An enhanced NSGA-II with Q-learning and VNS for multi-objective scheduling in additive manufacturing

Additive manufacturing (AM) is a key enabler of modern intelligent manufacturing, yet its widespread industrial adoption is hindered by long processing times and substantial energy overheads. To address this challenge, this paper formulates a multi-objective AM scheduling model that jointly minimizes makespan and total energy consumption by integrating part-to-machine allocation, batch grouping, and candidate build orientation planning. To efficiently navigate the resulting high-dimensional combinatorial search space, two domain properties—including a machine-allocation pruning rule and a batch-height/support-volume orientation optimization mechanism—are mathematically derived to restrict redundant decision paths. Based on these analytical insights, an improved non-dominated sorting genetic algorithm II enhanced with Q-learning-guided variable neighborhood search, termed NSGA-II-QLVNS, is proposed. The algorithm incorporates a population segmentation and hybrid initialization strategy to co-optimize initial part orientations and machine assignments. Furthermore, property-guided neighborhood operators and an adaptive Q-learning control engine are embedded within the local search to dynamically adjust search intensity, balancing global exploration and intensive exploitation. Comprehensive numerical experiments against state-of-the-art metaheuristics and the commercial MIP solver Gurobi demonstrate that NSGA-II-QLVNS consistently yields superior Pareto fronts with substantial reductions in both makespan and energy consumption, while maintaining favorable computational scalability.