The recent development of network technologies that offer centralized control of explicit routes opens the door to the online optimization of explicit routing. For this kind of Traffic Engineering optimization, raising the calculation speeds by using multi-core processors with effective parallel algorithms is a key goal. This paper proposes an effective parallel algorithm for General purpose Programming on Graphic Processing Unit (GPGPU); its massively parallel style promises strong acceleration of calculation speed. The proposed algorithm parallelizes not only the search method of the Genetic Algorithm, but also its fitness functions, which calculate the network congestion ratio, so as to fully utilize the power of modern GPGPUs. Concurrently, each execution is designed for thread-block execution on the GPU with consideration of thread occupancy, local resources, and SIMT execution to maximize GPU performance. Evaluations show that the proposed algorithm offers, on average, a nine fold speedup compared to the conventional CPU approach.