Renewable energy systems provide a dependable, environment-friendly, and cost-effective alternative for producing electricity in remote regions. The growing use of meta-heuristic algorithms is attributed to their ability to provide rapid, accurate, and optimal results for intricate optimization challenges. Therefore, in this work, an Evolved Opposition-based Mountain Gazelle Optimizer (EOBMGO) algorithm is explored to achieve the optimal design for the combination of off-gird hybrid renewable energy systems (HRES) that incorporate solar photovoltaic (PV) modules, wind turbines, and battery systems. The primary objective of the optimization process is to minimize the total net annual cost while maintaining an acceptable loss of power supply probability (LPSP), considering levelized energy costs and the generation of excess power. The designed EOBMGO technique has been evaluated for three distinct LPSP values (0%, 0.5%, and 1%), with each value tested across 25 independent runs and 50 iterations. The designed algorithm is then assessed against several established optimizers, including Grey Wolf Optimizer (GWO), Artificial Rabbit Optimization (ARO), Brown-bear Optimization Algorithm (BOA), and White Shark Optimizer (WSO). Statistical analysis has been performed to highlight the superiority of the EOBMGO algorithm over others, which included an evaluation of mean, standard deviation, variance, and crest values. The simulation outcomes revealed that the EOBMGO technique achieved a lower oscillation rate, a low standard deviation, and superior balancing of exploitation and exploration capabilities. Further, EOBMGO is found robust in the sensitivity analysis with variation in capital cost of the major components. These outcomes will provide researchers with a valuable reference for choosing the optimal technique for sizing problems.