Efficient multi-objective optimization algorithm for hybrid flow shop scheduling problems with setup energy consumptions

This paper proposes an energy-aware multi-objective optimization algorithm (EA-MOA) for solving the hybrid flow shop (HFS) scheduling problem with consideration of the setup energy consumptions. Two objectives, namely, the minimization of the makespan and the energy consumptions, are considered simultaneously. In the proposed algorithm, first, each solution is represented by two vectors: the machine assignment priority vector and the scheduling vector. Second, four types of decoding approaches are investigated to consider both objectives. Third, two efficient crossover operators, namely, Single-point Pareto-based crossover (SPBC) and Two-point Pareto-based crossover (TPBC) are developed to utilize the parent solutions from the Pareto archive set. Then, considering the problem structure, eight neighborhood structures and an adaptive neighborhood selection method are designed. In addition, a right-shifting procedure is utilized to decrease the processing duration for all machines, thereby improving the energy consumption objective of the given solution. Furthermore, several deep-exploitation and deep-exploration strategies are developed to balance the global and local search abilities. Finally, the proposed algorithm is tested on sets of well-known benchmark instances. Through the analysis of the experimental results, the highly effective proposed EA-MOA algorithm is compared with several efficient algorithms from the literature.