To achieve an optimal trade-off between production efficiency and energy benefits in complex manufacturing environments, this paper addresses the Green Flexible Job Shop Scheduling Problem (GFJSP) by establishing a multi-objective mathematical model that minimizes both makespan and total energy consumption. An Improved Non-dominated Sorting Genetic Algorithm II (INSGA-II) is proposed to solve this model. In the population initialization phase, chaotic mapping is integrated with multiple heuristic rules to generate a high-quality and uniformly distributed initial population. Furthermore, an enhanced elite selection mechanism is employed to effectively prevent premature convergence. Subsequently, adaptive crossover and mutation operators are designed to enable differentiated evolution across sub-populations, effectively coordinating global exploration and local exploitation. Finally, experimental results on the Brandimarte and Hurink benchmark datasets demonstrate the superiority of the proposed algorithm in terms of convergence and diversity, providing a robust solution for optimizing green industrial production scheduling.

To address the trade-off between production efficiency and sustainable manufacturing, this study investigates the green flexible job shop scheduling problem (GFJSP) by simultaneously minimizing makespan and total energy consumption. An improved decomposition-based multi-objective evolutionary algorithm (IMOEA/D) is proposed. The algorithm integrates a hybrid initialization strategy combining heuristic dispatching rules and chaotic diversification, a two-layer encoding scheme, a stagnation-triggered memory archive, an objective-oriented variable neighborhood search (VNS), and dynamic neighborhood updating. The encoding and decoding procedures preserve schedule feasibility, while the memory archive and VNS enhance the search for high-quality solutions. Experiments are conducted on 18 Brandimarte, Hurink, and Kacem benchmark instances. Ablation analyses show the proposed components have different effects on makespan and energy consumption, reflecting the conflicting nature of the two objectives. Sensitivity analyses of the control parameter, initialization schemes, and stagnation threshold show the adopted configuration provides a stable balance between convergence performance, energy consumption, and search diversification across the tested instances. Compared with five representative multi-objective algorithms, IMOEA/D achieves an average improvement of 54.79% in Hypervolume (HV) and an average reduction of 69.93% in Inverted Generational Distance (IGD) against their overall averages. The results indicate that IMOEA/D provides an effective approach for deterministic bi-objective GFJSP optimization.