Reconfigurable Intelligent Surfaces (RISs) provide a promising avenue for enhancing performance and implementation efficiency in multiuser wireless communication systems by enabling the manipulation of radio wave propagation. In this paper, an Augmented Jellyfish Search Optimization Algorithm (AJFSOA) is specifically designed to optimize the achievable rate in RIS-equipped systems. AJFSOA distinguishes itself from previous approaches through the integration of a novel quasi-reflection operator, which aids in escaping local optima, and an adaptive neighborhood search mechanism that improves the algorithm's exploitation capabilities. These enhancements enable AJFSOA to efficiently refine promising solutions near the current best solution. Unlike prior research, our work explores two objective models: maximizing the average achievable rate for all users to ensure balanced system performance and maximizing the minimum achievable rate for individual users to improve worst-case scenarios. The comprehensive analysis demonstrates that AJFSOA effectively increases system capacity and supports a larger number of users simultaneously. An extensive testing is performed on communication systems with twenty and fifty users, comparing AJFSOA's performance against existing algorithms, including the standard JFSOA, Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Genetic Algorithm (GA) and Differential Evolution (DE). Results show that AJFSOA outperforms the other algorithms significantly, with improvements of 26.59%, 9.75%, 14.71%, 0.29% and 13.52% over JFSOA, PSO, ACO, GA and DE, respectively, for the first objective model, and 21.66%, 10.6%, .17.44%, 2.71% and 22.36% for the second model. These findings highlight the distinct advantages and superior performance of the presented AJFSOA in efficient optimizing multiuser wireless networks.