This review paper delves into the original MRFO and its variants, focusing on single-objective algorithms including but not limited to hybrid algorithms, learning strategies, multiple populations and dynamic parameter adjustment, highlighting the improvements made to enhance the algorithm's efficiency in global optimization, accelerate convergence rates, and improve its capacity to evade local optima. MRFO has emerged as an effective tool for solving complex optimization problems across various domains, including energy optimization, biomedical field, engineering problems, and others. A comprehensive analysis of applications of MRFO in different fields is provided, emphasizing its adaptability and efficacy. The paper concludes with a discussion on the challenges faced by MRFO and potential future research directions, aiming to consolidate the current research status and guide future investigations.