In this paper, we investigate a reconfigurable intelligent surface (RIS) aided multi-pair communication system, in which multi-pair users exchange information via an RIS. We derive an approximate expression for the achievable rate by assuming that statistical channel state information (CSI) is available. A genetic algorithm (GA) to solve the rate maximization problem is proposed as well. In particular, we consider implementations of RISs with continuous phase shifts (CPSs) and discrete phase shifts (DPSs). Simulation results verify the obtained results and show that the proposed GA method has almost the same performance as the globally optimal solution. In addition, numerical results show that three quantization bits can achieve a large portion of the achievable rate for the CPSs setup. Index Terms-Reconfigurable intelligent surface (RIS), intelligent reflecting surface (IRS), statistical channel state information (CSI), multi-pair communication, genetic algorithm (GA).