Lithium-ion batteries (LiBs) have become the leading choice for energy storage systems (ESS) in electric vehicles (EVs) due to their superior performance characteristics. However, their sensitivity compared to other battery technologies necessitates the use of advanced battery management systems (BMS) for reliable and safe operation. Accurate parameter identification for LiBs is essential to assess the performance of energy storage systems within BMSs and EVs. This research explores the Fully Informed Search Algorithm (FISA), a novel optimization method, to determine the parameters of 2nd and 3rd order equivalent circuit models (ECM) for LiBs. As an enhanced version of the Rao algorithm, FISA is recognized for its efficiency in tackling real-world optimization problems while maintaining the simplicity and parameter-free nature of its predecessor. The study focuses on minimizing the error between the ECM-predicted voltage and the actual battery voltage measurements. To validate the proposed approach, a high dynamic profile (HDP) is employed, alongside a comparative analysis of FISA and the Rao algorithm. The simulation results demonstrate that FISA achieves highly accurate and stable parameter estimation, surpassing the precision of the Rao method. Moreover, findings indicate that the 3rd order ECM provides superior accuracy in capturing the parameters of the battery model.