Multi-objective green flexible job shop scheduling optimization based on constraint-aware transformer reinforcement learning

Driven by global carbon neutrality goals, manufacturing industries face dual challenges of production efficiency and environmental impact. This research addresses the multi-objective green flexible job shop scheduling problem (MO-GFJSP) by establishing a mathematical optimization model that comprehensively considers intelligent machine configuration, time-period-specific carbon emission factors, and multi-dimensional energy consumption modeling to simultaneously optimize three conflicting objectives: makespan, weighted total tardiness, and total energy consumption. To overcome the limitations of traditional solution methods in constraint handling and multi-objective optimization, we propose the Constraint-Aware Transformer Reinforcement Learning (CA-TRL) algorithm. The algorithm features a four-stage masking architecture corresponding to the hierarchical job-operation-machine-speed action space, where additive negative infinity masking combined with forward completability checking achieves empirically verified solution feasibility across all tested instances. A constraint-aware attention mechanism directly embeds hard constraints from the mathematical model into the neural network computation, while a multi-objective cooperative optimization mechanism based on vector rewards and generalized advantage estimation enables deep integration of reinforcement learning with multi-objective optimization. Experimental results on 33 standard benchmark instances demonstrate that CA-TRL achieves an average relative error of 1.5% compared to CPLEX optimal solutions on small-scale instances, the best IGD convergence accuracy of 0.162, competitive overall ranking among nine algorithms from evolutionary, deep reinforcement learning, and tree search paradigms, and sub-quadratic empirical time complexity with an exponent of 1.417. Analytical benchmark validation on classical test functions with varying Pareto front geometries confirms the effectiveness of the weighted scalarization design for the predominantly convex fronts observed in scheduling applications. Green scheduling evaluation shows that the algorithm achieves a 30.3% carbon emission reduction rate, 18.5% energy consumption reduction, and 45.0% nighttime utilization rate, providing effective technical support for low-carbon transformation in manufacturing.