In spite of concerns about pollution and high operational costs, diesel engines continue to dominate local electricity generation in off-grid areas. However, there is significant untapped potential worldwide for utilizing local renewable energy sources (RES) instead of fossil fuel generation, particularly in remote regions. To address the intermittent nature of RES, energy storage systems are crucial for off-grid communities, enabling them to rely on locally collected renewable energy. This study explores various off-grid renewable power system configurations, including batteries and hydrogen as energy storage options, to determine the most economically viable setup for remote areas. The analysis includes the Nickel-Iron (Ni-Fe) battery and considers electrolysis technology for hydrogen production. Two Integrated Hybrid Renewable Energy System (IHRES) configurations are modeled and evaluated: PV/Diesel Generator (DG)/Battery(Ni-Fe) and PV/Wind Turbines (WT)/DG/Hydrogen Storage System (HSS). The study employs a cycle charging (CC) strategy. An effective optimization algorithm called Quadratic interpolation-based artificial rabbits optimization (QIARO) is introduced to optimize the sizing of system components, ensuring cost-effective and reliable fulfillment of load demands. The effectiveness of the QIARO algorithm is initially validated through a comprehensive performance assessment, comparing it with the original artificial rabbits optimization (ARO) algorithm and other established optimization techniques across 7 benchmark functions. The results demonstrate that the QIARO algorithm surpasses the ARO algorithm, as well as other optimization techniques such as beluga whale optimization (BWO), pelican optimization algorithm (POA), weighted mean of vectors (INFO), and RUNge Kutta optimizer (RUN), in terms of convergence speed and solution quality. After validation, the proposed algorithm is applied to the Baris Oasis in New Valley, Egypt, chosen as a representative case study of insular microgrid environments. The resulting outcomes are compared with those obtained using the original ARO algorithm, further highlighting the effectiveness of the proposed approach. Using the QIARO algorithm, the PV/DG/Battery(Ni-Fe) configuration and PV/WT/DG/HSS configuration achieve optimal Life Cycle Cost values of 645,271 USD and 1,852,421 USD, respectively.