This paper focuses on the development of optimization-based distributed scheduling strategies for the coordination of an energy intet (EI) with multi-microgrids with consideration of forecast uncertainties. All microgrids have flexible loads, schedulable loads and critical loads;some microgrids have distributed generators, such as micro-turbines, wind turbines, photovoltaic panels;besides, a few microgrids have energy storage devices, such as battery storage. Each microgrid is considered as an individual entity and has its individual objective, these objective functions of microgrids are formulated by mixed integer programming (MIP) models. A game theory based parallel distributed optimization algorithm is proposed to coordinate the competitive objectives of the microgrids with only a little information interaction. A model predictive control (MPC) framework which integrates the distributed optimization algorithm is developed to reduce the negative impacts introduced by the uncertainties of the EI. Simulation results show that our method is flexible and efficient.