Parallel computing essentially consists of computation and communication and, in many cases, communication performance is vital. Many parallel applications use collective communications, which often dominate the performance of the parallel execution. This paper focuses on collective communication performance to speed-up the parallel execution. This paper firstly offers our experimental result that splitting a session of collective communication to small portions (slices) possibly enables efficient communication. Then, based on the results, this paper proposes a new concept cup-stacking with a genetic algorithm based methodology. The preliminary evaluation results reveal the effectiveness of the proposed method.