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This paper considers the solving of a multiobjective flexible job shop problem. This scheduling problem has two main characteristics: first, the flexibility of machines that have the potential to process all the operations with different processing times, and secondly taking into account the three criteria to be optimized simultaneously. The solving of this problem is based on a multiobjective evolutionary algorithm utilizing Pareto dominance. It makes use of direct coding of the solutions and exploits the NSGA II algorithm. A set of mutation heuristics are proposed in a view to direct mutation towards the best solutions. The efficiencies of these heuristics are compared with one another and also with lower bounds for every criteria.