Energy management (EM) for Fuel Cell Hybrid Electric Vehicles (FCHEVs) focuses on optimizing the use of both the Fuel Cell (FC) and the battery to balance power supply and enhance vehicle range. Drawbacks include elevated operating costs from expensive hydrogen fuel and maintenance, increased H2 consumption, which impacts overall cost-effectiveness, and potentially lower overall efficiency due to the complexity of integrating multiple energy sources. To overcome these drawbacks, this manuscript proposes a hybrid approach for optimizing EM in FCHEV. The proposed hybrid method is the joint execution of Ladybug Beetle optimization (LBO) and Heterogeneous Context-Aware Graph Convolutional Network (HCAGCN). Hence, it is named as the LBO–HCAGCN method. The novel approach aims to minimize operational costs as well as decrease hydrogen fuel consumption to enhance the overall FCHEV performance. The proposed LBO distributes power between the FC and battery effectively for improved optimization purposes. HCAGCN serves as a prediction tool for anticipated future energy needs of vehicles. Multiple implementations of the suggested method appear in Matrix Laboratory alongside Cheetah Optimization-Spiking Neural Network, Genetic Algorithm-Fuzzy logic Control, Deep Reinforcement Learning, Jellyfish Search Optimizer–Reptile Search Algorithm, and Wavelet Neural Network-Particle Swarm Optimization for evaluation testing. The proposed method demonstrates a 161.23 g H2 consumption rate along with an operating cost of 564$ and achieves an efficiency rate of 92%. The suggested optimization method proves superior when comparing H2 consumption and operating cost together with overall efficiency to current methods for optimizing EM in FCHEVs.