Optimization of machine configuration and scheduling in the hybrid flow shop using a linear programming-driven evolutionary approach

• A LP-driven evolutionary algorithm is developed that integrates LP-based neighborhood search for sequence refinement. • Proposed the mixed-integer linear programming (MILP) model for HFSP-MC. • Three LP strategy are presented to adapt to the problem size and the solution speed. • Through ablation experiments and comparative experiments , the effectiveness of the proposed approach is verified and the impact on different scale are discussed. The growing demand for flexible production systems is driven by product diversity and fluctuating order volumes. Seasonal variations can lead to imbalances between available machines and order demands, making efficient resource configuration critical before production begins. This paper addresses the optimization of machine configuration and scheduling in the hybrid flow shop, incorporating the order delivery time window. Most previous studies have focused on fixed machine numbers, while this study considers uncertain machine availability. This paper presents the mixed-integer linear programming model of the problem, and a linear programming (LP)-driven variable strategies evolutionary approach. The proposed approach combines an evolutionary algorithm with LP-driven neighborhood search for sequence optimization. Three strategies are constructed by narrowing down the search scope, which effectively reduces the algorithm's stagnation time and speeds up the convergence. To evaluate the effectiveness of the approach, the scales of application of the three LP strategies are first tested. Then ablation and comparison experiments are conducted, which show that the proposed approach generally agrees with the MILP results on small-scale problems and with smaller time resources. Experiments on 60 sets of large-scale problems show that the proposed approach has significant advantages over 5 state-of-the-art evolutionary algorithms and the MILP model. Additionally, the experiments show that the LP-driven strategy can improve the algorithm efficiency by about 13.32 % compared with the conventional strategy. These results demonstrate the potential of the LP-driven evolutionary approach for solving the complex scheduling problem.