## 1 Introduction  
Since the manufacturing industry is one of the most energy-intensive sectors, the question of how to effectively improve energy efficiency while maintaining production efficiency is currently a major focus within the industry [1]. Energy-efficient scheduling (EES) utilizes limited resources to rationally arrange production and optimize the production process, which is an effective way to effectively reduce the energy consumption in manufacturing systems [2]. Recently, EES has been successfully applied to various scheduling problems in discrete manufacturing industries, yielding positive results. As an extension of the classic job shop scheduling problem (JSP), the multi-stage, multi-level assembly job shop scheduling problem (MsMIAJP) not only involves multiple stages of production from processing to assembly but also considers complex assemblies composed of multiple jobs with a tree-like multi-level structure consisting of components and subassembibles [3]. It plays an important role in quickly responding to the manufacturing of customized products with multi-variety and small batches. However, as the complexity of the problem increases, leading to more product structural levels and manufacturing stages, constraints become more complex. This results in idle time between and within stages, significantly increasing idle energy consumption [4]. Therefore, further research is needed to explore the energy-efficient multi-stage, multi-level assembly job shop scheduling problem (EEMsMIAJP) for complex multi-level products. The EEMsMIAJSP is highly complex with a vast solution space, presenting challenges for efficient resolution. Currently, solutions to such complex energy-efficient scheduling problems typically focus on two main areas: energy-efficient strategies and algorithm design. Energy-efficient strategies primarily include three key approaches: turning off/on [5], block-moving strategy [6], and machine speed adjustment [7]. Among these, the block-moving energy-efficient strategy is one of the most widely used techniques [8]. It allows for a reduction in energy consumption by adjusting the processing sequence of operations without compromising other objectives. However, while this strategy has been extensively applied, an area that has not been fully explored is how to enhance its computational efficiency while maintaining solution quality. In terms of algorithm design, the imperialist competitive algorithm (ICA) has been successfully applied to various energy-efficient scheduling problems due to its strong global and local search capabilities [9; 10]. However, further research is needed to explore and design mechanisms that can effectively balance the exploration and exploitation capabilities of the ICA when solving large-scale, complex scheduling problems like the EEMsMIAJSP. To address these issues, we propose an improved ICA based on Q-learning (IICA-QL) to solve the EEMsMIAJSP, aiming to minimize the maximum completion time and total energy consumption. The main contributions of this paper are as follows:  
1. A mathematical model for the EEMsMIAJSP with the optimization objectives of minimizing the maximum completion time and total energy consumption is established. 2. An energy-efficient strategy decoding trigger mechanism is designed to simultaneously enhance solution quality and search efficiency. 3. A dynamic adaptive adjustment strategy for the assimilation operator parameter is 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. The specific structure of this paper is as follows: The literature review and related work are shown in Section 2. The problem definition and mathematical model are established in Section 3. The encoding and decoding design is presented in Section 4. The introduction of the improved imperialist competitive algorithm based on Q-learning (IICA-QL) is described in Section 5.