Feature selection (FS) aims to identify the most relevant and non-redundant feature subset for improving the classification accuracy, which is regarded as a NP-hard problem. Some heuristic methods, such as particle swarm optimization (PSO) have achieved great success, however, with the increase of feature quantity, the solution space is too large, resulting in lower search efficiency. Recent discretization-based FS methods map the search of feature domain into cut-point domain, which shrinks the solution space and improve the performances significantly. In this paper, considering the conflicts between different objectives, we proposed an evolutionary multi-objective optimization framework for discretization-based FS. To obtain the Pareto solutions, a flexible cut-point PSO (FCPSO) which can select an arbitrary number of cut-points for discretization is introduced to help better explore the relevant features. In FCPSO, a particle update and a novel adaptive mutation operator are alternatively used to effectively find the relevant features and remove the redundant features. At last, to select the best feature subset, a Pareto ensemble method is designed to generate a number of feasible solutions based on Pareto set followed by a hierarchical solution selection process. We implemented the proposed framework by using three representative multi-objective evolutionary algorithms and compared them with some state-of-the-art methods. Experimental results on ten benchmark microarray gene datasets demonstrate that our proposed framework significantly outperforms other methods in terms of test classification accuracy with a competitive size of feature subset.

特征选择（FS）旨在识别最相关且非冗余的特征子集以提高分类准确性，这被认为是NP难题。一些启发式方法，例如粒子群优化（PSO）取得了巨大的成功，但是，随着特征量的增加，求解空间太大，导致搜索效率降低。最近的基于离散化的FS方法将特征域的搜索映射到切入点域，这缩小了解决方案空间并显着提高了性能。在本文中，考虑到不同目标之间的冲突，我们为基于离散化的FS提出了一种进化的多目标优化框架。要获得帕累托解决方案，引入了灵活的切点PSO（FCPSO），可以选择任意数量的切点进行离散化，以帮助更好地探索相关特征。在FCPSO中，可替代地使用粒子更新和新型自适应变异算子来有效地找到相关特征并删除多余特征。最后，为了选择最佳特征子集，设计了Pareto集成方法，以基于Pareto集生成许多可行的解决方案，然后进行分层的解决方案选择过程。我们通过使用三种代表性的多目标进化算法来实现提出的框架，并将它们与一些最新方法进行比较。