Distribution system reconfiguration problem is a complex optimization process to find a structure with minimum losses in which the satisfaction of both sides, that is consumers and distribution system companies, need to be met. One of the most significant parameters in this regard is to increase the reliability of system. This parameter, on one hand, increases the satisfaction of power consumption and on the other hand, improves the economic benefits of distribution companies. Distribution system reconfiguration, considering the reliability parameters, seems to make the attempts to solve the problem of optimization difficult. In this paper, a new heuristic approach for distribution system reconfiguration in order to decrease the power losses cost and damage cost due to power supply interruption of consumers has been presented. Radial network construction and all energized nodes constraints are the most important ones that should be considered in distribution system reconfiguration problem. Hence, in this paper a new codification is proposed which is computationally efficient and guarantees to generate only feasible radial topologies all times. In order to illustrate the performance of proposed heuristic method, modified 33-bus and 119-bus distribution networks have been employed which have led to the desired results.