**6. Conclusions**

In this study, we constructed a model of CS with *Q*-Learning and genetic operators, and then solved the address of logistics distribution center with DMQL-CS algorithm in which adopts *Q*-Learning scheme to learn the individual optimal step size strategy according to the e ffect of individual multi-steps. The most appropriate step size control strategy is chosen as a parameter for the current step size evolution of the cuckoo, which increases the adaptability of individual evolution. At the same time, to accelerate the convergence of the algorithm, genetic operators and hybrid operations are added to DMQL-CS algorithm. Crossover and mutation operations expand the search area of the population, and accelerate the convergence of the DMQL-CS algorithm.

To verify the performance of DMQL-CS, DMQL-CS was employed to solve fifteen benchmark test functions and CEC 2013 test suit. The results show that the proposed DMQL-CS algorithm clearly outperforms the standard CS algorithm. Comparing with some improved CS variants and DE variants, we found that DMQL-CS algorithm outperforms the other algorithms on a majority of benchmarks. In addition, the e ffectiveness of the proposed method was further verified by comparing with CS, ICS, CCS, and IGA for both 6 and 10 distribution centers.

In the future, we will focus our research work on the study of special cases to strengthen the algorithm in more complex conditions. We will determine how to generalize our work to handle combinatorial optimization problems and to extend DMQL-CS optimization algorithms to in the realistic engineering areas and feature selection for machine learning [102].

**Author Contributions:** Conceptualization, J.L.; methodology, H.L.; software, D.-d.X. and T.Z.; validation, T.T.; writing—original draft preparation, J.L. and H.L.; writing—review and editing, D.-d.X. and T.Z.; funding acquisition, J.L. and T.T.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by doctoral Foundation of Wuhan Technology and Business University (No. D2019010) and the National Natural Science Foundation of China (No. 61503220).

**Acknowledgments:** The authors would like to thank the anonymous reviewers and the editor for their careful reviews and constructive suggestions to help us improve the quality of this paper.

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