Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm

Permutation flow shop scheduling problems (PFSPs) have been extensively studied because of its broad industrial applications. However, setup and transportation time are usually ignored in most research, which causes a huge gap between the theoretical research and practical application. Meanwhile, energy saving has attracted growing attention due to the advent of sustainable manufacturing. Thus, we investigate an energy-efficient PFSP with sequence-dependent setup and controllable transportation time from a real-world manufacturing enterprise. First of all, a novel multi-objective mathematical model considering both makespan and energy consumption is formulated based on a comprehensive investigation. Then, a hybrid multi-objective backtracking search algorithm (HMOBSA) is proposed to solve this problem. Furthermore, a new energy saving scenario is developed to simultaneously ensure the service span of machines and energy saving. Finally, to evaluate the effectiveness of the proposed HMOBSA and energy saving scenario, we compare our proposal with other two famous multi-objective algorithms including NSGA-II and MOEA/D by conducting a real-world case study. The experimental results indicate that the proposed HMOBSA is superior to NSGA-II and MOEA/D for this case. Additionally, the proposed energy saving scenario also outperforms its competitors.