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An attempt has been made in this paper to reveal the trends and challenges in optimization techniques for operating and controlling the Microgrid, a controllable part of the smart grid. The Operation and control of Microgrid clearly fits into the broad area of multi-objective optimization problem. A critical analysis of the through literature review indicates that the alternative intelligent methods as compared to the slower conventional methods are showing better promise in the area of optimization. The latest trend shows the shift towards computational alternatives from the traditional iterative techniques (gradient based methods) due to the need of deriving near-optimum results in short periods of time. The computational alternatives include evolutionary, heuristic, and nonclassical algorithms.