A multi-critical-path co-driven evolutionary algorithm addressing the dual-resource flexible job shop scheduling problem with offline operations and job priority constraints

In the customised manufacturing of complex structural components, such as precision instruments and ships, jobs often have different priorities and involve a mix of online and offline operations. To address these challenges, this paper studies the dual-resource flexible job shop scheduling problem with special workers and job priority constraints (DRFJSP-OJP). Correspondingly, a mixed-integer linear programming (MILP) model is developed, and a multi-critical-path co-driven evolutionary algorithm (MCPEA) is proposed, which includes three key innovations. Firstly, a priority-driven three-layer segmented encoding and priority-based multi-segment active decoding scheme is designed. Secondly, a migration operator based on exemplar selection is introduced to accelerate the convergence. Finally, the global critical-path of the problem and local critical-paths with priorities are defined, then a problem-specific neighbourhood structure is designed. The experimental results indicate that the constructed MILP model can successfully solve small-scale problems. Meanwhile, MCPEA demonstrates superior overall performance than other methods, not only improving production efficiency but also ensuring the timely processing of high-priority jobs. Finally, MCPEA is applied to a real-world case from a complex structural component manufacturing enterprise. The optimised scheduling scheme shortens makespan by 49.60%, and decreases delay rate by 33.33%.