## 1 Introduction
[9] studied the FJSP with preparation time and transportation time, and established a mathematical model by integrating these two kinds of adjustment time and processing time. The multi-agent system approach has also been found to converge faster than the comparison algorithms. On the basis of considering the adjustment time and processing time, [PERSON] and [PERSON] [10] proposed a scheduling problem of multi-equiment work centers with the goal of minimizing the makespan. In order to solve the FJSP with different adaptive properties, a lot of heuristic population evolution algorithms have been applied to various studies. [PERSON] et al. [11] proposed a hybrid algorithm combining the cooperative particle swarm optimization and the gravitational search, which used the ability of rapid optimization during the late evolution period to escape local optimization in time and ensure global optimization. The simulation results showed that the algorithm is superior to PSO and GA in solving the FJSP. [PERSON] et al. [12] developed a novel bionic-mixed bacteria foraging optimization algorithm, which, combined with a simulated annealing algorithm, effectively solved the flexible job shop scheduling problem with flexible sequencing. [PERSON] et al. [13] proposed a new variable neighborhood descent hybrid genetic algorithm to address the issues of the slow convergence speed and low precision of the genetic algorithm. The mutation operator based on BPSO, hybrid heuristic initialization strategy, and VND based on improved multi-level neighborhood structure were integrated into the framework of standard genetic algorithm, which proved the convergence performance and solution accuracy. On the basis of the brainstorming optimization (BSO) algorithm, [PERSON] et al. [14] introduced the delayed acceptance hill climbing method and three-neighborhood method to overcome the shortcomings of slow convergence speed and low global search ability. Numerical experiments showed that the performance of this algorithm is better than that of the original BSO algorithm. [PERSON] [15] combined the gravitational search algorithm with a memetic algorithm to establish a new algorithm, which can not only solve the multi-objective combinatorial optimization problem, but also keeps searching for the global optimal solution efficiently. [PERSON] et al. [16] studied the FJSP with the constraints of setup time, transportation time, and delivery time, aiming at minimizing the maximum completion time, total workload, workload of key machines, and late punishment. Three initialization methods, entropy, weight method, and non-dominated sorting method, are used in the improved ant colony optimization algorithm to improve the quality and diversity of the scheme and screen the superior and inferior solutions, respectively. Among many meta-heuristic algorithms, the shuffled frog leading algorithm is famous for its simple content, few parameters, strong searching ability, and strong computing ability. Many scholars have also improved the SFLA to solve specific FJSPs. [PERSON] et al. [17] integrated the concept of fuzzy logic into the SFLA, and selected frogs to form sub-members through fuzzy roulette wheel, which significantly improved the performance of the algorithm in solving the FJSP. [PERSON] et al. [18] integrated employee and job scheduling, and designed a set of SFLA to solve the FJSP with employee scheduling choice, pointing out that the jumping of the SFLA under multiple constraints effectively improved the efficiency of selection. [PERSON] [19] analyzed the disadvantages of the SFLA, and improved the local search strategy by introducing an adaptive migration factor, which avoided the algorithm from falling into the local optimum and improved the convergence speed and optimization accuracy.