Today, paying attention to the interests of suppliers in supply chain management strategies is one of the important points in the success of long-term and strategic relationships with suppliers. Not paying enough attention to these points sometimes causes irreparable damage to the overall structure of the organization. In response to this need, researchers have developed and proposed different models according to different approaches. This research has presented a special model with the approach of answering these problems. This approach, which is based on the cuckoo optimization algorithm (COA), can solve the problems in multi-objective methods in addition to single-objective problems. This method based on the COA and the ε-constraint method named COA/ε-Constraint. The general approach of this method is to turn a multi-objective problem into a single-purpose problem, which is associated with increased efficiency. The model studied in this paper, with the aim of creating coordination between buyers and suppliers in the problem of supplier selection, is a three-objective model of cost, quality and delivery time, which is implemented to evaluate the performance of the proposed method. The results show the superiority of the proposed method over similar approaches in terms of creating a Pareto frontier.