Modified and hybrid artificial fish swarm algorithm for solving discrete fuzzy multi- objective unrelated parallel machine scheduling problem

The Unrelated Parallel Machines Scheduling Problem (UPMSP) is a discrete optimization problem widely applied in industrial decision-making. However, it often involves fuzzy uncertainty due to imprecise measurements and incomplete data. Moreover, identifying optimal solutions using exact algorithms is challenging, especially when multiple objectives are involved. Thus, this research proposes a modified Artificial Fish Swarm Algorithm (AFSA), originally designed for continuous problems, to minimize fuzzy multi-objective makespan and total tardiness. The proposed modified algorithm incorporates aspiration behavior, improved parameters, and a transformation method to adapt to discrete UPMSP. Three problem sets with varying job and machine sizes were generated to evaluate the modified AFSA algorithm. Using statistical measures including minimum, maximum, mean, standard deviation, and the Wilcoxon signed-rank test, its performance was compared with the standard AFSA and five of its variants proposed in the literature. The modified algorithm achieved the best minimum value of makespan and total tardiness in three of ten small instances and in nine of ten medium and large instances. This demonstrated that the proposed algorithm significantly outperformed the others existing algorithms, particularly for medium and large-sized problems. However, due to inferior results for machine sizes four to ten, improvements were made by hybridizing the modified AFSA with a neighborhood search algorithm. The hybrid algorithm benefits from AFSA’s global exploration, and the robust local exploitation provided by neighborhood operations, leading to more superior results. A comparison with three sets of algorithms including the modified AFSA, single metaheuristics, and hybrid metaheuristics was conducted to assess performance. The computational results confirmed that the hybrid algorithm significantly surpassed its competitors. Overall, this study contributes to improving job scheduling and enhances the efficiency of solving discrete problems, particularly UPMSP using modified and hybrid AFSA, ultimately leading to better scheduling quality across various industries. The proposed algorithms can also be extended to solve combinations of multi-objectives in more complex scheduling environments, such as job shop or flow shop scheduling