Air pollution, greenhouse gas problems and the rapid increase in demand for clean energy have led to increase in the demand for electric vehicles (EVs). However, unscheduled charging and discharging of EVs can cause many technical and economic issues for the upstream power grid, such as security and reliability concerns. Therefore, smart scheduling of EVs charging and discharging is essential. In this paper, a PSO-based algorithm is proposed for optimal scheduling of EVs charging and discharging in smart parking lots under real-world conditions. This algorithm is based on the initial and final values of the State Of Charge (SOC) of all EVs and the expected time information of entering and exiting the parking lot. For the uncertain behaviors of EV owners, penalties paid to the parking lot is considered. In the corresponding optimization problem, the profit of smart parking and the cost of EV owners are maximized. The proposed algorithm has been successfully tested with four real scenarios. According to the test results, the more flexibility is included in the uncertain behavior of EV owners, the parking profit decreases due to the reduction of penalty costs received from EV owners and vice versa. In scenario 2 with the highest fault flexibility, the parking profit decreases to a minimum of £2245. Also, in scenario 1, where no flexibility is allowed in the uncertain behavior of EV owners, parking profit reaches its maximum value of £20512. Also. cost of EV owners is minimized in scenario 2 and maximized in scenario 1.