Carbon dioxide emission from transportation systems surpassed emission from any other energy sector. Thus, electric vehicles (EV) have gained extensive awareness among society as this can scale down the greenhouse gas emissions. Present internal combustion engine vehicles have considerable performance and none of the alternative source can individually replace them. Hence, hybridization of multiple sources is indispensable. In this paper, a multi-objective optimization problem is developed to optimally size a battery unit (BU)-ultracapacitor (UC) hybrid energy supply system (HESS) of an EV. The performance indices considered for optimization are the investment cost of the source system, combined weight of multi-sources and dynamic source degradation. Initially, the dynamic variation of source parameters is contemplated in the modelling. Then the power demand by the electric vehicle power train is shared amongst the BU and UC using the wavelet transformation approach. The property of multi resolution analysis makes the wavelet technique very attractive in analysis and synthesis. Thus, the power splitting can be realized between BU and UC effectively. In this work the butterfly optimization algorithm is implemented to optimize BU-UC HESS sizing for a given drive cycle. The problem is solved for the combination of urban dynamometer driving schedule and Artemis rural drive cycle. The simulation results show that the proposed method can provide least possible cost and weight with less BU and UC degradation for HESS in EV.