This study aims to look at multi-target optimization of two-stage bevel helical gearboxes to determine the best major design factors for reducing gearbox bottom area (GBA) and increasing gearbox efficiency (GE). Grey relation analysis (GRA) and the Taguchi technique were used to address the problem in two steps. Prioritizing the closure of the variable level gap, the single-objective optimization problem was addressed, followed by the multi-objective optimization problem, which identified the ideal primary design variables. Additionally, the first-stage gear ratio, allowable contact stresses (ACS), and first and second-stage coefficients of wheel face width (CWFW) were calculated. The outcomes of the study were used to determine the best values for five essential design features of a two-stage bevel helical gearbox (BHG).