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Solving multi-objective energy-efficient flexible job shop problems by a dual-level NSGA-II algorithm

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Abstract

Incorporating energy consumption into optimization has attracted increasing attention in both academia and industry. Nevertheless, the integration of green, flexible, and dynamic manufacturing in literature remains underexplored. To this end, we focus on a dynamic flexible job shop scheduling problem (dFJSP) relevant to aerospace structural components. The following challenging issues are considered, such as processing route flexibility, limited machine and tool resources, transportation time, setup time, new job arrivals, machine breakdowns, and various machine processing speeds. To address this complex problem, a dual-level multi-objective algorithm based on the nondominated sorting genetic algorithm II (hereafter called DLNSGAII) is developed. The first level incorporates a dynamic diffusion-based strategy (D-DBS), which aims to balance exploration and exploitation effectively. This is achieved by quickly identifying high-quality solutions and discarding inferior ones while also ensuring ample computational resources allocated for exploration to avoid convergence on local optima. At the second level, a static convergence-based search strategy (S-CBS) is conducted to allocate resources according to the potential of solutions to achieve faster convergence. Additionally, to tackle the disruptions, two sets of rescheduling mechanisms have been designed: one includes five strategies for integrating new job arrivals, and another encompasses two strategies for responding to machine breakdowns. Furthermore, to enhance the search capabilities toward different objectives, two critical-path-based neighborhood structures have been incorporated. Utilizing hypervolume (HV) and inverted generational distance (IGD) as evaluation metrics, a comparative analysis of algorithmic performance was conducted. Among the 35 experiments, DLNSGAII exhibited superiority in 88.57% and 63% of the total experiments based on the HV and IGD metrics, respectively, emphasizing its advantages in terms of convergence and generalizability.

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Acknowledgements

This research is partially supported by National Science Foundation of China under Grant 62473331, 62173216, Key projects of Yunnan Province Basic Research Program (202401AS070036), Yunnan Key Laboratory of Modern Analytical Mathematics and Applications (No. 202302AN360007).

Funding

National Natural Science Foundation of China, 62173216

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Authors and Affiliations

  1. Department of Mathematics, Yunnan Normal University, Kunming, 650500, China

    Junqing Li & Jiake Li

  2. School of Information Engineering, HengXing University, Qingdao, 266199, China

    Junqing Li

  3. School of Information Science and Engineering, Shandong Normal University, Jinan, 252014, China

    Junqing Li & Weimeng Zhang

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  1. Junqing Li
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Contributions

Junqing Li: Writing, Validation, Review & Editing, Funding acquisition. Wei-meng Zhang: Conceptualization, Methodology, Software, Validation. Jia-ke Li: Investigation, Writing, Experimental analysis, Reviewing.

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Correspondence to Junqing Li.

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Li, J., Zhang, W. & Li, J. Solving multi-objective energy-efficient flexible job shop problems by a dual-level NSGA-II algorithm. Memetic Comp. 17, 10 (2025). https://doi.org/10.1007/s12293-025-00449-3

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