A Hierarchical Evolutionary Search Framework with Manifold Learning for Powertrain Optimization of Flying Vehicles

Hybrid electric vertical take-off and landing (HEVTOL) flying vehicles serve as effective platforms for efficient transportation, forming a cornerstone of the emerging low-altitude economy. However, the current lack of co-optimization methods for powertrain component sizing and energy controller design often leads to suboptimal HEVTOL performance. To address this, this paper proposes a hierarchical manifold-enhanced Bayesian evolutionary optimization (HM-BEO) approach for HEVTOL systems. This framework employs lightweight manifold dimensionality reduction to compress the decision space, enabling Bayesian optimization (BO) on low-dimensional manifolds for a global coarse search. Subsequently, the approximate Pareto solutions generated by BO are utilized as initial populations for a non-dominated sorting genetic algorithm III (NSGA-III), which performs fine-grained refinement in the original high-dimensional design space. The co-optimization aims to minimize fuel consumption, battery state-of-health (SOH) degradation, and manufacturing costs while satisfying dynamic and energy management constraints. Evaluated using representative HEVTOL duty cycles, the HM-BEO demonstrates significant improvements in optimization efficiency and solution quality compared to conventional methods. Specifically, it achieves a 5.3% improvement in fuel economy, a 7.4% mitigation in battery SOH degradation, and a 1.7% reduction in system manufacturing cost compared to standard NSGA-III-based optimization.