Microgrids assisted by renewable energy resources are complex man made systems of various interconnected components. A number of real life scenarios relating to resource management in microgrids are modeled as multi-objective optimization formulations where multiple objectives may or may not conflict with each other. While considering the type of application, input and output of the problem, the nature of optimization problem changes. To address various types of optimization problems relating to microgid design, planning and operation, there exist a number of optimization solution types. We investigate the existing literature to classify different optimization objectives with respect to designing, planning and operation of microgrids. Some mathematical formulations for commonly used objectives relating to resource management in microgrids have been tabulated. We also classified the optimization types being used to address various optimization problems relating to resource management in microgrids. Various types of solution approaches along with the relevant simulation tools are also presented. We also reviewed the multicriteria optimization for different application areas of smart grid. The article can serve as a foundation for further research in the area of multicriteria decision making relating to resource management in micrgorids.