In this paper, a novel optimization methodology based on single and multi-objective formulation is proposed for optimal allocation of electric fast charging stations (EFCSs). The suggested methodology is planned for selecting the optimal candidate buses to supply the EFCSs in mesh transmission networks. Moreover, the algorithm locates the EFCSs geographically by determining the service line length of the connecting cable between the EFCS and the candidate bus. Afterwards, this problem is solved using the enhanced slime mould algorithm (ESMA) characterized by a novel searching technique, adaptive grouping strategy, and efficient learning operator. The adapted objective aims to minimize the summation of voltage deviations at all buses due to the high-power demand of EFCSs. Additionally, another objective is formulated concerning the line stability aspect and solved using the multi-objective version of SMA (called MOSMA). Finally, the problem gets more comprehensive by incorporating an economic perspective of minimizing the total running energy cost during the whole charging process. It is worth mentioning that the proposed ESMA’s performance is validated and compared with other competitors such as the traditional SMA, particle swarm optimizer, and osprey optimization algorithm. In all cases, the ESMA outperforms all other competitors by attaining the minimum objective function values satisfying all the operational constraints. Using the computed metrics for each simulation set, the outcomes of the multi-objective particle swarm optimizer and the multi-objective water cycle algorithm are compared to the proposed MOSMA. Highlighting some results, the MOSMA achieves total voltage deviations of 14.9 % and energy cost of $4109.55 in the IEEE 14-bus benchmark test case. Undoubtedly, the MOSMA establishes its superiority in solving this complicated optimization problem either in 2-D or 3-D objective formulations.