EDSs are mainly designed meshed but operated radially for some technical and financial concerns. Distribution networks can be represented with a graph in ordered pairs consisting of a set of vertices, i.e. buses and a set of edges, i.e. branches; in terms of mathematics this equivalents to a sparse matrix which its non-zero elements signifies the existence of an edge in the system. On this basis a typical distribution network is radial if it forms a tree where each load bus is exactly supplied from one source node, i.e. substation bus . This suggests MOEDNRC problem as identifying the set of non-dominated trees of the given graph. In this section we’ve devised a heuristic technique based on this idea as well as the rules defined in  to retain the connectivity and radial properties of individuals during the optimization process. It’s worth mentioning that these properties are broadly disturbed by EAs due to the stochastic nature of these algorithms unless a heuristic plan is devised to preserve the mentioned properties. As a result generation of infeasible agents in sheer numbers by EAs is quite a normal observation. The proposed technique is able to prevail over this shortcoming and would increase the performance of EAs as well. Before proceeding with the designed technique, some terminologies are first introduced to set the stage for the plan.
• Loop vectors (LVs)
The term LV is used to identify branches contributing to forming loops in EDSs when all