The flexible job shop scheduling problem (FJSP) is an extension of the classical job shop scheduling problem and one of the more well-known NP-hard problems. To get better global optima of the FJSP, a novel hybrid whale optimization algorithm (HWOA) is proposed for solving FJSP, in which minimizing the makespan is considered as the objective. Firstly, the uniformity and extensiveness of the initial population distribution are increased with a good point set (GPS). Secondly, a new nonlinear convergence factor (NCF) is proposed for coordinating the weight of global and local search. Then, a new multi-neighborhood structure (MNS) is proposed, within which a total of three new neighborhoods are used to search for the optimal solution from different directions. Finally, a population diversity reception mechanism (DRM), which ensures to some extent that the population diversity is preserved with iteration, is presented. Seven international benchmark functions are used to test the performance of HWOA, and the results show that HWOA is more efficient. Finally, the HWOA is applied to 73 FJSP and four Ra international instances of different scales and flexibility, and the results further verify the effectiveness and superiority of the HWOA.

The flexible job shop scheduling problem (FJSP) is of great importance for realistic manufacturing, and the problem has been proven to be NP-hard (non-deterministic polynomial time) because of its high computational complexity. To optimize makespan and critical machine load of FJSP, a discrete improved grey wolf optimization (DIGWO) algorithm is proposed. Firstly, combined with the random Tent chaotic mapping strategy and heuristic rules, a hybrid initialization strategy is presented to improve the quality of the original population. Secondly, a discrete grey wolf update operator (DGUO) is designed by discretizing the hunting process of grey wolf optimization so that the algorithm can solve FJSP effectively. Finally, an adaptive convergence factor is introduced to improve the global search ability of the algorithm. Thirty-five international benchmark problems as well as twelve large-scale FJSPs are used to test the performance of the proposed DIGWO. Compared with the optimization algorithms proposed in recent literature, DIGWO shows better solution accuracy and convergence performance in FJSPs at different scales.