The distribution system is demanded to be more efficient, more flexible and more intelligent due to the continued growth of the electricity loads, the high efficiency of energy utilization and the environmental protection. The traditional distribution systems are facing the challenge of evolving from passive networks to the active distribution networks (ADN) with the integration of multiple controllable resources. This paper presents an optimal operation and schedule model of the ADN, considering a variety of controllable resources such as distributed generations, battery storages and interruptible loads. To solve the optimization problem, a modified fuzzy adaptive PSO assisted by Kriging model (KMA-MFAPSO) is developed in this paper. In KMA-MFPSO, a novel constraint handling technique (CHT) based on the PSO is proposed to handle the constraints effectively. In addition, under the premise of ensuring the accuracy of the calculation, the Kriging model is used in KMA-MFAPSO to calculate the power flow the ADN approximately, which greatly speeds up the solving process. Finally, the effectiveness of the proposed algorithm is tested on a modified IEEE-123 system. The optimal results obtained by the proposed method are compared with the results obtained by using other solving algorithms. The simulation results indicate that KMA-MFAPSO is very robust and fast to solve the optimization problem so that it can be used in practical systems.