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

Abstract

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.

The authors' abstract, as published at the source. Expert Systems with Applications, 2026 · DOI ↗