Electric vehicles are among the elements which can play an effective role in improving the network's reliability. To utilize this potential, creating desirability in vehicle owners can increase their participation in plans offered by electric utilities. Thus, reduction of distances traveled by vehicles from their initial place to parking lots, in addition to sharing the benefits raised form their participation in the plan with them, can increase this cooperation. In this paper, by proposing a statistical model for the presence of electric vehicles in the network and by introducing two scenarios for choosing the parking lots, the improvement of network's reliability is dealt with besides the reduction of the distances traveled by vehicles. The effects of car owners' behavior in choosing the parking lots as well as the effects of the distance between the vehicles and parking lots are among the innovations of this paper. The combination of goals using fuzzy function, along with utilizing and comparing the performance of Genetic Algorithm, Particle Swarm Optimization and Gravitational Search, are the other subjects of this paper.