## 2 Background
### Related Work  
_(1) Automated design of dispatching rules._ Job-shop scheduling (JSS) is a combinatorial optimization problem that falls under the category of nondeterministic polynomial-time (NP) hard problems. It entails the allocation of various manufacturing tasks to machines at specific time intervals, with the aim of minimizing a set of objectives. The complexity of large-scale production issues poses challenges for the implementation of precise optimization techniques [19]. Hence, various heuristic optimization techniques, including the genetic algorithm [20], simulated annealing [21], and the ant colony algorithm [22], have been devised, to obtain near-optimal solutions for the static job-shop scheduling problem within a reasonable computational timeframe. In DJSS, it is possible for jobs to exhibit stochastic arrival patterns and their corresponding attributes may not be ascertainable prior to their arrival. Hence, conventional techniques for optimizing solutions are not feasible for dynamic scheduling problems, due to the restricted information horizon. Dispatching rules have been applied extensively to solve DJSS problems due to their computational efficiency. The reason for their widespread acceptance can be ascribed to their practical applicability, low computational complexity, and minimal information demands. In most cases, dispatching rules are regarded as a priority function, utilized to allocate priority to every job that is in the queue to be processed by a machine. Consequently, the tasks that hold the highest priority will be given precedence in processing. A large number of dispatching rules have been created by both practitioners and researchers to address diverse manufacturing conditions. Additional information can be found in various scholarly articles [23]. Dispatching rules are usually designed by experts in a tedious trial-and-error process, with candidate rules being tested in a simulation environment, modified, and retested until they fulfill the requirements for actual implementation in practice. In recent years, several researchers have suggested the automatic design of suitable dispatching rules by means of a hyperheuristic approach for JSS problems. Hyperheuristics combine the components utilized in current heuristics by different operators to build new heuristics, which are then trained on training problem cases and developed to become more successful. Regarding the automated construction of scheduling rules, it has been shown that GP is a promising hyperheuristic method, outperforming conventional machine learning techniques [24]. _(2) GP/GEP-based hyperheuristic for DJSS._ GP hyperheuristics have enabled the automatic evolution of high-quality heuristics, resulting in successful problem-solving outcomes in various domains, including (but not limited to) bin packing [25], cloud computing [26; 27], and vehicle routing [28; 29]. [PERSON] et al. [15] proposed a classification scheme for hyperheuristic methods based on their search procedures, encompassing the selection and generation of hyperheuristics. A succinct summary of the utilization of hyperheuristics in addressing diverse scheduling and combinatorial optimization problems was also devised. According to the authors, GP is a suitable approach for adapting dispatching rules in dynamic scenarios, despite its infrequent utilization for directly addressing production scheduling issues. [PERSON] et al. [30] designed GP algorithms with the goal of reducing mean flowtime as much as possible and demonstrating that their results are superior to those obtained using traditional dispatching rules. [PERSON] et al. [31] and [PERSON] et al. [32] are the only authors to have focused on shops with stochastic processing times. However, the former did not benchmark evolving rules against existing methods, while the latter considered deterministic job arrivals. Many researchers have emphasized the significance of increasing algorithmic effectiveness. For example, surrogate models allow for quicker fitness computation.