## 1 Introduction  
The flexible job-shop scheduling problem (FJSP) is an expanded version of the traditional job-shop scheduling problem (JSSP), with additional flexibility and complexity in the scheduling process [1]. The FJSP involves determining the operation sequence for executing operations with satisfied constraints and the selection of suitable machines to carry out these operations, considering factors such as compatibility, efficiency, and resource utilization [2]. Consequently, the FJSP emerges as a highly demanding problem, characterized by its status as an extremely nondeterministic polynomial-time hard (NP-hard) problem that demands intensive computational effort to derive optimal solutions [3]. Scheduling has received a lot of research attention, but most of it has focused on static scheduling. In real-world smart factories, production environments must deal with uncertainty, as various unpredictable and dynamic occurrences frequently arise. In industry, such events are referred to as dynamic scheduling problems [4]. These include issues such as machine breakdowns [5], unexpectedly arriving jobs [6], and order cancellations [7]. Such unpredictable events add complexity to the scheduling and coordination of operations, highlighting the need for scheduling methodologies to address the dynamic flexible job-shop scheduling problem (DFJSP), which deals with two types of datasets: single-purpose machine datasets and multi-purpose machine datasets. The method that can help to solve the dynamic event problem is rescheduling; this approach involves rescheduling when a new event occurs [8].  
The GA is widely used for scheduling and optimization problems due to its ability to explore the solution space and find the near-optimal solution, but it has a low convergence rate and is capable of falling into the local optima, which can result in longer computational times and may impact performance [9; 10]; to avoid these conditions, many studies have proposed the hybrid algorithms explained above. Therefore, this study suggests using a hybrid genetic algorithm, simulated annealing, and variable neighborhood search (GASAVNS) algorithms to enable strong local search ability with global optimization. Another contribution is the influence of the hybrid algorithm on various dynamic scenarios observed in the context of flexible job-shop scheduling. The method that is used for dynamic scheduling is rescheduling with the hybrid GASAVNS algorithm by extracting the static scheduling data. All observations for dynamic events will be carried out on the obtained datasets and datasets from [11]. The simulation results show that the proposed method works well in both scheduling and rescheduling for the FJSP and DFJSP, respectively.  
The structure of the remaining manuscript is as follows: A literature review is presented in Section 2. Section 3 gives a brief description of the FJSP formulation of both datasets, namely the single-purpose machine and multi-purpose machine datasets, along with the required assumptions to initiate the FJSP. Section 4 explains the proposed method, the hybrid GASAVNS algorithm, while Section 5 elaborates on the proposed rescheduling method for dynamic events such as machine breakdown and job arrival. Section 6 presents the experimental results and analysis for the FJSP and various dynamic events using both datasets. The conclusion is provided in Section 7.