## 2 State of the Art
Moreover, the VNS paradigm proposed by [PERSON] and [PERSON] [34] systematically explores increasingly distant neighborhoods to intensify and diversify the search, delivering effective results when used on FSSP [35]. These local search strategies offer deep search capabilities that contribute to the effectiveness of hybrid algorithms like MAs. Recent advancements in scheduling research have explored diverse methodologies to address complex industrial challenges, from hybrid metaheuristics to AI-driven optimization and maintenance-integrated frameworks. [PERSON] et al. [36] proposed a hybrid spider monkey optimization (HSMO) algorithm for parallel PCB assembly lines to maximize profit by optimizing line assignment, component allocation, and sequencing, though it did not consider machine efficiency decay or maintenance. Similarly, [PERSON] et al. [37] introduced an improved spider monkey optimization (ISMO) algorithm for PCB assembly, addressing multi-objective challenges such as energy consumption, maintenance time, and completion time through features like Q-learning-based parameter tuning and Paretoentropy balancing. While these approaches focus on specific industrial contexts, they highlight the potential of hybrid metaheuristics for broader applications. [PERSON] et al. [38] advanced AI-driven optimization with their two-stage double deep Q-network (TS-DDQN) algorithm, effectively managing dynamic job-shop scheduling with multi-objective considerations like tardiness and utilization, though maintenance and efficiency decay remain unaddressed. [PERSON] et al. [39] emphasized the integration of preventive and corrective maintenance in multifactory assembly scheduling, leveraging mixed-integer programming for deterministic and stochastic scenarios to optimize makespan. While these studies offer significant contributions, our research extends these frameworks by uniquely addressing the job-shop scheduling problem with variable machine efficiency and maintenance activities (JSSP-VME-MT), bridging critical gaps in adaptability and realism. Finally, memetic algorithms (MA) combine the evolutionary framework with local search techniques and have been effectively applied to tackle the JSSP. This class of hybrid algorithms leverages the strengths of global and local search strategies, resulting in better solutions. Notably, [PERSON] et al. [40] employed a memetic algorithm to solve the permutation flow shop problem to minimize total tardiness. [PERSON] et al. [41] proposed a memetic algorithm that incorporates a critical path-based crossover operator to manage search processes for the job-shop scheduling problem effectively. Finally, [PERSON] et al. [42] utilized a Q-learning-driven multipopulation memetic algorithm incorporating flexible preventive maintenance, demonstrating the adaptability of memetic algorithms to account for maintenance considerations. These studies illustrate the potential of memetic algorithms to deliver high-quality solutions in diverse job-shop scheduling scenarios. As summarized in Table 1, prior research on maintenance planning in production scheduling has addressed various objectives and methodologies, but key gaps remain. Limited focus has been placed on integrating variable machine efficiency into maintenance models or developing dynamic approaches that adapt to real-time changes. Additionally, the application of hybrid optimization methods to joint job scheduling and maintenance remains underexplored. This study bridges these gaps by proposing an integrated approach that addresses these critical challenges. \begin{table}
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