These algorithms have predominantly been designed for the purpose of solving single-objective optimization problems and have been extensively utilized in several domains, including but not limited to network configurations, telecommunications, and engineering design [8; 12; 13]. Nevertheless, as meta-heuristic methods continued to advance, they were also expanded to be applicable to multi-objective scenarios. This expansion gave rise to algorithms such as Non-Dominated Sorting Genetic Algorithm II (NSGA-II) [16], Differential Evolution for Multi-objective Optimization (DEMO) [17], and the more recent multi-objective non-dominated advanced BOA (MONSBOA) [18]. The utilization of enhanced meta-heuristic optimization algorithms has led to the rise in the popularity and effectiveness of multi-objective optimization (MOO) as a viable method for addressing complex problems across diverse domains, including engineering, finance, and economics [19; 20]. In engineering design, to reduce the structure volume and transmission power loss and to disclose the influence of the profile shift factor on the optimal structure fitness, researchers performed a multi-objective optimization of a corrected spur gear pair with objectives including volume, center distance, and efficiency, while contact stress, bending stress, face coefficient, and tooth-tip interference served as constraints [21]. The results reveal that the structural design is compact compared to typical ones and that it has a decent efficiency for a medium contact ratio. Researchers considered the multi-objective optimization of a two-stage helical gearbox with a wide range of constraints introduced into the optimization problem, such as bending stress, pitting stress, and tribological constraints [22]. To minimize these objective functions for three distinct gear profiles, four varieties of ISO oil grades, and two speeds, a specially formulated discrete version of the NSGA-II was implemented. The obtained results show that there is a high probability of wear failure, but when using the multi-objective approach, the total power loss of the gearbox is reduced by half. In order to reduce the weight, improve the efficiency, and prevent premature failures in planetary gearboxes, the authors developed a novel multi-objective optimization of planetary gearboxes with the minimization of weight and total power loss as objective functions [23]. Three distinct gear profiles were investigated on an industrial planetary gearbox, which exhibited significant weight and power loss improvements while also being safer in scuffing. Using volume, power output, and center distance as the objectives and eight design variables, two geometric constraints, and three design constraints, a two-stage spur gearbox's multi-objective optimization problem is formulated [24], and the NSGA-II evolutionary algorithm is used to find the Pareto frontiers. Variation and sensitivity analyses reveal that module, pinion tooth number, and face-width variables have a strong influence on volume, offering vital insights for the design of compact gearboxes. Another study considered the performance of gear systems regarding the vibration and noise produced in the process of gear transmission, and the authors formulated an optimal appropriate multi-objective modification design method for helical gear [25]. The proposed model shows that it can effectively reduce vibration and noise while ensuring even load distribution on the tooth surface. In addition, the authors developed an algorithmic framework inspired by deterministic multi-objective optimization methods, which they paired with a direct-search global optimization algorithm to generate globally Pareto-optimal solutions [26]. Two tests show that the suggested method efficiently obtains answers from the global Pareto front.