Elevator Group Supervisory Control System (EGSCS) is a very large scale stochastic dynamic optimization problem. Due to its vast state space, significant uncertainty, and numerous resource constraints such as finite car capacities and registered hall/car calls, it is hard to manage EGSCS using conventional control methods. Recently, many solutions for EGSCS using Artificial Intelligence (AI) technologies have been reported. Genetic Network Programming (GNP), which is proposed as a new evolutionary computation method several years ago, is also proved to be efficient when applied to EGSCS problem. In this paper, we propose an extended algorithm for EGSCS by introducing Reinforcement Learning (RL) into GNP framework, and expect to make an improvement of the EGSCS' performances since the efficiency of GNP with RL has been clarified in some other studies like tile-world problem. Simulation tests using traffic flows in a typical office building have been made, and the results show an actual improvement of the EGSCS' performances comparing to the algorithms using original GNP and conventional control methods.