This thesis provides an analysis of the application for evolutionary scheduling of collective communications. It proposes possible ways to accelerate the application using general purpose computing on graphics processing units (GPU). This work offers a theoretical overview of systems on a chip, collective communications scheduling and more detailed description of evolutionary algorithms. Further, the work provides a description of the GPU architecture and its memory hierarchy using the OpenCL memory model. Based on the profiling, the work defines a concept for parallel execution of the fitness function. Furthermore, an estimation of the possible level of acceleration is presented. The process of implementation is described with a closer insight into the optimization process. Another important point consists in comparison of the original CPU-based solution and the massively parallel GPU version. As the final point, the thesis proposes distribution of the computation among different devices supported by OpenCL standard. In the conclusion are discussed further advantages, constraints and possibilities of acceleration using distribution on heterogenous computing systems.