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Particle swarm optimization is a population-based stochastic algorithm designed to solve difficult optimization problems, such as the flexible job shop scheduling problem. This problem consists of scheduling a set of operations on a set of machines while minimizing a certain objective function. This paper presents a two-level particle swarm optimization algorithm for the flexible job shop scheduling problem. The upper level handles the operations-to-machines mapping, while the lower level handles the ordering of operations on machines. A lower bound-checking strategy on the optimal objective function value is used to reduce the number of visited solutions and the number of objective function evaluations. The algorithm is benchmarked against existing state-of-the-art algorithms for the flexible job shop scheduling problem on a significant number of diverse benchmark problems.