Q2HO-MFTV: a binary hippopotamus optimization algorithm for feature selection with a brief review of binary optimization

Feature selection is a crucial step for enhancing classification accuracy and reducing computational complexity, especially in high-dimensional datasets. Although metaheuristic algorithms have been successful in continuous optimization, their binary counterparts often suffer from premature convergence and limited exploration. To overcome these challenges, we introduce the Quantum Q-Learning Hippopotamus Optimizer with Fuzzy Time-Varying Transfer Functions (Q2HO-MFTV), a novel binary variant of the Hippopotamus Optimization Algorithm, which is binarized through the integration of Fuzzy Time-Varying transfer functions (FTVs). This method leverages FTVs for smooth state transitions, incorporates a quantum-inspired chaotic initialization to boost population diversity, and employs a Q-learning mechanism to dynamically balance exploration and exploitation. We evaluated Q2HO-MFTV on 41 benchmark datasets from diverse domains, including text, image, and biomedical, with up to 22,283 features. The algorithm consistently outperformed 14 state-of-the-art methods such as Binary Marine Predator Algorithm (BMPA-TVSinV), Binary Grey Wolf Optimizer (BGWO), and Binary Salp Swarm Algorithm (BSSA). Q2HO-MFTV achieved 98.56 % accuracy on the BreastCancer dataset with 43 % feature selection, 99.26 % on COVID-19 II with just 10.63 %, and 100 % on Colon with only 0.10 %. It also recorded the lowest fitness values (e.g., 0.0151 on KrvskpEW), ranked first in the Friedman test (mean rank = 1.2976), and showed an average speed-up of 22 %, saving over 500 s on large problems. These results demonstrate that Q2HO-MFTV is a robust, scalable, and efficient solution for feature selection in classification tasks.