Distributed Heterogeneous Hybrid Flow-Shop Scheduling under Uncertain Processing Times: A Deep Learning and Multi-Objective Evolutionary Algorithms Framework
Abstract
With economic globalisation and the growing demand for customisation, distributed manufacturing has become a dominant production pattern, introducing considerable scheduling challenges due to diverse product types and heterogeneous machine capabilities. This study addresses the Distributed Heterogeneous Hybrid Flow-Shop Scheduling Problem (DHHFSP) under uncertain processing times. An enhanced Long Short-Term Memory (LSTM) is developed to predict Production Completion Times (PCT) by capturing temporal dependencies across varying products and machine configurations. The optimal prediction performance is achieved with 10,000 training samples, yielding a MAE of 2.176, a MAPE of 1.32%, and a coefficient of determination (R2) of 0.959. These predictions are integrated into a multi-objective optimisation framework based on Multi-Objective Evolutionary Algorithms (MOEAs) to minimise total order earliness and tardiness and balance production line workloads. Parameter sensitivity experiments are conducted to identify effective algorithmic configurations, ensuring fair and representative comparisons. A constructive heuristic based on a novel task assignment strategy is further introduced to generate high-quality initial solutions. Experimental results on real-world cases demonstrate that the NSGA-II, combined with heuristic initialisation, achieves the most balanced trade-off between objectives. This hybrid framework provides a robust and intelligent scheduling strategy for complex manufacturing environments by combining data-driven prediction, parameter-optimised evolutionary search, and heuristic enhancement.