Community detection is a widely researched area in network science. In recent years, multi-objective evolutionary algorithms (MOEAs) have been widely used in community detection. Continuous coding is able to transform the discrete problem into a continuous one. However, the original continuous coding ignores the relationship between node structures, resulting in a low quality encoded population, which degrades the performance of community detection. In addition, continuous coding needs to be decoded into label-based coding in the optimization process to compute the objective function. To alleviate this, we design the surrogate model adaptive switching strategy that selects the optimal surrogate model for the task. Then, the adaptive surrogate-assisted evolutionary multi-objective community detection algorithm with core node learning is proposed. A core node learning method is used to improve the connection between nodes in augmented sequential coding, which helps initialize the population using the node similarity matrix. The core nodes of the network are then obtained based on the node weights. Thereafter, these core nodes are used to construct a surrogate model between the continuous coding and the objective function. The surrogate model is updated during the optimization process, while effectively improves the accuracy and efficiency of community detection tasks. Experimental results on synthetic and real networks show that the algorithm has better performance compared with seven community detection algorithms.

Problem transformation based optimization for large-scale multi-objective problems usually have excellent con-vergence yet insufficient diversity. Improving the distributivity of the search subspace in the decision space may prompt diversity to some extent. Therefore, we intend to propose a novel search subspace construction method to enhance the diversity. Firstly, a set of reference solutions is obtained by the algorithm. New solutions can be generated by a linear combination of two reference solutions, and thus locating a search subspace by these two reference solutions. Furthermore, a set of reference solutions locates a series of subspaces well-distributed in the original decision space. Once subspaces are determined, the algorithm firstly searches the subspaces to find solutions close to the Pareto set (PS) efficiently. Then, it searches the original decision space based on these solutions to make the population cover the PS uni-formly. Compared with three state-of-the-art large-scale multi-objective algorithms on well-known benchmark suite with up to 2000 decision variables, the experimental results demonstrate the competitive performance of the proposed algorithm.

Evolutionary multiobjective clustering (MOC) algorithms have shown promising potential to outperform conventional single-objective clustering algorithms, especially when the number of clusters k is not set before clustering. However, the computational burden becomes a tricky problem due to the extensive search space and fitness computational time of the evolving population, especially when the data size is large. This article proposes a new, hierarchical, topology-based cluster representation for scalable MOC, which can simplify the search procedure and decrease computational overhead. A coarse-to-fine-trained topological structure that fits the spatial distribution of the data is utilized to identify a set of seed points/nodes, then a tree-based graph is built to represent clusters. During optimization, a bipartite graph partitioning strategy incorporated with the graph nodes helps in performing a cluster ensemble operation to generate offspring solutions more effectively. For the determination of the final result, which is underexplored in the existing methods, the usage of a cluster ensemble strategy is also presented, whether k is provided or not. Comparison experiments are conducted on a series of different data distributions, revealing the superiority of the proposed algorithm in terms of both clustering performance and computing efficiency.

In the past several years, it has become apparent that the effectiveness of Pareto-dominance-based multiobjective evolutionary algorithms deteriorates progressively as the number of objectives in the problem, given by M , grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically M ≥ 4 ). As a consequence, research efforts have been driven in the general direction of developing solution ranking methods that do not rely on Pareto dominance (e.g., decomposition-based techniques), which can provide sufficient selection pressure. However, it is still a nontrivial issue for many existing non-Pareto-dominance-based evolutionary algorithms to deal with unknown irregular Pareto front shapes. In this article, a new many-objective evolutionary algorithm based on the generalization of Pareto optimality (GPO) is proposed, which is simple, yet effective, in addressing many-objective optimization problems. The proposed algorithm used an "( M-1 ) + 1" framework of GPO dominance, ( M-1 )-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply M symmetrical cases of ( M-1 )-GPD, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed algorithm is very competitive with the state-of-the-art methods to which it is compared, on a variety of scalable benchmark problems. Moreover, experiments on three real-world problems have verified that the proposed algorithm can outperform the others on each of these problems.

Dynamic multiobjective optimization problems (DMOPs) challenge multiobjective evolutionary algorithms (MOEAs) because those problems change rapidly over time. The class of DMOPs whose objective functions change over time steps, in ways that exhibit some hidden patterns has gained much attention. Their predictability indicates that the problem exhibits some correlations between solutions obtained in sequential time periods. Most of the current approaches use linear models or similar strategies to describe the correlations between historical solutions obtained, and predict the new solutions in the following time period as an initial population from which the MOEA can begin searching in order to improve its efficiency. However, nonlinear correlations between historical solutions and current solutions are more common in practice, and a linear model may not be suitable for the nonlinear case. In this paper, we present a support vector regression (SVR)-based predictor to generate the initial population for the MOEA in the new environment. The basic idea of this predictor is to map the historical solutions into a high-dimensional feature space via a nonlinear mapping, and to do linear regression in this space. SVR is used to implement this process. We incorporate this predictor into the MOEA based on decomposition (MOEA/D) to construct a novel algorithm for solving the aforementioned class of DMOPs. Comprehensive experiments have shown the effectiveness and competitiveness of our proposed predictor, comparing with the state-of-the-art methods.

This paper introduces a differential prediction model to predict the varying Pareto-Optimal Solutions (POS) when solving dynamic multiobjective optimization problems (DMOPs). In dynamic multiobjective optimization problems, several competing objective functions and/or constraints change over time. As a consequence, the Pareto-Optimal Solutions and/or Pareto-Optimal Front may vary over time. The differential prediction model is used to forecast the shift vector in the decision space of the centroid in the population through the centroid's historical locations in three previous environments. This differential prediction model is incorporated into a multiobjective evolutionary algorithm based on decomposition to solve DMOPs. After detecting the environmental change, half of individuals in the population are forecasted their new positions in the decision space by using the differential prediction model and the others' positions are retained. The proposed model is tested on a number of typical benchmark problems with several dynamic characteristics. Experimental results show that the proposed model is competitively in comparisons with the other state-of-the-art models or approaches that were proposed for solving DMOPs.