Energy-oriented Scheduling for Hybrid Flow Shop With Limited Buffers Through Efficient Multi-Objective Optimization

Efficient scheduling benefits productivity promotion, cost savings, and customer satisfaction. In recent years, with a growing concern about the energy price and environmental impact, energy-oriented scheduling is going to be a key issue for sustainable manufacturing. In this paper, we investigate an energy-oriented scheduling problem deriving from the hybrid flow shop with limited buffers. First, we formulate the scheduling problem with a mixed integer linear programming (MILP) model, which considers two objectives including minimizing the total weighted tardiness (TWT) and non-processing energy (NPE). To solve the NP-hard problem in the strong sense, we develop an efficient multi-objective optimization algorithm under the framework of the multi-objective objective evolutionary algorithm based on decomposition (MOEA/D). We devise a job-permutation vector to represent the scheduling solution and cover its search space. Since NPE is a non-regular function, we develop a two-pass decoding procedure composed of a discrete-event system (DES) simulation procedure and a greedily post-shift procedure. Besides, we apply an external archive population (EAP) to guide the algorithm to converge on a Pareto frontier and a local search procedure to enhance the diversity of the population. Finally, we conduct extensive computational experiments to verify the effectiveness of the proposed energy-oriented multi-objective optimization (EOMO) algorithm. The results presented in this paper may be useful for future research on energy-oriented scheduling problems in realistic production systems.