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Flexible job shop scheduling problem (FJSP) is a very important problem in the modern manufacturing system. It is an extension of the classical job shop scheduling problem. It allows an operation to be processed by any machine from a given set. It is also a NP-hard problem. This paper proposes a multi-swarm collaborative evolutionary algorithm (MSCEA) to solve FJSP. Experimental studies have been used to test the approach, and the comparisons have been made between this approach and some previous approaches to indicate the adaptability and superiority of the proposed approach. The experimental results show that the proposed approach is a promising and very effective method on the research of FJSP.