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Feature selection has been considered as an effective method to solve imbalanced classification problems. It can be formulated as a multiobjective optimization problem (MOP) aiming to find a small feature subset while achieving a high classification accuracy. With traditional MOP, the focus is on deriving an optimal solution (i.e., a feature subset), while ignoring the diversity in solution space (e.g., there could exist multiple feature subsets achieving the same accuracy). Providing more options for feature selection would be beneficial since some features can be more difficult to obtain than others. In this work, we treat feature selection as a multimodal MOP (MMOP) whose goals are to find an excellent Pareto front in objective space and as many equivalent Pareto optimal solutions (feature subsets) as possible in feature space. Note that though several multimodal multiobjective evolutionary algorithms (MMEAs) have been proposed, their use of a convergence-first selection criterion could cause the loss of solution diversity in an objective and feature space. To address the issue, a novel competition-driven mechanism is designed to assist the existing multimodal MMEAs in locating more equivalent feature subsets and a desired Pareto front. The effectiveness of the proposed mechanism is first verified on all 22 MMOPs from CEC2019. Then, the proposed method is applied to feature selection in imbalanced classification problems and a real-world application, i.e., credit card fraud detection. Experimental results show that the proposed mechanism can not only provide more equivalent feature subsets but also improve classification accuracy. [ABSTRACT FROM AUTHOR]

Decomposition-based multiobjective evolutionary algorithm has shown its advantage in addressing many-objective optimization problem (MaOP). To further improve its convergence on MaOPs and its diversity for MaOPs with irregular Pareto fronts (PFs, e.g., degenerate and disconnected ones), we proposed a decomposition-based many-objective evolutionary algorithm with two types of adjustments for the direction vectors (MaOEA/D-2ADV). At the very beginning, search is only conducted along the boundary direction vectors to achieve fast convergence, followed by the increase of the number of the direction vectors for approximating a more complete PF. After that, a Pareto-dominance-based mechanism is used to detect the effectiveness of each direction vector and the positions of ineffective direction vectors are adjusted to better fit the shape of irregular PFs. The extensive experimental studies have been conducted to validate the efficiency of MaOEA/D-2ADV on many-objective optimization benchmark problems. The effects of each component in MaOEA/D-2ADV are also investigated in detail. [ABSTRACT FROM AUTHOR]

Domination-based sorting and decomposition are two basic strategies used in multiobjective evolutionary optimization. This paper proposes a hybrid multiobjective evolutionary algorithm integrating these two different strategies for combinatorial optimization problems with two or three objectives. The proposed algorithm works with an internal (working) population and an external archive. It uses a decomposition-based strategy for evolving its working population and uses a domination-based sorting for maintaining the external archive. Information extracted from the external archive is used to decide which search regions should be searched at each generation. In such a way, the domination-based sorting and the decomposition strategy can complement each other. In our experimental studies, the proposed algorithm is compared with a domination-based approach, a decomposition-based one, and one of its enhanced variants on two well-known multiobjective combinatorial optimization problems. Experimental results show that our proposed algorithm outperforms other approaches. The effects of the external archive in the proposed algorithm are also investigated and discussed. [ABSTRACT FROM PUBLISHER]