Statistical Learning-Assisted Evolutionary Algorithm for Digital Twin-Driven Job Shop Scheduling with Discrete Operation Sequence Flexibility

With the rapid development of Industry 5.0, smart manufacturing has become a key focus in production systems. Hence, achieving efficient planning and scheduling on the shop floor is important, especially in job shop environments, which are widely encountered in manufacturing. However, traditional job shop scheduling problems (JSP) assume fixed operation sequences, whereas in modern production, some operations exhibit sequence flexibility, referred to as sequence-free operations. To mitigate this gap, this paper studies the JSP with discrete operation sequence flexibility (JSPDS), aiming to minimize the makespan. To effectively solve the JSPDS, a mixed-integer linear programming model is formulated to solve small-scale instances, verifying multiple optimal solutions. To enhance solution quality for larger instances, a digital twin (DT)–enhanced initialization method is proposed, which captures expert knowledge from a high-fidelity virtual workshop to generate high-quality initial population. In addition, a statistical learning-assisted local search method is developed, employing six tailored search operators and Thompson sampling to adaptively select promising operators during the evolutionary algorithm (EA) process. Extensive experiments demonstrate that the proposed DT-statistical learning EA (DT-SLEA) significantly improves scheduling performance compared with state-of-the-art algorithms, highlighting the effectiveness of integrating digital twin and statistical learning techniques for shop scheduling problems. Specifically, in the Wilcoxon test, pairwise comparisons with the other algorithms show that DT-SLEA has p-values below 0.05. Meanwhile, the proposed framework provides guidance on utilizing symmetry to improve optimization in complex manufacturing systems.