**6. Conclusions**

The present study investigated the FFSP–PB problem. Since the standard HNN algorithm easily falls into local extremum and is difficult for continuous evolution, this study proposed the SAA–HNN algorithm for global optimization. It adopts the Metropolis acceptance mechanism of the simulated annealing algorithm, such that the HNN algorithm can accept the non-optimal solution. Thus, the evolutionary vitality of the HNN algorithm is enhanced, rendering it the ability to jump out of the local extremum. Consecutively, considering the influence of the public buffer on the scheduling process, the reentrant rules of the electric flat carriage and workpiece transfer rules in the public buffer for controlling the movement of the workpiece are designed according to the transit time-cost of the workpiece among the workstation, the limited buffer, and the public buffer, as well as the processing status of the workpiece during the production. This phenomenon reduces the production blockage and improves the utilization of production resources. Finally, the simulation experiment proves that the SAA–HNN algorithm, combined with the improved local scheduling rules, can solve the FFSP–PB problem.

The actual production process has some local scheduling rules, such as setup time rules, process specification rules, and customer specification rules. If these local scheduling rules coexist with the relevant local scheduling rules established for the public buffer in the present study, the complexity of the whole scheduling optimization process would increase, and certain conflicts would occur between some of the local scheduling rules. Since the problem of conflict resolution between local scheduling rules are beyond the scope of this study, the main directions of future work are divided into the following:


**Author Contributions:** Conceptualization, Z.H. and C.H.; methodology, S.L.; validation, X.D. and H.S.; writing—original draft preparation, Z.H.; writing—review and editing, C.H.; supervision, H.S.; funding acquisition, Z.H.

**Funding:** This research was funded by the Liaoning Provincial Science Foundation, China (grant number: 2018106008), the Natural Science Foundation of China (grant number: 61873174), the Project of Liaoning Province Education Department, China (grant number: LJZ2017015), and the Shenyang Municipal Science and Technology Project, China (grant number: Z18-5-015).

**Conflicts of Interest:** The authors declare no conflicts of interest.
