A hybrid framework integrating machine-learning and mathematical programming approaches for sustainable scheduling of flexible job-shop problems

Flexible job shop scheduling has received considerable attention due to its extensive applications in manufacturing. High-quality scheduling solutions are desired but hard to be guaranteed due to the NP-hardness of computational complexity. In this work, a novel energy-efficient hybrid algorithm is proposed to effectively address the scheduling of flexible job shop problems within reasonable time frames. The hybrid framework hybridizes gene expression programming, variable neighborhood search, and simplified mixed integer linear programming approaches to minimize the total energy consumption. It is utilized to address 20 benchmark examples with moderate-or high-complexities. Computational results show that the hybrid algorithm can reach optimality for all considered moderate-size examples within two seconds. The proposed algorithm demonstrates significant competitive advantages relative to the existing mathematical programming approaches and a group-based decomposition method. Specifically, it shortens the computational time over one order of magnitude in some cases and leads to lower total energy consumption with a maximum decrease by 14.5%.