This paper presents a multi-objective design optimization approach for two-stage helical gearboxes featuring a dual-gear configuration in the first stage. The primary objectives are to minimize the bottom area (footprint) of the gearbox while maximizing its mechanical efficiency. To address the conflicting nature of these design goals, a decomposition-based evolutionary algorithm, MOEA/D-DE (Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution), is employed. The method systematically explores the Pareto-optimal trade-offs between volume reduction and power transmission performance. Comprehensive constraint handling related to gear geometry, strength, and contact ratio is integrated into the optimization framework. Results show that the proposed approach effectively generates a diverse set of high-quality solutions, enabling engineers to select optimal gearbox designs tailored to specific application needs. This study provides new insights into compact and efficient gearbox development through evolutionary multi-objective techniques.