This paper presents a framework to determine the optimal siting and sizing of Wind-based distributed generators (WDGs) and energy storage systems (ESSs) in a micro-grid (MG), considering the total active power losses in the system, the self-adequacy index (SAI), and the total annual cost (TAC) of the WDGs and the ESSs. The work in this paper employs multi-objective optimization (MOO) based on archived multi-objective simulated annealing in order to obtain a diverse set of Pareto optimal solutions. The analysis formulates the siting and sizing optimization problem considering a MG with a Fast Direct Current Charging Station (FDCCS). The results of the simulation have revealed that the optimal solution results in a trade-off between increasing SAI and increased TAC. Finally, it was seen that the optimal siting and sizing of the WDGs are highly affected by the location of the FDCCS.