In this paper an adaptive energy management strategy (EMS) based on fuzzy logic and the optimal sizing for a tramway with a hybrid energy storage system (ESS) combining batteries (BT) and supercapacitors (SC) are presented. The EMS applies a sliding window to estimate the forward energy consumption and adapt the instantaneous power target for BT and SC. The hybrid ESS sizing is obtained by an optimization with multi-objective genetic algorithms (GA). The fitness functions are expressed in economic terms, and correspond to the costs of the energy absorbed from the catenary as well as the operation cost of the hybrid ESS (investment and cycling cost). The selected case study is the tramway of Seville, which operates in zones with and without catenary. The aim is to minimize the daily operating cost of the tramway taking into account the BT and SC degradation approach (cycling) and fulfilling the performance of the tramway in the catenary-less zone. The proposed approach (adaptive EMS and optimal sizing) is compared with the current solution in the tramway (SC-based) and with a hybrid ESS managed by a rule-based EMS (RB-EMS) in terms of daily operating cost and energy harnessing during regenerative braking phase. The proposed approach show cost reductions up to 25.5% (from SC-based), 6.2% (from hybrid ESS with RB-EMS) and a global efficiency around 84.4%.