Electric vehicles (EVs) have witnessed a steady and continuous rise in the last few years. The increased prevalence of EVs results in high demand for electricity from the power grid and it can be effectively handled by combining EV charging infrastructure with renewable energy sources (RES). However, the intermittent characteristic of RES introduces an additional challenge to the power grid. This paper proposes a metaheuristic algorithm called self-adaptive elephant herd optimization algorithm (SA-EHO) to achieve the desired dispatch model of microgrid (MG) with EVs and RES. The proposed algorithm optimizes both economic and emission cost of MG which comprises diesel engine (DE), solar photovoltaic (PV), EVs, fuel cell (FC), wind turbine (WT), and loads. The output constraints associated with a distributed power supply such as power limits of distributed generators (DG) and charging of EVs followed by its discharging are subjected to optimization. Finally, the performance of the proposed model is compared and proved over other existing models. Especially, a minimal total cost of the proposed model is 16.79%, 21.58%, 20%, 26.67%, and 1.33% superior to traditional HSA, GA, EHO, MSA, and FS-MSA models at 100th iteration. Furthermore, the reserved cost of the proposed scheme for the third scenario is 77.78%, 90.91%, 85.71%, 90.91%, and 90.91% superior to existing models such as HSA, GA, EHO, MSA, and FS-MSA, respectively.