# Networked Microgrids: A Review on Configuration, Operation, and Control Strategies
## 2 Networked Microgrids' Configuration
### Formation
#### 2.1.3 Mixed-Integer Programming Methods  
Mixed-integer programming (MIP) serves as a mathematical optimization approach essential for addressing problems wherein decision variables can assume both continuous and discrete values, analogous to the challenges encountered in the formation of NMGs. In the context of NMG formation, the initial step involves creating a mathematical model that comprehensively represents all aspects of the microgrid-formation problems. Typically, graph theory methods, as discussed in references [22; 28; 30; 31; 32; 33; 34; 35; 36; 37], are employed to model the intricate relationships within the microgrid. Subsequently, the optimization objective is established, aiming to determine optimal values for decision variables that either minimize or maximize an objective function, while adhering to a set of constraints. This process enables the formulation of an efficient and effective optimization framework for configuring networked microgrids.  
Various types of MIP formulations are applied to address different aspects of forming NMGs. The specific MIP formulation used depends on the characteristics of the microgrid, the objectives, and the constraints of the problem. These methods are generally classified into three classes which include mixed-integer nonlinear programming (MINLP), mixed-integer linear programming (MILP), and mixed-integer second-order cone programming (MISOCP). MINLP extends MIP to handle scenarios where the objective function or constraints include nonlinear relationships, allowing decision variables to take both continuous and integer values. This approach is utilized in [27] to identify a set of viable microgrid clusters, aiming to maximize the restoration of loads within a radial distribution system. While MINLP methods ensure precision without resorting to linearization or convex relaxation that could impact solution accuracy, they suffer from computational inefficiency. Additionally, relaxing integer constraints during the solution process gives rise to nonconvex sub-problems due to the nonconvex nature of power flow equations. To overcome these challenges, MISOCP and MILP methods are introduced. MISOCP, a convex-based mixed-integer formulation, is proposed in [28; 39; 40] for the dynamic formation of NMGs, aiming to maximize served loads while considering radial and power flow constraints. This formulation strives to offer efficient and accurate solutions, steering clear of the computational inefficiencies and nonconvexity associated with MINLP.  
MILP proves to be faster than alternative methods, although it compromises some level of accuracy as its approach involves linearizing the objective function and constraints, along with restricting certain decision variables to integer values. MILP methods find common application in the swift restoration of critical loads in resilience-oriented NMGs' formation problems, as evidenced in various studies [22; 29; 30; 31; 32; 33; 34; 35; 36; 37]. The linearized consideration of power flow and radial topology constraints is employed in [29; 31; 32; 33; 34; 35; 36; 37; 38] to reduce problem complexity. While many studies integrate operation constraints related to power balance and limitations on power, voltage, and current, the inclusion of additional constraints, such as frequency limits [22], the count of switching events [32], hardening constraints [37], and the integration of demand-response measures [62], contributes to enhancing problem realism, bringing it closer to real-world conditions.  
In summary, according to research findings in [63], concerning NMG formation using MIP methods, MILP stands out for its rapid computational solutions and scalability. In contrast, MISOCP excels in providing superior accuracy, and MINLP ensures exactness despite the longer computational times.