Due to increased environmental pollution and global warming concerns, the use of energy storage units that can be supported by renewable energy resources in transportation becomes more of an issue and plays a vital role in terms of clean energy solutions. However, utilization of multiple energy storage units together in an electric vehicle makes the powertrain system more complex and difficult to control. For this reason, the present study proposes an advanced energy management strategy (EMS) for range extended battery electric vehicles (BEVs) with complex powertrain structure. Hybrid energy storage system (HESS) consists of battery, ultra-capacitor (UC), fuel cell (FC) and the vehicle is propelled with two complementary propulsion machines. To increase powertrain efficiency, traction power is simultaneously shared at different rates by propulsion machines. Propulsion powers are shared by HESS units according to following objectives: extending battery lifetime, utilizing UC and FC effectively. Primarily, to optimize the power split in HESS, a convex optimization problem is formulated to meet given objectives that results 5 years prolonged battery lifetime. However, convex optimization of complex systems can be arduous due to the excessive number of parameters that has to be taken into consideration and not all systems are suitable for linearization. Therefore, a neural network (NN)-based machine learning (ML) algorithm is proposed to solve multi-objective energy management problem. Proposed NN model is trained with convex optimization outputs and according to the simulation results the trained NN model solves the optimization problem within 92.5% of the convex optimization one.