Implementing microgrids in power systems will improve the network reliability and reduce the impact of outages on end-users. Determining the most efficient boundaries of microgrids under contingencies is one of the main challenges for utilities from reliability and economics points of view. Currently, most research works have been focused on predefined boundary or static microgrids regardless system conditions and priority or importance of customers. In this paper, a novel concept for designing and operation of flexible microgrids in order to improve the reliability of a power distribution system is proposed. Compared to current approaches, boundaries of the proposed flexible microgrids can be extended or shrunk based on generation and demand levels, technical constraints, and customers' comfort. Furthermore, a demand response (DR) program is performed to maintain a balance between generation and consumption in the microgrid. In this paper, genetic algorithm (GA) and mixed-integer linear programming (MILP) are simultaneously applied to a model and solve two-stage optimization considering utilities' profits and customers' satisfaction. In planning level, GA is utilized for sitting and sizing of distributed generations and placement of switches. In operation level, MILP is used to select target switches as boundaries of optimal microgrids, model priority of customers, and determine the contribution of each load in the DR program. The case study is also presented and final results show the superiority of the proposed method compared with the traditional fixed boundaries method in microgrids.