Particle swarm optimization is a population-based stochastic algorithm designed to solve difficult optimization problems, such as the flexible job shop scheduling problem. This problem consists of scheduling a set of operations on a set of machines while minimizing a certain objective function. This paper presents a two-level particle swarm optimization algorithm for the flexible job shop scheduling problem. The upper level handles the operations-to-machines mapping, while the lower level handles the ordering of operations on machines. A lower bound-checking strategy on the optimal objective function value is used to reduce the number of visited solutions and the number of objective function evaluations. The algorithm is benchmarked against existing state-of-the-art algorithms for the flexible job shop scheduling problem on a significant number of diverse benchmark problems.

中文翻译：

---

柔性作业车间调度问题的两级粒子群优化算法

粒子群优化算法是一种基于种群的随机算法，旨在解决困难的优化问题，例如灵活的车间调度问题。这个问题包括在最小化某个目标函数的同时在一组机器上调度一组操作。针对柔性作业车间调度问题，提出了一种两级粒子群优化算法。上层处理操作到机器的映射，而下层处理机器上的操作的顺序。最优目标函数值的下限检查策略用于减少访问解决方案的数量和目标函数评估的数量。