## 1 Introduction  
Distribution systems play a very important role as the final link between power utilities and customers and have been operated in a radial structure that aims for low cost and simple design. Due to the radial operation of distribution systems, a failure of components in the distribution system causes outages for the customers, which requires a fast and efficient service restoration (SR) plan for the outage loads in order to improve system reliability [1; 2; 3]. When a fault occurs in a distribution system, it is detected and located by utilizing distribution automatic equipment such as feeder remote terminal units (FRTUs) that sends the fault information to the distribution automation system (DAS) through communication links [4; 5]. Then, the fault is isolated from the main source by opening the upstream and downstream automatic switches of the fault. Restoration plans for outage loads are established by SR application in DAS considering various objectives (e.g., amount of load restored, network losses after changing system topology, number of switching required for the new topology), and constraints (e.g., voltage and line loading limits) according to the operation philosophy of a distribution system [6; 7; 8]. The SR can be regarded as a multi-objective non-linear problem of topology reconfiguration under a fault situation and optimization of switches (branches) in a distribution system [9]. Normally, distributed generations (DGs) are considered to be disconnected from a distribution system under a fault situation since islanding operations by DGs cause higher uncertainties and complexities in the operation under emergency conditions. However,intentional islanding schemes based on island partitioning have been studied to facilitate the self-sufficient capability of DGs for SR problems by forming microgrids since the islanding operation of DGs could be a means of power supply for important loads in outage areas [10; 11; 12; 13]. By utilizing the intentional islanding of DGs, benefits such as system reliability and outage cost can be achieved. The power balance, the difference between DG capacities and loads in an island, as well as normal constraints in distribution system operation, should be taken into account when a distribution system under faults is partitioned into several islands [14; 15]. The intentional islanding method of DGs using island partitioning has been studied by several researchers in recent years. The method in [16] uses minimum spanning tree and dynamic programming methods to quickly achieve distribution network island separation under the constraints. In [17], an energy-risk-evaluation-based island partition strategy considering the power supply and demand balance is proposed. The research [18] proposes a dynamic islanding planning method based on strong search capability under Dijkstra Algorithm optimizing controllable loads in the system. The study [19] presents the islanding strategy using a systematic reduction of tertiary loads and expanding the external supply capacity of the microgrid to include an islanding assessment metric for the reliability of the obtained strategy. In [20], an island partition scheme considering the importance of loads and their controllability is proposed based on the established mathematical model. Another research [21] presents a multi-objective reconfiguration optimization method to improve the minimum node voltage and reduce network loss. The islanding configuration is determined in [21] by a centralized controller that performs a load forecast to evaluate the probability of successful operation of any possible islanding. A procedure for autonomous partitions of a microgrid without connections to the main source is proposed in [22]. The study [23] proposes the improved leapfrog algorithm to solve the tree backpack island partition optimization model with a DG.