This article focuses on the application of a latest nature-inspired metaheuristic optimization algorithm named Grasshopper Optimization Algorithm (GOA) in the area of microgrid system sizing design problem. The proposed algorithm is applied to an autonomous microgrid system in order to determine the optimal system configuration that will supply energy demand reliably based on the deficiency of power supply probability (DPSP) and cost of energy (COE). Firstly, a robust rule-based energy management scheme (EMS) is proposed to coordinate the power flow among the various system components that formed the microgrid. Then, the GOA is integrated with the EMS to perform the optimal sizing for the hybrid autonomous microgrid for five units of residential in an off-grid location in Yobe State, Nigeria. The proposed microgrid comprises of photovoltaic modules, wind turbine, battery storage system and a diesel generator. The effectiveness of the proposed GOA in solving the optimization problem is examined and its performance is compared with particle swarm optimization (PSO) and cuckoo search (CS) optimization algorithm. In addition, a sensitivity analysis is performed on the COE to highlight the impact of varying sensitive system inputs. The proposed optimization is programmed using MATLAB simulation package. The simulation results confirm that GOA is able to optimally size the system as compared to its counterparts, CS and PSO. In which, a decrement of 14% and 19.3% is achieved in the system capital cost, respectively.