This study presents a multi-objective optimization framework for the design of two-stage helical gearboxes with a dual-gear first stage. The optimization aims to simultaneously minimize the gearbox volume and maximize the transmission efficiency, two inherently conflicting objectives. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed to generate Pareto-optimal solutions, capturing the trade-off between compactness and efficiency. Subsequently, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method was applied to rank the Pareto solutions and select the most balanced design. The results reveal clear trends: larger transmission ratios tend to reduce efficiency while increasing gearbox volume, and the optimal compromise strongly depends on the ratio distribution between stages. Pareto fronts across different transmission ratios demonstrate the volume-efficiency trade-off, while TOPSIS effectively identifies design points that balance both objectives. The proposed hybrid approach provides a systematic methodology for designing compact and energy-efficient gearboxes, offering valuable insights for practical engineering applications.