Multi-population genetic algorithm with greedy job insertion inter-factory neighbourhoods for multi-objective distributed hybrid flow-shop scheduling with unrelated-parallel machines considering tardiness

Distributed manufacturing is gradually becoming the future trend. The fierce market competition makes manufacturing companies focus on productivity and product delivery. The hybrid flow shop scheduling problem (HFSP) is common in manufacturing. Considering the difference of machines at the same stage, the multi-objective distributed hybrid flow shop scheduling problem with unrelated parallel machines (MODHFSP-UPM) is studied with minimum makespan and total tardiness. An improved multi-population genetic algorithm (IMPGA) is proposed for MODHFSP-UPM. The neighbourhood structure is essential for meta-heuristic-based solving algorithms. The greedy job insertion inter-factory neighbourhoods and corresponding move evaluation method are designed to ensure the efficiency of local search. To enhance the optimisation ability and stability of IMPGA, sub-regional coevolution among multiple populations and re-initialisation procedure based on probability sampling are designed, respectively. In computational experiments, 120 instances (including the same proportion of medium and large-scale problems) are randomly generated. The IMPGA performs best in all indicators (spread, generational distance, and inverted generational distance), significantly outperforming existing efficient algorithms for MODHFSP-UPM. Finally, the proposed method effectively solves a polyester film manufacturing case, reducing the makespan and total tardiness by 40% and 60%, respectively.