An Attention-Based Multiobjective Optimization Evolutionary Algorithm for Community Detection in Attributed Networks

Community structures are fundamental in understanding the structure and functionality of complex networks. Different optimization algorithms, including both single-objective and multi-objective approaches, have been employed to address the challenge of community detection. Recently, multi-objective evolutionary algorithms (MOEAs) have attracted many researchers to identify communities in static networks. Many algorithms have been proposed to find a solution that achieves a trade-off between exploring new areas of the solution space and improving the quality of existing solutions. In this trade-off is crucial; whereas exploitation improves existing solutions, it may fail to find better solutions from insufficiently explored regions of the solution space. Therefore, mutation in evolutionary algorithms greatly impacts community detection within social networks. Conventional mutation methods usually tend to apply too much randomness, which results in convergence being less precise about finding a suitable optimum solution. This paper introduces a new mutation called community strength enhancement (CSE) to enhance the search efficiency of the Multi-Objective Evolutionary Algorithm with Decomposition (MOEA/D) and speed up the convergence of the suggested algorithm. Moreover, the proposed algorithm overcomes the limitations of traditional MOEA/D by accurately and effectively identifying communities across a wide range of social networks. The enhanced algorithm was evaluated on two groups of datasets (twenty synthetic and four real-world) using normalized mutual information (NMI) and modularity (Q) across five baseline models. Integrating the CSE mutation strategy led to significant improvements in performance, particularly under high mixing parameters and in large-scale networks, as evidenced by increased NMI and modularity scores

Various evolutionary multiobjective optimization (EMO) algorithms have been used in the field of evolutionary fuzzy systems (EFS), because EMO algorithms can easily handle multiple objective functions such as the accuracy maximization and complexity minimization for fuzzy system design. Most EMO algorithms used in EFS are Pareto dominance-based algorithms such as NSGA-II, SPEA2, and PAES. There are a few studies where other types of EMO algorithms are used in EFS. In this paper, we apply a multiobjective evolutionary algorithm based on decomposition called MOEA/D to EFS for fuzzy classifier design. MOEA/D is one of the most well-known decomposition-based EMO algorithms. The key idea is to divide a multiobjective optimization problem into a number of single-objective problems using a set of uniformly distributed weight vectors in a scalarizing function. We propose a new scalarizing function called an accuracy-oriented function (AOF) which is specialized for classifier design. We examine the effects of using AOF in MOEA/D on the search ability of our multiobjective fuzzy genetics-based machine learning (GBML). We also examine the synergy effect of MOEA/D with AOF and parallel distributed implementation of fuzzy GBML on the generalization ability.

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.

A large number of multi-objective optimization evolutionary algorithms(MOEAs) have been developed in the past two decades. To compare these methods rigorously, or to measure the performance of a particular MOEA quantitatively, a variety of performance measures have been proposed. In this paper, some existing widely-used performance measures are briefly reviewed and compared according different properties. Two new performance measures computing the convergence towards the Pareto front and the solution diversity on the Pareto front are proposed. And an outlook on how to further deepen insight in performance measures of MOEAs is given.

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

In recent years, multi-objective evolutionary optimization algorithms have shown success in different areas of research. Due to their efficiency and power, many researchers have concentrated on adapting evolutionary algorithms to generate Pareto solutions. This paper proposes a new memetic adaptive multi-objective evolutionary algorithm that is based on a three-term backpropagation network (MAMOT). This algorithm is an automatic search method for optimizing the parameters and performance of neural networks, and it relies on the use of the adaptive non-dominated sorting genetic algorithm-II integrated with the backpropagation algorithm, being used as a local search method. The presented MAMOT employs a self-adaptive mechanism toward improving the performance of the proposed algorithm and a local optimizer improving all the individuals in a population in order to obtain better accuracy and connection weights. In addition, it selects an appropriate number of hidden nodes simultaneously. The proposed method was applied to 11 datasets representing pattern classification problems, including two-class, multi-class and complex data reflecting real problems. Experiments were performed, and the results indicated that the proposed method is viable in pattern classification tasks compared to a multi-objective genetic algorithm based on a three-term backpropagation network (MOGAT) and some of the methods mentioned in the literature. The statistical analysis results of the t test and Wilcoxon signed-ranks test also show that the performance of the proposed method is significantly better than MOGAT.

In this paper we investigate the performance of well known multi-objective optimization evolutionary algorithms (MOEA) applied to the design of all-optical networks. We focused on the simultaneous optimization of the network topology and the device specifications in order to both minimize the total cost to build the network, i.e. the capital expenditure, and to maximize the overall network performance. We used the network blocking probability to assess the quality of the network service. We have considered the following five different MOEA: NSGAII, SPEA2, PESAII, PAES and MODE. In order to suggest a suitable algorithm to solve the problem, we performed a set of simulations aiming to analyze the convergence ability and the diversity of the generated solutions. We used four well known metrics to compare the achieved Pareto Fronts: hypervolume, spacing, maximum spread and coverage. From our results, we believe that the NSGAII and the SPEA2 algorithms are more suitable to solve this specific problem.

A method of designing fuzzy rule based classification systems (FRBCSs) using multi-objective optimization evolutionary algorithms (MOEAs) clearly depends on evolutionary quality. There are two types of such algorithms: Genetic Algorithms (GAs) and Swarm Intelligence (SI). Naturally arises a question how strongly utilized evolutionary algorithms influence on the efficiency of a method of designing FRBCS making this better than another. Particle swarm optimization (PSO) algorithm [13, 14] is among SI series. This paper represents an application of the multi-objective PSO algorithm with fitness sharing (MO-PSO) proposed in [8] to optimize the semantic parameters of linguistic variables and fuzzy rule selection in designing FRBCSs based on hedge algebras proposed as in [7] (using GSA-genetic simulated annealing algorithm). By simulation, MO-PSO is shown to be more efficient and produces better results than GSA-algorithm. That is to show a method of the FRBCS design is better than another one using MOEA, the same MOEA must be used.

This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (e -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( e MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the e MOEA greatly outperforms the NSGAII and the e -NSGA-II.

Recent decades have witnessed great advancements in multiobjective evolutionary algorithms (MOEAs) for multiobjective optimization problems (MOPs). However, these progressively improved MOEAs have not necessarily been equipped with scalable and learnable problem-solving strategies for new and grand challenges brought by the scaling-up MOPs with continuously increasing complexity from diverse aspects, mainly, including expensive cost of function evaluations, many objectives, large-scale search space, time-varying environments, and multitask. Under different scenarios, divergent thinking is required in designing new powerful MOEAs for solving them effectively. In this context, research studies on learnable MOEAs with machine learning techniques have received extensive attention in the field of evolutionary computation. This article begins with a general taxonomy of scaling-up MOPs and learnable MOEAs, followed by an analysis of the challenges that these MOPs pose to traditional MOEAs. Then, we synthetically overview recent advances of learnable MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive directions (i.e., learnable evolutionary discriminators for environmental selection, learnable evolutionary generators for reproduction, learnable evolutionary evaluators for function evaluations, and learnable evolutionary transfer modules for sharing or reusing optimization experience). The insight of learnable MOEAs is offered to readers as a reference to the general track of the efforts in this field.

Network robustness optimization is crucial for enhancing the resilience of industrial networks and social systems against malicious attacks. Existing studies typically evaluate the robustness by simulating the sequential removal of nodes or edges and recording the residual connectivity at each step. However, the attack simulation is computationally expensive and becomes impractical for large-scale networks. Therefore, this paper proposes a multiobjective evolutionary algorithm assisted by a graph isomorphism network (GIN)-based surrogate model to efficiently optimize network robustness. First, the robustness optimization task is formulated as a multiobjective problem that simultaneously considers network robustness against attacks and the structural modification cost. Then, a GIN-based surrogate model is constructed to approximate the robustness, replacing the expensive simulation assessments. Finally, the multiobjective evolutionary algorithm is employed to explore promising network structures guided by the surrogate model, which is continuously updated via online learning to improve both prediction accuracy and optimization performance. Experimental results in various synthetic and real-world networks demonstrate that the proposed algorithm reduces the computational cost of the robustness evaluation by about 65% while achieving comparable or even superior robustness optimization performance compared with those of baseline algorithms. These results indicate that the proposed method is practical and scalable and can be applied to enhance the robustness of industrial and social networks.

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

Community detection is one of the most active fields in complex network analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing the network structure in such cohesive subgroups to be revealed. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand index, normalized mutual information, etc). However, this type of comparison neglects the topological properties of the communities. In this paper, we present a comprehensive comparative study of a representative set of community detection methods, in which we adopt both types of evaluation. Community-oriented topological measures are used to qualify the communities and evaluate their deviation from the reference structure. In order to mimic real-world systems, we use artificially generated realistic networks. It turns out there is no equivalence between the two approaches: a high performance does not necessarily correspond to correct topological properties, and vice versa. They can therefore be considered as complementary, and we recommend applying both of them in order to perform a complete and accurate assessment.

Community detection is one of the primary tools to discover useful information that is hidden in complex networks. Some community detection algorithms for bipartite networks have been proposed from various viewpoints. However, the performance of these algorithms deteriorates when the community structure becomes unclear. Enhancing community structure remains a nontrivial task. In this paper, we propose a community detection algorithm, called ECD, that enhances community structure in bipartite networks. In the proposed ECD, the topology of a network is modified by reducing unnecessary edges that are connected to neighboring low-weight communities. Therefore, an ambiguous community structure is converted into a structure that is much clearer than the original structure. The experimental results on both artificial and real-world networks verify the accuracy and reliability of our algorithm. Compared with existing community detection algorithms using state-of-the-art methods, our algorithm has better performance.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization