This work presents an optimal approach to the embodiment stage of the engineering design of a gear train of a hybrid electric off-road vehicle. The powertrain of the given vehicle has a series configuration and is designed for extreme operation conditions, including narrow paths, highly irregular surface roughness and high grade scenarios. The gear train of interest has a predetermined configuration with a fixed total reduction ratio. The gear train is composed by three stages: first, a spur gear pair; in the second stage a bevel gear pair; finally in the third stage a planetary gear transmitting motion to the wheel. In addition to the structural constraints, the design optimization is strongly constrained by space limitations (packaging). The objective function is to minimize the overall mass of the gear train.

Three optimization routines were applied for the solution of this optimization problem: a gradient based optimization (GBA), genetic algorithms (GA) and a branch and bound algorithm for mixed integer problems (B&B). For the initial guess of each routine, a Sobol low discrepancy sequence (LDS) was used. After the formal statement of the optimization problem, a comparison between the performances of the different optimization algorithms is presented. The numerical results are also compared with some analytical results previously obtained.

It was found that the branch and bound algorithm developed was the most effective to find the mixed integer solution. The genetic algorithm was quite inaccurate, due to the binding geometric constraints of the problem.

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