Multimodal Lotus Effect Algorithm for Engineering Optimization Problems

Multimodal optimization problems (MMOPs) are critical in fields like game theory and robotics, where identifying multiple optimal solutions simultaneously is essential, yet challenging due to the need for effective global exploration and precise localization of optima. This study introduces the multimodal lotus effect algorithm (M-LEA), a novel extension of our previously published lotus effect optimization algorithm (LEA), which was designed for single-modal optimization and thus struggled to maintain multiple optima in complex multimodal spaces. M-LEA addresses this limitation by incorporating a roaming technique with independently evolving subpopulations, enabling it to navigate multimodal spaces without requiring parameters such as radius or prior information about the number or distribution of optima. Its robustness is demonstrated through comparisons with five algorithms on the IEEE CEC2013-2015 challenge, where M-LEA consistently outperformed competitors. The algorithm's practical utility is further validated in two applications: identifying Nash equilibrium points in game theory and localizing resources via robotic systems. ... mehrResults show that M-LEA achieves superior performance and stability, making it well-suited for scenarios demanding high efficiency and precision. These findings highlight M-LEA's potential for diverse domains, paving the way for its application in game theory, robotics, and other fields requiring advanced multimodal optimization techniques.