## 1 Introduction
### Literature Review and Motivation  
Studies in this field should take into account the effects of the operational performance in MGs. However, numerous researches on MGs have only focused on the optimization of their operations. In such studies, the optimization of the operational cost as well energy savings and emission reductions are the primary objectives, and different algorithms are employed to solve the optimization problem. A method for the economic dispatch optimization of MGs, which considers the load as well as microturbine (MT) constraints was proposed with the aim of minimizing the fuel cost [11]. Low-cost operations and energy management are generally considered as necessary for MGs to ensure that they can meet the power demand, facilitate improved penetration levels of renewable energy, and allow for control over the power exchanged with the utility grid [12; 13]. The power flow and cost management of MGs have been studied in depth [14; 15]. A decentralized architecture for multiagent systems has also been proposed for the economic dispatch of MG [16]. However, their operation is complicated by the bidirectional energy exchange between the MGs and DN [17]. Therefore, further research on power system operation is necessary to determine a suitable approach for cooperation between the DN and MG.  
Furthermore, various uncertainties pertaining to the economic operation of MGs have been considered. These factors are based on the assumption that low-voltage DNs sell energy to the MGs at real-time pricing tariffs [18]. In addition to these studies, which have only focused on the economic operation of MGs, several works have explored the benefits of using MGs with the DN. In this regard, an integrated solution that considered both the load dispatch of the MGs and reconfiguration of the main grid was proposed in an attempt to minimize the total operational costs of the main grid with multiple MGs [19]. Moreover, a co-optimization planning model for MGs was proposed, which considered the reliability of the power system as well as several economic criteria relating to the generation and transmission systems and the MG [20]. However, these co-optimization problems cannot be resolved directly using conventional optimal algorithms. Optimal operation of the entire power system should enable the decision makers to optimize their respective objective functions independently while simultaneously cooperating with one another. Thus, several researchers have studied bi-level optimization models to address this issue [21; 22; 23]. However, only the DN operation has been optimized in these studies, without the tie-line control being considered in the analysis. Therefore, further research relating to the decision-making framework that considers the tie-line control is required to achieve optimal cooperation between the DN and MG.  
Recent work has also introduced various structures and methods for optimizing the operation of MGs, including approaches that use various optimization algorithms for MGs with different DERs. In particular, attempts at optimizing MG operations using a mixed integer nonlinear programming (MINLP) model have been reported, in which the aim was to minimize an objective function that considered the initial investment, operations, repair and maintenance, and environmental costs [24].  
However, the mathematical solutions for models, such as that based on MINLP cannot be used to optimize large-scale nonlinear problems, which must be addressed using heuristic techniques. As a solution to this problem, the non-dominated sorting genetic algorithm II (NSGA-II) was used to allocate power to the units in the power system economically [25]. Although this algorithm incorporates several advanced concepts, including elitism, fast non-dominated sorting, and diversity maintenance along the Pareto solution, it still exhibits shortcomings in sustaining lateral diversity and acquiring the Pareto solution with high uniformity.