A learning-guided multi-objective approach for energy-oriented hybrid flow shop scheduling with limited buffers

To support the goal of sustainable manufacturing, recent studies have emphasized energy-efficient production scheduling, with the energy-oriented hybrid flow shop scheduling problem with limited buffers (EO-HFSP-LB) being particularly relevant in energy-intensive industries such as steel, cement, and aluminum. In this paper, we investigate an EO-HFSP-LB that simultaneously minimizes total weighted tardiness (TWT) and non-processing energy (NPE), two conflicting and non-regular objectives. To address this problem, we propose a learning-guided multi-objective evolutionary algorithm (LgMOEA) that can efficiently search for Pareto-optimal solutions by leveraging problem-specific knowledge. The main components of LgMOEA include: (1) a forward–backward scheduling procedure for solution decoding; (2) objective-guided genetic and neighborhood operators to effectively explore and exploit the solution space; and (3) a learning-guided operator selection module that dynamically balances exploration and exploitation. The proposed algorithm is evaluated on 25 well-synthesized benchmark instances. Computational results show that: (1) the LgMOEA outperforms state-of-the-art multi-objective algorithms in terms of hypervolume, spacing, and success rate; and (2) each module positively contributes to the search for Pareto-optimal solutions. The source code of LgMOEA is made available at: https://github.com/janason/Soft-Scheduling/tree/master/LgMOEA .