A Pareto-based two-stage evolutionary algorithm for flexible job shop scheduling problem with worker cooperation flexibility

The previous studies on the flexible job shop scheduling problems (FJSP) with machine flexibility and worker flexibility normally assume that each machine is operated by one worker at any time. However, it is not accurate in many cases because many workers may be required for machines in processing complex operations. Hence, this paper studies a universal version, i.e., FJSP with worker cooperation flexibility (FJSPWC), which defines that each machine can be used only if their required workers are prepared. A mixed-integer linear programming model tuned by CPLEX is established for the problem aiming to collaboratively minimize the makespan, maximum workload of machines and maximum workload of workers. To solve the problem efficiently, a Pareto-based two-stage evolutionary algorithm (PTEA) is proposed. In the PTEA, a well-tailored initialization operator and the NSGA-II structure are designed for global exploration in the first stage, and a competitive objective-based local search operator is developed to improve its local search ability and accelerate the convergence in the second stage. Extensive experiments based on fifty-eight newly formulated benchmarks are carried out to validate the effectiveness of the well-designed initialization operator and two-stage architecture. Comprehensive experiments are performed to evaluate the proposed PTEA, and the results reveal that the PTEA is superior to four comparison algorithms concerning the distribution, convergence, and overall performance.