Minimizing the number of selected features and maximizing the classification performance are two main objectives in feature selection, which can be formulated as a biobjective optimization problem. Due to the complex interactions between features, a solution (i.e., feature subset) with poor objective values does not mean that all the features it selects are useless, as some of them combined with other complementary features can greatly improve the classification performance. Thus, it is necessary to consider not only the performance of feature subsets in the objective space, but also their differences in the search space, to explore more promising feature combinations. To this end, this paper proposes a tri-objective method for bi-objective feature selection in classification, which solves a bi-objective feature selection problem as a triobjective problem by considering the diversity (differences) between feature subsets in the search space as the third objective. The selection based on the converted triobjective method can maintain a balance between minimizing the number of selected features, maximizing the classification performance, and exploring more promising feature subsets. Furthermore, a novel initialization strategy and an offspring reproduction operator are proposed to promote the diversity of feature subsets in the objective space and improve the search ability, respectively. The proposed algorithm is compared with five multi-objective-based feature selection methods, six typical feature selection methods, and two peer methods with diversity as a helper objective. Experimental results on 20 real-world classification datasets suggest that the proposed method outperforms the compared methods in most scenarios.

中文翻译：

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分类中双目标特征选择的三目标方法。

最小化所选特征的数量和最大化分类性能是特征选择的两个主要目标，可以将其表述为双目标优化问题。由于特征之间复杂的相互作用，目标值较差的解决方案（即特征子集）并不意味着它选择的所有特征都是无用的，因为其中一些特征与其他互补特征相结合可以极大地提高分类性能。因此，不仅需要考虑特征子集在目标空间中的性能，还要考虑它们在搜索空间中的差异，以探索更有前景的特征组合。为此，本文提出了一种分类中双目标特征选择的三目标方法，该方法将搜索空间中特征子集之间的多样性（差异）视为三目标问题，将双目标特征选择问题解决为三目标问题。第三个目标。基于转换后的三目标方法的选择可以在最小化所选特征的数量、最大化分类性能和探索更有前途的特征子集之间保持平衡。此外，提出了一种新颖的初始化策略和后代繁殖算子，分别促进目标空间中特征子集的多样性并提高搜索能力。该算法与五种基于多目标的特征选择方法、六种典型特征选择方法和两种以多样性为辅助目标的对等方法进行了比较。在 20 个真实世界分类数据集上的实验结果表明，所提出的方法在大多数情况下都优于对比方法。