## 5 IICA-QL for EEMsMIAJSP
### Revolution Based on Hyper-Heuristic Variable Neighborhood Search
Through the research presented, the proposed IICA-QL has demonstrated its effectiveness in addressing the dual objectives of minimizing the maximum completion time and total energy consumption. The superiority of the proposed IICA-QL can be attributed to its two key designs:

1. The energy-efficient decoding trigger mechanism is one of the key innovations of the IICA-QL. This mechanism ensures that, while maintaining high-quality solutions, the search process is significantly accelerated. This approach not only maintains the quality of the solutions but also expedites the convergence process, allowing the algorithm to explore the solution space more efficiently. 2. IICA-QL achieves a balance between exploration and exploitation by using Q-learning to dynamically adjust operator parameters based on search feedback. This adaptive mechanism helps the algorithm explore new areas while refining high-quality solutions, ensuring efficient convergence, maintaining diversity, and avoiding premature stagnation. ## 7 Conclusions

This study addressed the multi-stage, multi-level assembly job shop scheduling problem, aiming to minimize the maximum completion time and total energy consumption. An improved imperialist competitive algorithm based on Q-learning (IICA-QL) was proposed. First, a mathematical model of the problem was established, and an energy-efficient strategy decoding trigger mechanism was designed to simultaneously enhance solution quality and search efficiency. Second, the IICA-QL for solving the EEMsMIAJSP was proposed. In IICA-QL, two heuristic rules and a random generation method are used to collaboratively construct an initial population with high quality and diversity. A dynamic adaptive adjustment strategy for the assimilation operator parameter was implemented based on Q-learning to enhance convergence speed while maintaining population diversity; thus, the exploration and exploitation capabilities of the algorithm are better balanced. A hyper-heuristic variable neighborhood search-guided revolution operation was designed to conduct detailed searches on identified high-quality colonies. The competitive phase was replaced with a joint imperialist invasion operation to achieve cooperative co-evolution and information exchange among multiple empires, resulting in more evenly distributed non-dominated solutions. Finally, the effectiveness of the proposed algorithm in solving the EEMsMIAJSP was verified through experimental results and comparison with other algorithms. However, this study has certain limitations. First, the current model assumes static energy prices, but in real industrial environments, energy prices may fluctuate over time, which can significantly influence scheduling decisions. Therefore, future research could incorporate dynamic energy pricing models to better align with real production scenarios. Second, uncertainty is another important aspect not addressed in this study. We assumed a deterministic production environment, without considering uncertainties such as processing time fluctuations or machine breakdowns, which could greatly impact scheduling decisions in practice. Therefore, we will explore robust scheduling or scenario-based scheduling to address these uncertainties in future work. **Author Contributions:** Conceptualization, Y.D. and W.L. ; methodology, Y.D. and W.L. ; software, Y.D. ; formal analysis, Y.D., W.L. and G.X. ; investigation, Y.D., W.L. and G.X. ; resources, W.L. ; data curation, Y.D., W.L. and G.X. ; writing--original draft preparation, Y.D. ; writing--review and editing, Y.D. and W.L. ; visualization, G.X. ; supervision, W.L. ; project administration, Y.D. and W.L. ; funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Chengdu Science and Technology Project of the Chengdu Science and Technology Bureau, Sichuan Province (NO: 2023-JB00-00020-GX). **Informed Consent Statement:** Not applicable.