The purpose of feature selection (FS) is to eliminate redundant and irrelevant features and leave useful features for classification, which can not only reduce the cost of classification, but also improve the classification accuracy. Existing algorithms mainly focus on finding one best feature subset for an optimization target or some Pareto solutions that best fit multiple targets, neglecting the fact that the FS problem may have more than one best feature subset for a single target. In fact, diffident feature subsets are likely to exhibit similar classification ability, so the FS problem is also a multimodal optimization problem. This paper firstly attempts to study the FS problem from the perspective of multimodal optimization. A novel multimodal niching particle swarm optimization (MNPSO) algorithm, aiming at finding out all the best feature combinations in a FS problem is proposed. Unlike traditional niching methods, the proposed algorithm uses the Hamming distance to measure the distance between any two particles. Two niching updating strategies are adopted for multimodal FS, and the two proposed variants of MNPSO are termed MNPSO-C (using crowding clustering) and MNPSO-S (using speciation clustering) respectively. To enable the particles in the same niche to exchange information properly, the particle velocity update is modified based on the best particle in the niche instead of the traditional globally best one. An external archive is applied to store the feature subsets with the highest classification accuracy. Datasets with various dimensions of attributes have been tested. Particularly, the number of multimodal solutions and the successful rates of the proposed algorithms have been extensively analyzed and compared with the state-of-the-art algorithms. The experimental results show that the proposed algorithms can find more multimodal feature solutions and have advantages in classification accuracy.

特征选择（FS）的目的是去除冗余和不相关的特征，留下有用的特征进行分类，既可以降低分类成本，又可以提高分类精度。现有算法主要侧重于为优化目标寻找一个最佳特征子集或一些最适合多个目标的帕累托解，而忽略了一个事实，即 FS 问题可能对单个目标具有多个最佳特征子集。事实上，不同的特征子集很可能表现出相似的分类能力，所以FS问题也是一个多模态优化问题。本文首先尝试从多模态优化的角度研究FS问题。一种新的多模态缝隙粒子群优化（MNPSO）算法，提出了旨在找出 FS 问题中所有最佳特征组合的方法。与传统的缝隙化方法不同，所提出的算法使用汉明距离来测量任意两个粒子之间的距离。多模态 FS 采用了两种利基更新策略，MNPSO 的两个提议变体分别称为 MNPSO-C（使用拥挤聚类）和 MNPSO-S（使用形态聚类）。为了使同一生态位中的粒子能够正确交换信息，基于生态位中的最佳粒子而不是传统的全局最佳粒子来修改粒子速度更新。外部存档用于存储具有最高分类精度的特征子集。已经测试了具有各种属性维度的数据集。特别，已广泛分析了多模态解决方案的数量和所提出算法的成功率，并与最先进的算法进行了比较。实验结果表明，所提算法能够找到更多的多模态特征解，在分类精度上具有优势。