The completion problem arises in various domains, including flexible manufacturing systems, logistics, telecommunications, and marketing. Its objective is to group or cluster a given set of available orders or customers within distribution warehouses or marketing management. This problem is widely recognized as a challenging discrete optimization problem classified as NP-Hard. This paper introduces an augmented population method that combines two key features: discrete particle swarm optimization and an \(\varepsilon \) -enlarging threshold operator. The method adopts an oscillating strategy, alternating between the \(\varepsilon \) -enlarging threshold operator and the periodic enhancement operator of particle positions at each step. This strategy aims to exploit information acquired through the enlarging strategy to extend the search to unvisited search spaces. Throughout the search process, both strategies work to maintain the diversity of the reference set, preventing premature convergence and stagnation on local optima. To evaluate the proposed method’s behavior and performance, benchmark instances from the existing literature are used. The proposed method’s results are then compared to those achieved by the best methods available in the literature. This comparative analysis enables the establishment of new performance bounds for the problem, highlighting the effectiveness of the proposed method.
