A matheuristic-based multi-objective evolutionary algorithm for flexible assembly jobs shop scheduling problem in cellular manufacture

The flexible assembly job shop scheduling problem (FAJSP) and its extensions have received increased attention. However, multi-objective FAJSP in cellular manufacture (FAJSP-CM), a real-world extension of FAJSP with important applications in the mass customization of complex products, is barely considered in most previous studies. Hence, this study first addresses the multi-objective FAJSP-CM problem via a mixed-integer linear programming model (MILP). Then, a matheuristic-based multi-objective evolutionary algorithm (MMOEA), with a matheuristic decoding method, knowledge-guided initialization and learning-based local intensification method, is presented to efficiently tackle the FAJSP-CM problem in polynomial-time. The matheuristic decoding method, which hybrids a decomposition linear programming model (D-LP) that can quickly and optimally allocate the execution times of all operations, to search for the optimal solution in a specific space. The knowledge-guided initialization is extended to get a high-quality and great-diversity initial population for accelerated convergence. Meanwhile, the learning-based local intensification method is developed to adaptively coordinate five problem-specific local search operators to enhance the exploitation ability of the MMOEA algorithm. Finally, comprehensive experiments based on 720 instances are conducted to evaluate the proposed MILP model and MMOEA algorithm. The results of the first experiments illustrate the MILP model can obtain the Pareto solutions of small-scale instances. The remaining experiments demonstrate that the proposed MMOEA algorithm outperforms its competitors by 0.21 and 0.72 in hypervolume ratio and coverage indictors, along with approximately a 25% improvement in success rate.