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This paper presents a multi-objective mathematical model for a flexible job shop scheduling problem (FJSSP) with fuzzy processing times, which is solved by a hybrid intelligent algorithm (HIA). This problem contains a combination of a classical job shop problem with parallel machines (JSPM) to provide flexibility in the production route. Despite the previous studies, the number of parallel machines is not pre-specified in this paper. This constraint with other ones (e.g., sequence-dependent setup times, reentrant workflows, and fuzzy variables) makes the given problem more complex. To solve such a multi-objective JSPM, Pareto-based optimization algorithms based on multi-objective meta-heuristics and multi-criteria decision making (MCDM) methods are utilized. Then, different comparison metrics (e.g., quality, mean ideal distance, and rate of achievement simultaneously) are used. Also, this paper includes two major phases to provide a new model of the FJSSP and introduce a new proposed HIA for solving the presented model, respectively. This algorithm is a hybrid genetic algorithm with the SAW/TOPSIS method, namely HGASAW/HGATOPSIS. The comparative results indicate that HGASAW and HGATOPSIS outperform the non-dominated sorting genetic algorithm (NSGA-II) to tackle the fuzzy multi-objective JSPM.

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