## 1 Introduction  
The production and assembly of large and complex mechanical products, such as airplanes, ships, and automobiles [1, 2], are typically based on group technology (GT). Specifically, products are divided into several structural components that form independent assembly units, based on their overall structural characteristics and the requirements of the production process. These components comprise varying numbers of parts, with each part undergoing specific processing operations to create subassemblies. All subassemblies then advance to the assembly stage, where they are combined to form the final product. This production mode, which encompasses both processing and assembly operations, is commonly classified as the assembly job shop scheduling problem (AJSP) [3]. In most studies on AJSP, there is limited consideration of the flexibility in selecting processing machines and assembly teams. Additionally, processing times are typically treated using fixed standard processing times, which may not accurately reflect real-world scenarios. Fluctuations in processing times complicate scheduling in assembly job shops, thereby impacting the execution of production plans [4]. This underscores the necessity to investigate flexible assembly job shop scheduling problems with uncertain processing times. The establishment of standard processing times is a crucial measure for enhancing production efficiency in the machining industry. However, in the assembly job shop environment, some production and assembly operations are fully automated, while others may necessitate human-machine collaboration or may be performed completely manually. Consequently, various factors complicate the accurate determination of processing times in the production of complex mechanical products [5; 6]. For instance, in the case of prototype products, the process routes are often not fully defined during the trial production phase, leading to numerous initial trial productions. Consequently, processing times exhibit significant uncertainty. In assembly operations, assembly time is closely linked to workers' proficiency; variability in skill levels among workers introduces considerable uncertainty in assembly operation times [7]. In traditional shop scheduling optimization, it is generally assumed that actual processing times align with standard processing times. These standard processing times are typically derived by collecting multiple processing times for batch-produced products and calculating either the mean or median. Scheduling solutions generated under this assumption will inevitably deviate significantly from reality during execution, resulting in degraded schedule performance or even rendering the schedule infeasible [8]. Additionally, various forecasting methods are frequently employed in actual production, such as estimating processing times based on work factors and the workload associated with different tasks. However, these methods often lack sufficient accuracy, and when the number of operations is large, the accumulation of errors can significantly affect production plans. Currently, most manufacturing enterprises possess the capability to collect and store production process data [9; 10]. Through the statistical analysis of historical data, uncertain processing times can be represented in different mathematical forms, among which interval numbers are the most common and practical representation. In light of this, this work addresses a FAJSP with uncertain interval processing times. According to the problem definition, the FAJSP is an extension of the traditional job shop scheduling problem (JSP) [11]. In addition to the basic assumptions of the JSP, the FAJSP studied in this work also takes into account the process sequence constraints in both the processing and assembly stages, the flexibility of machine selection, and the handling of interval processing times. Compared to JSP, FAJSP has a wider range of applications, but the corresponding difficulty in solving the problem is also significantly greater.