## 2 State of the Art  
[PERSON] [17] introduced the job-shop scheduling problem (JSSP), which has been one of the fundamental challenges in operations research. This problem has attracted substantial attention due to its omnipresence in various industrial contexts and combinatorial nature, leading to computational intractability for even modest-sized problems [2]. This problem continuously sparks interest in the academic field, with novel variations and solution strategies consistently being introduced. Over the years, the academy has introduced numerous variants of the classical JSSP to accommodate more realistic production settings. These variations include varying processing times, random processing interruptions, and the integration of maintenance activities. For example, [PERSON] [18] explored the inclusion of variable processing times by formulating a tabu search algorithm in a study involving sequence-dependent setup times. In other research, [PERSON] et al. [19] addressed the unpredictability of processing interruptions, incorporating uncertainty into the permutation flow shop predictive scheduling problem. Lastly, [PERSON] et al. [20] considered maintenance activities in job scheduling by developing tailored metaheuristics for the flow-shop scheduling problem with an integrated maintenance activity component. These modifications to the traditional JSSP reflect an evolving comprehension of the complexities involved in real-world production environments. The need for more efficient solutions prompted authors to propose numerous heuristics to address the JSSP and its variations. These heuristic methods range from basic rule-based priority procedures to sophisticated metaheuristics. For instance, [PERSON] et al. [21] employed simple yet effective heuristics for the no-wait, flow-shop scheduling problem aiming at total flow time minimization. [PERSON] and [PERSON] [22] proposed a Tabu Search optimization approach designed explicitly for no-wait, hybrid, flow-shop scheduling with dedicated machines. [PERSON] et al. [23] combined a particle swarm optimization and simulated annealing in a hybrid algorithm to address the job-shop scheduling problem considering transport resources. Although these heuristics do not guarantee global optimality, they have proven effective in delivering high-quality solutions within reasonable computational times. Population-based algorithms, which build upon the foundation of heuristics, have demonstrated their value in solving complex scheduling problems. These algorithms, such as genetic algorithms (GAs), ant colony optimization (ACO), and particle swarm optimization (PSO), harness the power of populations of solutions to explore the search space broadly and efficiently. [PERSON] [24] laid the groundwork for GAs, an evolutionary-based search method extensively applied to JSSPs [25]. Similarly, ACO algorithms mimic the behavior of ants and their ability to find efficient paths. [PERSON] et al. [26] successfully implemented these algorithms by tackling combinatorial optimization problems, including JSSPs [27]. [PERSON] and [PERSON] [28] developed PSO, a swarm intelligence-based approach that adjusts the trajectory of individual solutions (particles) based on their performance and that of their neighbors, showing its efficacy on JSSP [29]. These population-based algorithms balance exploiting and exploring the solution space, which is essential for such combinatorial problems. Local search algorithms, including simulated annealing (SA), tabu search (TS), and variable neighborhood search (VNS), are renowned for their ability to explore the neighborhood of a given solution intensively. [PERSON] et al. [30] first proposed SA, which employs a probabilistic acceptance criterion that allows escaping local optima. It was efficiently used for JSSPs by [PERSON] et al. [31]. [PERSON] [32] introduced TS memory-based rules to prevent cycling. This method has shown impressive results on JSSP [33].