Benefiting From Single-Objective Feature Selection to Multiobjective Feature Selection: A Multiform Approach

Evolutionary multiobjective feature selection (FS) has gained increasing attention in recent years. However, it still faces some challenges, for example, the frequently appeared duplicated solutions in either the search space or the objective space lead to the diversity loss of the population, and the huge search space results in the low search efficiency of the algorithm. Minimizing the number of selected features and maximizing the classification performance are two major objectives in FS. Usually, the fitness function of a single-objective FS problem linearly aggregates these two objectives through a weighted sum method. Given a predefined direction (weight) vector, the single-objective FS task can explore the specified direction or area extensively. Different direction vectors result in different search directions in the objective space. Motivated by this, this article proposes a multiform framework, which solves a multiobjective FS task combined with its auxiliary single-objective FS tasks in a multitask environment. By setting different direction vectors, promising feature subsets from single-objective FS tasks can be utilized, to boost the evolutionary search of the multiobjective FS task. By comparing with five classical and state-of-the-art multiobjective evolutionary algorithms, as well as four well-performing FS algorithms, the effectiveness and efficiency of the proposed method are verified via extensive experiments on 18 classification datasets. Furthermore, the effectiveness of the proposed method is also investigated in a noisy environment.