## 1 Introduction  
Large-scale scheduling optimization problems have attracted much attention from both academia and industry. Scheduling problems involving more than 20 machines and 50 parts are defined as large-scale scheduling problems [1]. As manufacturing tasks and resources increase, the space of feasible solutions for an algorithm to solve large-scale scheduling problems increases exponentially. Finding an optimal solution within a reasonable computation time is challenging for most algorithms [2]. At the same time, diversification and personalization of products receive attention, resulting in the need for manufacturing enterprises to quickly meet the market demand for variety and small batches. Inter-cell scheduling has gradually become an essential method for sharing resources in manufacturing. Inter-cell scheduling problems involve intra-cell scheduling optimization and inter-cell scheduling optimization of exceptional parts, which is more complicated than job-shop scheduling problems [3]. Therefore, it is necessary for algorithms to have high searching capability to solve large-scale inter-cell scheduling problems. There are two common ways to solve large-scale scheduling optimization problems. One is to decompose large-scale scheduling problems into several sub-problems, based on decomposition strategies [4]. According to decomposition mode, methods to decompose a large-scale scheduling problem can be classified into time-oriented, machine-oriented, and job-oriented decomposition methods, etc. The time-oriented decomposition method is to divide a large-scale scheduling problem into several sub-problems by segmenting the total scheduling time into multiple time intervals. For example, refs. [5, 6] divided the total time of a scheduling problem into several time windows and each sub-problem within a time window was optimized independently. However, the time-oriented decomposition method is difficult to apply for problems with unclear time segments. It is concluded that decomposition methods often rely too heavily on model constraints and decomposition modes. Other researchers [7; 8] have proposed machine-based decomposition methods to reduce the complexities of solving large-scale scheduling problems. Machines were divided into several cells based on process similarity or constraints. Each cell was scheduled individually. However, exceptional parts in inter-cell scheduling problems require transportation to other cells, which makes sub-problems interconnected. The machine-oriented decomposition method has difficulty solving inter-cell scheduling problems. The job-oriented decomposition method is to divide jobs into several batches based on certain properties (e.g., due date of jobs) and schedule them independently [9; 10]. It reduces the complexities of scheduling problems by reducing the number of jobs to be scheduled. Key issues for the method include job combination and batch size, which require a deep understanding of the problems [11]. In addition, not only the job-oriented decomposition method but also all the decomposition methods mentioned above find it difficult to yield global optimal solutions for original large-scale problems due to focusing on scheduling sub-problems [12]. Although these decomposition methods can simplify large-scale scheduling optimization problems, there are still some limitations and problems in real applications. Another way to solve large-scale scheduling problems is to improve intelligent optimization algorithms. As spaces of feasible solutions and computational complexity increase exponentially with the scale of scheduling problems, it is difficult for intelligent optimization algorithms to yield acceptable solutions within a reasonable calculation time [13]. In order to solve large-scale scheduling problems, it is essential for intelligent optimization algorithms to improve their searching ability and convergence speed [14]. Efforts have been made using various methods to improve the performance of algorithms.