Hybrid energy systems (HESs) have garnered significant attention as a sustainable solution to meet the world's growing energy demands while minimizing environmental impact. Achieving cost-effective and resilient HES solutions requires considering economic and reliability factors for optimal design. This research delves into the optimization and design of a wind-PV system integrated with a hybrid energy storage system using the Multi-Objective African Vultures Optimization Algorithm (MOAVOA) in both standalone and grid-connected modes. A comprehensive case study is conducted in Tabuk, Saudi Arabia, focusing on a microgrid and incorporating wind speed, solar radiation, and load data. The effectiveness of MOAVOA is verified using the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) methods in achieving the Pareto front of optimal system designs. Then, the mean, entropy, and criteria importance using the inter-criteria correlation (CRITIC) methods are utilized to assign weights to each objective in the obtained Pareto front. Finally, the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method is employed to select the optimal system design from the Pareto front. The results underscore the significance of the optimization approach in assessing the cost, dependability, and ideal configurations of the system. Furthermore, they highlight the diverse outcomes produced by different optimization techniques. While the entropy method yields more cost-effective designs, the mean and CRITIC methods produce comparable results. However, the mean and CRITIC approaches exhibit higher levels of reliability. For instance, in the grid-connected mode, the entropy weighting method yields an optimal system design with a total cost of M$ 42.2 and a reliability index of 91.73 %, while using the mean method, the selected system configuration has a total cost of M$ 42.98 and a reliability index of 92.89 %. The study emphasizes the benefits of diversifying renewable resources by considering different scenarios involving wind and solar generation. For example, in the wind-PV grid-connected system, the total cost is 22.65 % less than in the PV-only grid-connected system with a higher system reliability. The findings provide valuable guidance for system designers in selecting optimal optimization techniques and promoting the integration of renewable energy sources in hybrid energy systems. By presenting a comprehensive framework that incorporates economic and reliability assessments through the utilization of MOAVOA, this study contributes to the field of HES design.