<b>Enhanced Multi-Objective Evolutionary Algorithm for Community Detection Using a Community Strength-Based Mutation Strategy</b>

Community detection is an important topic in complex network analysis which can explore valuable relationships in the networks, such as protein-protein interactions, advertisement recommendations, etc. Recently, the structure and attributes of a network are expected to be integrated to obtain a more accurate community division. But existing community detection algorithms based on multiobjective optimization evolutionary algorithms (MOEAs) for attributed networks have two common problems. First, their encoding strategies completely depend on the network structure, which limits their use of attribute information in search. Second, the calculation of the attribute objective function is time-consuming. In this paper, we propose a novel algorithm that combines the nodes’ embedding vectors generated by a Skip-Gram model with an attention-based multiobjective optimization evolutionary algorithm to discover overlapping communities on networks with attributes. With the help of embedding vectors, the attention-based encoding strategy can overcome the problem of the limited searching capability of traditional MOEAs’ encoding schemes that depend only on a network structure, and an attribute objective function based on embedding vectors is designed which can be calculated in linear time to improve the computational efficiency. The statistical results in artificial and real-world networks demonstrate the feasibility and effectiveness of the proposed method.KeywordsCommunity detectionMultiobjective optimizationAttributed networkAttention-based encoding

Balancing topology structure and node attribute in evolutionary multi-objective community detection for attributed networks

Community detection is crucial in the analysis of social networks. Its main goal is to find groups of users densely connected among them, and sparsely connected between themselves. There are so many algorithms which makes it difficult for researchers to choose the best one for a specific dataset. In this paper, we provide a thorough comparison between five Community Detection (CD) algorithms- Girman-Newman (GN), Clauset-Newman-Moore (CNM), Label Propagation Algorithm (LPA), Louvain and Leiden. To evaluate in real social network datasets like Zachary's Karate Club, Dolphin networks and bigger ones such as Facebook, Twitter, LinkedIn along with citation networks we used different metrics modularity and NMI. We employed Normalized Mutual Information (NMI) to quantify the agreement of detected communities with their true ground-truth score and modularity for evaluating the overall quality of partitions given by diverse methods. Our experiments show that greedy and modularity-optimization algorithms are particularly well-suited. Notably, the Leiden algorithm had a better modularity value than Louvain (Q = 0.9141 and Q = 0.9051 of LinkedIn Network respectively) in most of the dataset. The NMI plot provided more explanation about Clauset-Newman-Moore (CNM), Louvain and Label Propagation Algorithm (LPA)which are in good agreement on community detection and their NMI score. These results would allow us to choose more rationally among the different community detection algorithms for social network analysis, by providing accurate quantitative benchmarks.

Community Detection method based on Random walk and Multi objective Evolutionary algorithm in complex networks

A multi-objective adaptive evolutionary algorithm to extract communities in networks

As dynamic systems, social networks exhibit continuous topological changes over time, and are typically modeled as temporal networks. In order to understand their dynamic characteristics, it is essential to investigate temporal community detection (TCD), which poses significant challenges compared to static network analysis. These challenges arise from the need to simultaneously detect community structures and track their evolutionary behaviors. To address these issues, we propose TCDA-NE, a novel TCD algorithm that combines evolutionary clustering with convex non-negative matrix factorization (Convex-NMF). Our method innovatively integrates community structure into network embedding, preserving both microscopic details and community-level information in node representations while effectively capturing the evolutionary dynamics of networks. A distinctive feature of TCDA-NE is its utilization of a common-neighbor similarity matrix, which significantly enhances the algorithm’s ability to identify meaningful community structures in temporal networks. By establishing coherent relationships between node representations and community structures, we optimize both the Convex-NMF-based representation learning model and the evolutionary clustering-based TCD model within a unified framework. We derive the updating rules and provide rigorous theoretical proofs for the algorithm’s validity and convergence. Extensive experiments on synthetic and real-world social networks, including email and phone call networks, demonstrate the superior performance of our model in community detection and tracking temporal network evolution. Notably, TCDA-NE achieves a maximum improvement of up to 0.1 in the normalized mutual information (NMI) index compared to state-of-the-art methods, highlighting its effectiveness in temporal community detection.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

Community detection is a fundamental task in network analysis in that it can express the characteristics of individual behaviors and the relationships between individuals in complex networks, thus revealing the functional and structural properties of various networks. However, as networks become larger and larger, how to quickly and accurately detect the community structure of large-scale networks has become a huge challenge nowadays. In this paper, an efficient algorithm, called Local Search for Community Detection (LSCD), is proposed to solve the multi-objective community detection problem. In the algorithm, an iterated local search is performed to search for non-dominated solutions in the solution space. To search for higher quality non-dominated solutions, this paper employs a learning-based strategy to select nodes in each round of the search. The strategy learns from the historical movement of the nodes and changes their selection probability according to their importance. Moreover, to search the entire solution space, this paper proposes a local search strategy that restricts one objective with a bound for a certain round, as well as an adaptive bound update mechanism. Experimental results on synthetic and real-world networks show that the proposed algorithm outperforms several state-of-the-art algorithms in terms of multi-objective optimization performance and accuracy in detecting the community structure of complex networks, since it performs best on 44 instances out of 46 in terms of Modularity (Q) and 29 out of 39 in terms of Normalized Mutual Information (NMI). In addition, the results show that the proposed algorithm has a good ability to handle large-scale networks.

A cascade information diffusion based label propagation algorithm for community detection in dynamic social networks

The detection of communities is an important problem in social network analysis, which has applications in various domains like sociology, biology, computer science, and marketing. In this context, genetic algorithms have proven to be effective in detecting communities by optimizing the modularity score of the network. The proposed work in this research paper uses an elitism-based genetic algorithm with some modified crossover and mutation techniques to detect communities in social networks. The proposed methodology incorporates the concepts of elitism, N-point crossover, and inverse mutation to enhance the effectiveness of genetic algorithms in solving optimization problems. The idea introduced in this article significantly extends the current understanding of optimization and evolutionary algorithms. We present an advanced methodology that leverages various genetic operators to improve the performance of a genetic algorithm in solving community detection problems in complex networks. Numerous research papers have extensively showcased the practicality of evolutionary and swarm-based algorithms in addressing real-world problems across diverse domains like viral marketing, link prediction, influence maximization, political polarization, etc. Hybridizing these algorithms with other optimization techniques has improved the performance and convergence speed, leading to enhanced optimization outcomes.

Community detection in graphs can be viewed as the estimation of a partition map that remains stable under admissible perturbations of graph topology and node attributes. While modern graph neural networks (GNNs) achieve strong empirical accuracy, they often exhibit severe assignment drift under minor perturbations, leading to illusory community structures. In this work, we propose DISPEL-GNN, a stability-aware graph learning framework that integrates spectral operator regularization, Bayesian uncertainty modeling, and risk-aware dynamic attention for perturbation-bounded community detection. The model explicitly constrains graph operators through uniform spectral norm bounds, high-frequency energy suppression, and commutator alignment while dynamically modulating message passing based on node-level spectral risk and epistemic uncertainty. We further formalize instability via assignment of drift functional and establish perturbation bounds linking drift to operator norms and spectral gaps, complemented by a PAC-Bayesian generalization guarantee. Extensive experiments on real-world benchmarks including Cora, Citeseer, Pubmed, Cora-Full, and DBLP demonstrate that DISPEL-GNN consistently reduces assignment drift by 18–35% under feature noise and edge perturbations while improving clustering quality with up to +3.0 NMI and +0.04 ARI compared to strong baselines such as GAT and Bayesian GNNs. The normalized mutual information (NMI), adjusted Rand index (ARI), and PAC-Bayesian (PAC) constraints serve as evaluative and theoretical instruments in this study. Additional studies on synthetic graphs with controlled spectral gaps confirm that the proposed method maintains stable community assignments in low-gap regimes where classical spectral and GNN-based methods degrade sharply. These results establish DISPEL-GNN as a mathematically grounded and practically effective framework for robust and interpretable community detection. A metric-wise dominance analysis shows that DISPEL-GNN achieves metric-wise dominance across most accuracy and robustness criteria, with minor tradeoffs in modularity on selected datasets. These results indicate that explicitly modeling stability and uncertainty provides a principled pathway toward reliable and interpretable community detection in noisy graph environments.

In this paper we propose a methodology based on an evolutionary multiobjective optimization algorithm for the problem of up-grading (expansion) the physical topology of transparent optical networks. The aim is to define the new topology layout and the specification of the new optical devices that should be deployed in an existing network in order to improve its performance, considering simultaneously the total installation cost (capital cost) and the total network blocking probability (performance criteria). To accomplish that, we propose a capital cost model for the network. We considered the following physical layer impairments: losses in optical devices, amplified spontaneous emission in optical amplifier and homodyne crosstalk in optical cross connect. The multiobjective optimization evolutionary algorithm used in the optimization process is the NSGA-II. Our proposed methodology can solve the expand physical topology design problem taking into account the physical layer impairments and the capital costs simultaneously. We also present a case study to show the effectiveness of our methodology.

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

Multi-criteria algorithms for portfolio optimization under practical constraints

We critically evaluate normalized mutual information (NMI) as an evaluation metric for community detection. NMI exaggerates the leximin method’s performance on weak communities: Does leximin, in finding the trivial singletons clustering, truly outperform eight other community detection methods? Three NMI improvements from the literature are AMI, rrNMI, and cNMI. We show equivalences under relevant random models, and for evaluating community detection, we advise one-sided AMI under the $$\mathbb {M}_\mathbf{all }$$ model (all partitions of $$n$$ nodes). This work seeks (1) to drive a conversation on robust measurements (2) to advocate evaluations which do not give “free lunch”.