Advanced manufacturing processes frequently require scheduling, optimization, and decision-making, areas where evolutionary multi-objective optimization (EMO) has demonstrated strong capabilities. The Pareto front estimation has gained significant attention due to its remarkable performance on EMO. Recent studies have proposed few Pareto front (PF) estimation strategies, which could guide the search direction according to the geometric characteristics of the approximated Pareto front. However, when handling the complicated MOPs with irregular Pareto fronts, these strategies encounter significant challenges. This paper proposes a local Pareto front shape estimation approach based on Minimum Manhattan distance, which estimates the geometric information at a fine-grained level. Then an adaptive fitness function based geometric information is used to guide the search direction. Experiments on benchmark problems show that the proposed algorithm is highly competitive compared with state-of-the-art multiobjective evolutionary algorithms.

Multi-view semi-supervised feature selection, aims to simultaneously exploit both labeled and unlabeled samples to select a subset of features from multiple feature representations, has become an important task. However, the performance of existing methods is susceptible to the quality of graph due to the following reasons: 1) The samples from different classes located near the boundary are quite close and fail to be classified accurately, causing the unclear neighbor structures. 2) The graph is directly derived from the original space, such that the low-quality features will undermine the true relation between samples. To address above issues, we propose a novel multi-view semi-supervised feature selection method (MVFS), which exploits the regression losses of samples to correct the label information inaccurately propagated via the unreliable neighbor structures on the boundary samples, so as to enhance the discrimination of prediction labels. Moreover, the data representation generated by graph convolutional networks (GCN), which integrates the features, neighbor structures and label information, is incorporated to adaptively update similarity graph to better capture the neighbor structures of samples. Benefiting from these, the discriminative prediction labels and a reliable similarity graph are learned to facilitate the final feature selection. An efficient solution is designed to iteratively optimize MVFS, and comprehensive experiments demonstrate the effectiveness of MVFS.

Most machine intelligence or cloud computing can be formulated as multi-objective optimization problems (MOPs) with constraints, while evolutionary multi-objective optimization (EMO) is a powerful means to deal with them. However, its adaptation for dealing with complex constrained MOPs (CMOPs) keeps being under the scope of recent investigations. The main challenges are as follows. 1) The existing algorithms can not make full use of infeasible solution information in the evolution process. 2) There is no effective infeasible solution in the initial population, which causes the algorithms fall into local optimal feasible regions. In light of these two issues, this paper proposes an adaptive epsilon-constraint-handling technique with a detect-and-escape strategy to make full use of infeasible solutions in the whole evolution process. Then, the feasible solutions are saved to the external archive and take part in the population evolution by non-dominated sorting. Finally, the proposed method is embedded into the decomposition based multi-objective evolutionary framework (MOEA/D). Experiments on benchmark problems show that the proposed algorithm is highly competitive compared with state-of-the-art constrained evolutionary algorithms.

Recent studies in multiobjective particle swarm optimization (PSO) have the tendency to employ Pareto-based technique, which has a certain effect. However, they will encounter difficulties in their scalability upon many-objective optimization problems (MaOPs) due to the poor discriminability of Pareto optimality, which will affect the selection of leaders, thereby deteriorating the effectiveness of the algorithm. This paper presents a new scheme of discriminating the solutions in objective space. Based on the properties of Pareto optimality, we propose the dominant difference of a solution, which can demonstrate its dominance in every dimension. By investigating the norm of dominant difference among the entire population, the discriminability between the candidates that are difficult to obtain in the objective space is obtained indirectly. By integrating it into PSO, we gained a novel algorithm named many-objective PSO based on the norm of dominant difference (MOPSO/DD) for dealing with MaOPs. Moreover, we design a Lp-norm-based density estimator which makes MOPSO/DD not only have good convergence and diversity but also have lower complexity. Experiments on benchmark problems demonstrate that our proposal is competitive with respect to the state-of-the-art MOPSOs and multiobjective evolutionary algorithms.