Elevator Group Supervisory Control System (EGSCS) is a traffic system, which provides the transportation services for passengers in modern buildings. As the elevator systems include uncertainty due to the future arrival of the passengers, it difficult to model, analyze, and optimize the elevator group supervisory control system. Recently, artificial intelligence technology has been used in such complex systems. Genetic Network Programming(GNP), a graph-based evolutionary method extended from genetic algorithm and genetic programming, has been already applied to EGSCS. On the other hand, since energy consumption is becoming one of the greatest challenges in the society, it should be taken as one of the criteria of the elevator operations. The elevators with maximum energy efficiency are therefore required. In this paper, the GNP is used to solve EGSCS with energy consumption (EC). Moreover, the idle car assignment has been embedded in the proposed method. Finally, the simulations show that some factors should be introduced into GNP in order to deal with the higher EC in the light traffic of the elevator systems.