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Flexible job-shop scheduling problem (FJSP) is one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical job shop scheduling problem where an operation can be processed by several different machines. The FJSP contains two sub-problems, namely machine assignment problem and operation sequencing problem. In this paper, we propose and compare a discrete firefly algorithm (FA) and a genetic algorithm (GA) for the multi-objective FJSP. Three minimization objectives are considered, the maximum completion time, workload of the critical machine and total workload of all machines. Five well-known instances of FJSP have been used to evaluate the performance of the proposed algorithms. Comparisons among our methods and state-of-the-art algorithms are also provided. The experimental results demonstrate that the FA and GA have achieved improvements in terms of efficiency. Solutions obtained by both algorithms are comparable to those obtained by algorithms with local search. In addition, based on our initial experiments, results show that the proposed discrete firefly algorithm is feasible, more effective and efficient than our proposed genetic algorithm for solving multi-objective FJSP.

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