The ability to withstand extreme disasters has a profound impact on the distribution network operation. This paper proposes a novel optimal operation strategy for an active distribution network to enhance system resilience.. The objectives in the proposed optimal strategy include, the resilience, operation cost, and its pollutant emissions. According to the existence of uncontrollable distributed energy resources in the active distribution network, the problem which takes the uncertainty most into account, is this multi-objective optimization problem. Thus, it can be treated as a min-max dual robust optimization problem. Benders decomposition is employed to decouple the problem, then non-dominated sorting genetic algorithm II is applied to search the multi-objective optimal solution which has an extremely low CPU time. The modified standard IEEE 34-node system, with different distributed energy resources types, is employed, as a studied case, to demonstrate the effectiveness of the proposed optimal operation strategy. The simulation results illustrate that, compared to other economic-oriented robust optimal operation models, the proposed strategy can enhance system resilience without a significant increase in the operation cost and pollutant emissions.