One of the key functions of a supercomputer resource manager is to allocate jobs to the nodes within clusters or distributed computer systems. When running parallel jobs, different parts of the process interact with varying intensity, and how well the jobs are assigned to computing nodes directly impacts the efficiency of the job and the overall computing performance. Each time a job runs, the graph representing the application program needs to be matched with the graph of nodes that make up a subset of the computer system. Since both graphs are not known in advance, this mapping must be carried out within a reasonable timeframe while also managing resources. In our research, we have explored a cyclic composite mapping algorithm. This algorithm consists of two cyclic stages: parallel versions of simulated annealing and a genetic algorithm. Our experiments demonstrated that the proposed algorithm outperformed known mapping algorithms based on simulated annealing and genetic approaches in terms of both mapping quality and runtime.