In [2], the researchers developed a framework for the multi-objective uncertainty optimization design of the planetary gear train used in electric vehicles, where the volume, transmission efficiency, manufacturing size, material, and load input are taken into consideration. The results of this study show that the enhanced version of NSGA-II exhibits superior convergence efficiency in comparison to the conventional NSGA-II. In [27], the authors focused on the automatic decision making of the Pareto front applied to the design of spur gears utilizing a multi-objective optimization model solved using NSGA-II algorithm, where the variables under consideration are gear module, teeth number, transmission ratio, center distance, bearing capacity coefficient, and meshing efficiency. The study utilized three distinct methods for decision making, namely Shannon Entropy, LINMAP, and TOPSIS, to calculate the optimal solution from the Pareto frontier, showing insights into the design of spur gears. In study [28], the authors outline a technique for mitigating vibration and noise levels in the gearbox of an electric bus through the utilization of a multi-objective optimization algorithm, where the optimization of gear micro-geometry is performed. The findings indicate that the improved optimization technique, which is utilized to solve this task, can efficiently and rapidly decrease the vibration and noise levels of the gearbox. In [29], the authors consider constrained multi-objective optimization for the design of spur gear pair, where L10 life is used with various tribological constraints, including micro-pitting, flank fracture, wear, scuffing, and scoring, incorporated as constraints in the optimization problem. The study takes into account various objectives, including weight, power loss, and heat treatment duration of the gear. The CRITIC approach is utilized to determine the most optimal solution among the Pareto-optimal solutions that have been acquired via GA optimization. The study [30] employed a genetic algorithm to optimize the parameters of gear pairs with the aim of minimizing transmission volume and power losses. The findings indicate that an optimal outcome can be achieved through the utilization of a blend of lower gear modules, face width, profile shift coefficients, and number of teeth. This paper presents a hybridization of the PSO and BOA algorithms named the Multi-objective Hybrid Butterfly Optimization and Particle Swarm Optimization Algorithm (HMOBPSO). The objective of this algorithm is to improve optimization performance in solving complex MOO problems, with a specific focus on the formulated planetary gearbox optimization presented in this study. This paper presents a hybridization approach to mitigate the limitations encountered in optimizing conventional PSO and BOA. Specifically, the proposed method incorporates the PSO velocity update scheme into the equations governing butterfly movement. The utilization of the crowding distance has been implemented for the purpose of selecting the optimal individual within the population, with the aim of facilitating the application to multi-objective optimization problems. Moreover, the adaptive parameter has been suggested to determine the suitable expression for the individual position update in the present optimization scenario and to substitute the conventional switch probability. In summary, the findings indicate that the HMOBPSO algorithm proposed exhibits improved performance compared to the other algorithms examined with respect to both convergence rate and solution efficacy. The HMOBPSO algorithm was observed to be more efficient in discovering solutions that were characterized by greater diversity and a more uniform distribution across the Pareto front. The findings indicate that the algorithms employed were successful in enhancing the design of industrial gearboxes. Additionally, the study underscores the significance of incorporating various objectives during the design phase.