This paper addresses the challenge of optimal design and planning for a hybrid renewable energy system (HRES). The system comprises a wind turbine, a photovoltaic array, a battery storage unit, and an electrical load. The primary objective is to determine the optimal technical sizing of the system components to minimize the total annualized cost, which includes capital investment, operation and maintenance, and depreciation costs, while simultaneously ensuring a reliable power supply to meet the consumer demand. The solar panel area, the wind turbine rotor swept area, and the battery bank capacity are considered as the key decision variables. This complex optimization problem is formulated as a mathematical programming model with linearized constraints and objective function. The proposed model is then simulated using real-world data for solar radiation and wind speed from a specific location in Khorasan Razavi Province, Iran. To identify the optimal configuration, several meta-heuristic optimization algorithms are employed to solve the model. The results demonstrate that all the applied methods are capable of finding solutions near the global optimum; however, a comparative analysis of algorithm performance reveals that the Particle Swarm Optimization (PSO) algorithm yields the best results in terms of convergence accuracy and solution stability. This finding provides a valuable guideline for engineers and designers aiming to achieve economic optimization of hybrid energy systems in similar regions.