This paper proposes an optimal hybrid energy sources sizing methodology for hybrid electric vehicles comprising ultracapacitor (UC) and fuel cell (FC) with battery units (BU). For this purpose, a multi objective problem is formulated using dynamic-source models to evaluate the system’s initial cost, weight, running cost, and cost associated with source degradation. Furthermore, a novel adaptive energy management strategy (AEMS) that focuses on dynamic-source characteristics and drive cycle power demand is proposed as an integral part of the optimization problem. Finally, to solve the hybrid energy source optimization problem, the butterfly optimization algorithm (BOA) is improved by employing the quantum wave concept to explore the search space more effectively. The performance of the proposed method is evaluated with different hybrid source configurations and various drive cycles using improved BOA, BOA and particle swarm optimization. The Matlab® simulation results show that battery rating can be downsized by approximately 40% upon the inclusion of UC and FC units using improved BOA. Furthermore, when the proposed AEMS is compared with a conventional discrete wavelet transform power-splitting approach used in the optimization process, the proposed AEMS performs better and could reduce the system relative cost and weight for BU-UC-FC configuration by 16% and 10% respectively.