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 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-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. Support Vector Regression is used to implement this process. We incorporate this predictor into the Multiobjective Evolutionary Algorithm 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.

Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems. The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems (HEPs). The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations. Moreover, it is hard to traverse the huge search space within reasonable resource as problem dimension increases. Traditional evolutionary algorithms (EAs) tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results. To reduce such evaluations, many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years. Yet there lacks a thorough review of the state of the art in this specific and important area. This paper provides a comprehensive survey of these evolutionary algorithms for HEPs. We start with a brief introduction to the research status and the basic concepts of HEPs. Then, we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects. We also give comparative results of some representative algorithms and application examples. Finally, we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.

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.

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.