5G Cell-level multi-indicator forecasting method based on the dense-Multi-Layer Perceptron (MLP) neural network, which adds additional fully-connected layers between non-adjacent layers in an MLP network. The model forecasted the following week's traffic indicators of 13000 cells according to the six-month historical indicators of 65000 cells in the 4G&5G network, which got the highest weighted MAPE score (0.2484) in the China Mobile problem statement in the ITU-T AI/ML in 5G Challenge 2021. Furthermore, the proposed model has been integrated into the AsiaInfo 4G/5G energy-saving system and deployed in Jiangsu Province of China.

NetXplain: Real-time explainability of graph neural networks applied to networking

Recent advancements in Deep Learning (DL) have revolutionized the way we can efficiently tackle complex optimization problems. However, existing DL-based solutions are often considered as black boxes with high inner complexity. As a result, there is still certain skepticism among the networking industry about their practical viability to operate data networks. In this context, explainability techniques have recently emerged to unveil why DL models make each decision. This paper focuses on the explainability of Graph Neural Networks (GNNs) applied to networking. GNNs are a novel DL family with unique properties to generalize over graphs. As a result, they have shown unprecedented performance to solve complex network optimization problems. This paper presents NetXplain, a novel real-time explainability solution that uses a GNN to interpret the output produced by another GNN. In the evaluation, we apply the proposed explainability method to RouteNet, a GNN model that predicts end-to-end QoS metrics in networks. We show that NetXplain operates more than 3 orders of magnitude faster than state-of-the-art explainability solutions when applied to networks up to 24 nodes, which makes it compatible with real-time applications; while demonstrating strong capabilities to generalize to network scenarios not seen during training.

Controllability and Optimization of Complex Networks Based on Bridges

In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.

Dynamic Repair and Robust Optimization of Complex Networks

Network repair is indispensable for maintaining network security. Conventional static repair is relatively inefficient. In this study, by considering the energy transfer between nodes, a dynamic repair model was established. The fundamental reason for the secondary failure of repaired nodes during the dynamic repair process is the coupling structure of failure networks. A dynamic repair strategy was proposed that can effectively prevent the secondary failure of repair nodes influenced by energy during repair and can cause the redundant capacity of repair nodes to be used reasonably. By turning off the energy transfer function of the link to control the excessive flow of energy into the repair node to avoid the occurrence of secondary failure; on the other hand, by sharing part of the load of the failure node, realize the rational use of the redundant capacity of the repair node to reduce the impact of the failure node on the overall function of the network. The proposed strategy mitigated the effect of failure nodes on network functions and substantially improved the recovery efficiency of network functions. Furthermore, redundant edges, behaving as energy redundant links in a network structure, can considerably improve the robustness of the network by optimizing the removal of redundant edges. Dynamic repair is not only an efficient repair method but also a highly flexible choice for network repair.

A multi-agent complex network algorithm for multi-objective optimization

To deal with the multi-objective optimization problems (MOPs), this study proposes a new Multi-Objective Multi-Agent Complex Network Optimization Algorithm called MOMCNA based on the idea of Cellular genetic algorithm (CGA) and the Multi-agent complex network. Compared with the traditional CGA for multi objective problem, the individuals in the population of MOMCNA have more features of intelligent agent, the new form of neighborhood for the population, private archive for individuals, the new strategy of “local-global” genetic operator and the chaotic mutation are proposed in the new algorithm to balance the convergence and diversity of the algorithm. Seventeen unconstrained multi-objective optimization problems and seven many-objective problems are introduced and tested to evaluate the new algorithm, in addition, the classical traffic assignment problem based on different system optimum principle is also established to evaluate the new algorithm. The comparison between MOMCNA and other classical algorithms shows that the proposed MOMCNA proves to be competitive in dealing with multi-objective and many-objective optimization problems and the structure of the complex network made up of population also has effect on algorithm’s performance.

Comparison of Community Structure Partition Optimization of Complex Networks by Different Community Discovery Algorithms

In reality, complex problems can be transformed into complex networks. Through the community partition of complex networks, the relationship between nodes can be found more clearly. This paper briefly introduced three algorithms for community structure partition of complex networks, which were based on the similarity of common neighbor nodes, ant colony algorithm and density peak clustering, and compared the performance of the three algorithms by using six artificial networks whose chaotic factors gradually increased and two real networks in MATLAB software. The results suggested that the increase of chaotic factors in the artificial network reduced the normalized mutual information (NMI) of the partition results calculated by the three algorithms, but the NMI of the algorithm based on density peak clustering in the same artificial network was the highest, the next was the algorithm based on ant colony algorithm, and the lowest was the algorithm based on the similarity of common neighbor nodes; for the real network, the modularity of the algorithm based on density peak clustering was the highest, the algorithm based on ant colony algorithm was the second, and the algorithm based on the similarity of common neighbor nodes was the lowest. In conclusion, the more fuzzy the community structure is in the complex network, the lower the performance of the partition algorithm is, and the algorithm based on density peak clustering has the best performance.

Redundancy Optimization of Complex Networks with Capacity Delay Related Reliability Integrated Performance Measure

In this paper, an efficient heuristic method is presented for deciding the redundancy of complex networks in a constrained environment in an optimal manner. The proposed method is a heuristic approach to optimally maximize the Capacity Delay Related Reliability (CDRR) measure of the complex network by selecting the optimal component for each stage without violating the constraints. The proposed method is named as Proposed Heuristic Method (PHM). The problem of Redundancy Allocation Problem (RAP) is demonstrated for a five unit complex structure considering linear constraints and the solution obtained using PHM are compared and found to be better with existing heuristic methods.

Surrogate-Assisted Robust Optimization of Large-Scale Networks Based on Graph Embedding

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 article 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. The 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.

Shallow and deep neural network training by water wave optimization

It is well known that the performance of artificial neural networks (ANNs) is significantly affected by their structure design and parameter selection, for which traditional training methods have drawbacks such as long training times, over-fitting, and premature convergence. Evolutionary algorithms (EAs) have provided an effective tool for ANN parameter optimization. However, simultaneously optimizing ANN structures and parameters remains a difficult problem. In this study, we adapt water wave optimization (WWO), a relatively new EA, for optimizing both the parameters and structures of ANNs, including classical shallow ANNs and deep neural networks (DNNs). We use a variable-dimensional solution encoding to represent both the structure and parameters of an ANN, and adapt WWO propagation, refraction, and breaking operators to efficiently evolve variable-dimensional solutions to solve the complex network optimization problems. Computational experiments on a variety of benchmark datasets show that the WWO algorithm achieves a very competitive performance compared to other popular gradient-based algorithms and EAs.

Nonlinear Negotiation Approaches for Complex-Network Optimization: A Study Inspired by Wi-Fi Channel Assignment

At the present time, Wi-Fi networks are everywhere. They operate in unlicensed radio-frequency spectrum bands (divided in channels), which are highly congested. The purpose of this paper is to tackle the problem of channel assignment in Wi-Fi networks. To this end, we have modeled the networks as multilayer graphs, in a way that frequency channel assignment becomes a graph coloring problem. For a high number and variety of scenarios, we have solved the problem with two different automated negotiation techniques: a hill-climber and a simulated annealer. As an upper bound reference for the performance of these two techniques, we have also solved the problem using a particle swarm optimizer. Results show that the annealer negotiator behaves as the best choice because it is able to obtain even better results than the particle swarm optimizer in the most complex scenarios under study, with running times one order of magnitude below. Finally, we study how different properties of the network layout affect to the performance gain that the annealer is able to obtain with respect to the particle swarm optimizer.

Enhancing network synchronization by phase modulation.

Due to time delays in signal transmission and processing, phase lags are inevitable in realistic complex oscillator networks. Conventional wisdom is that phase lags are detrimental to network synchronization. Here we show that judiciously chosen phase lag modulations can result in significantly enhanced network synchronization. We justify our strategy of phase modulation, demonstrate its power in facilitating and enhancing network synchronization with synthetic and empirical network models, and provide an analytic understanding of the underlying mechanism. Our work provides an alternative approach to synchronization optimization in complex networks, with insights into control of complex nonlinear networks.