Optimization methods for a hybrid microgrid system that integrated renewable energy sources (RES) and supplies reliable power to remote areas, were considered in order to overcome the intermittent nature of RESs. The hybrid AC/DC microgrid system was constructed with a solar photovoltaic system, wind turbine, battery storage, converter, and diesel generator. There is a steady increase in the utilization of hybrid renewable energy sources with hybrid AC/DC microgrids; consequently, it is necessary to solve optimization techniques. Therefore, the present study proposed utilizing multi-objective optimization methods using evolutionary algorithms. In this context, a few papers were reviewed regarding multi-objective optimization to determine the capacity and optimal design of a hybrid AC/DC microgrid with RESs. Here, the optimal system consisted of the minimum cost of energy, minimum net present cost, low operating cost, low carbon emissions and a high renewable fraction. These were determined by using multi-objective optimization (MOO) algorithms. The sizing optimization of the hybrid AC/DC microgrid was based on the multi-objective grey wolf optimizer (MOGWO) and multi-objective particle swarm optimization (MOPSO). Similarly, multi-objective optimization with different evolutionary algorithms (MOGA, MOGOA etc.) reduces energy cost and net present cost, and increases the reliability of islanded hybrid microgrid systems.