The Horse Herd Optimization Algorithm (HOA) is a new meta-heuristic algorithm based on the behaviors of horses at different ages. The HOA was introduced recently to solve complex and high-dimensional problems. This paper proposes a binary version of the Horse Herd Optimization Algorithm (BHOA) in order to solve discrete problems and select prominent feature subsets. Moreover, this study provides a novel hybrid feature selection framework based on the BHOA and a minimum Redundancy Maximum Relevance (MRMR) filter method. This hybrid feature selection, which is more computationally efficient, produces a beneficial subset of relevant and informative features. Since feature selection is a binary problem, we have applied a new Transfer Function (TF), called X-shape TF, which transforms continuous problems into binary search spaces. Furthermore, the Support Vector Machine (SVM) is utilized to examine the efficiency of the proposed method on ten microarray datasets, namely Lymphoma, Prostate, Brain-1, DLBCL, SRBCT, Leukemia, Ovarian, Colon, Lung, and MLL. In comparison to other state-of-the-art, such as the Gray Wolf (GW), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA), the proposed hybrid method (MRMR-BHOA) demonstrates superior performance in terms of accuracy and minimum selected features. Also, experimental results prove that the X-Shaped BHOA approach outperforms others methods.

翻译：马群优化算法（HOA）是一种基于不同年龄段马匹行为的新型元启发式算法，近期被提出用于解决复杂高维问题。本文提出了一种二元版本的马群优化算法（BHOA），以解决离散问题并选择突出的特征子集。此外，本研究提供了一种基于BHOA与最小冗余最大相关性（MRMR）滤波方法的新型混合特征选择框架。这种计算效率更高的混合特征选择方法能够生成包含相关且信息丰富特征的有效子集。由于特征选择属于二元问题，我们应用了一种名为X形传递函数（X-shape TF）的新型传递函数，可将连续问题转化为二元搜索空间。同时，采用支持向量机（SVM）在十个微阵列数据集（包括Lymphoma、Prostate、Brain-1、DLBCL、SRBCT、Leukemia、Ovarian、Colon、Lung和MLL）上检验所提方法的效率。与灰狼（GW）算法、粒子群优化（PSO）算法和遗传算法（GA）等前沿方法相比，所提出的混合方法（MRMR-BHOA）在准确率和最少选定特征方面均展现出更优性能。实验结果表明，X形BHOA方法优于其他方法。