In this paper we propose a method of using a heuristic Genetic Algorithm (GA) to solve the Fast Fourier Transform subchannelization scheduling (FFTSS) problem in IEEE 802.16 broadband wireless access systems. In such a multi-user transmission system with quality of service (QoS) requirements, data from different users should be quickly scheduled and transmitted within the shortest transmission time period. In this paper, we propose a GA-based scheduler that will search the best configurations of the uplink and/or downlink sub-frames in order to obtain the optimal system throughput as well as quality of services. Due to the slow convergence of conventional GAs, we design a novel hardware architecture to accelerate the processing speed of GA which is used for scheduling the Down Link (DL) sub-frames. We then describe the procedure of using Field-Programmable Gate-Array (FPGA) to implement the designed hardware to verify the convergence of the algorithm. With this hardware implementation, the proposed method indeed helps us to construct a fast optimization tool to be applied in broadband wireless communication systems.