Pareto-Based multi-Objective optimization of a compact lepelletier transmission

Epicyclic gear trains are widely used in modern automatic transmissions due to their compactness, high power density, and ability to provide multiple speed ratios. Among compound planetary systems, Lepelletier gear trains offer an efficient architecture for achieving multiple forward and reverse gears with reduced structural complexity. However, their design remains a challenging multi-objective problem involving strict geometric feasibility, compactness, manufacturing simplicity, and high kinematic accuracy. This study presents a Pareto-based multi-objective framework for the constraint-driven synthesis of a Lepelletier multi-speed transmission. Symbolic expressions for velocity ratios are derived by decomposing the transmission into fundamental gear entities, ensuring exact kinematic representation under all coupling conditions. These formulations are integrated into a multi-objective genetic algorithm (MOGA) to determine discrete gear tooth numbers that satisfy predefined target ratios while enforcing geometric, angular, and structural constraints. The method generates a set of feasible integer solutions forming a Pareto front that captures the trade-off between ratio accuracy and structural complexity. Since multiple solutions can satisfy the same kinematic requirements, selection is performed based on engineering criteria including minimal ratio deviation, compactness, and smooth ratio progression. Accordingly, the proposed framework focuses on identifying and selecting feasible discrete configurations rather than quantifying improvement relative to a predefined baseline design. The selected configuration achieves eleven forward and one reverse operating modes with high accuracy and consistent ratio distribution. The obtained results confirm that the synthesized configurations achieve a very close agreement with the predefined target velocity ratios, with minimal deviation across all operating modes, demonstrating the effectiveness of the proposed constraint-driven synthesis approach. Integer refinement confirms the stability of the solution and convergence toward a discrete optimum. The results demonstrate that the proposed framework operates as a design-oriented synthesis tool, enabling systematic identification and selection of feasible Lepelletier transmission configurations under strict design constraints.