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Flexible job scheduling problem (FJSP) is an extension of classical job scheduling problem (JSP) and also a problem faced by flexible manufacture system (FMS). In this paper, FJSP is decomposed into two sub different problems which are process planning and job scheduling, and two representations are designed for the two sub problems respectively. A symbiotic evolutionary algorithm is proposed to solve FJSP by putting the two sub problems together. To strengthen the search ability, a neighbourhood multi-parent crossover operator and a neighbour-based fitness function are developed and utilized in this paper. The experimental results show the proposed symbiotic evolutionary algorithm can solve FJSP well.