This study presents a hybrid optimization approach combining the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA) method to design a two-stage helical gearbox that simultaneously minimizes the gearbox volume and maximizes transmission efficiency. A mathematical model is developed to express the gearbox volume and efficiency as functions of key geometric and operational parameters. NSGA-II is employed to generate a set of Pareto-optimal solutions, representing trade-offs between compactness and performance. The MOORA method is then applied to identify the best compromise solution from the Pareto front based on a structured decision-making framework. The proposed hybrid methodology proves effective in balancing structural compactness and mechanical performance, offering a practical solution for industrial gearbox design.