**5. Conclusions**

A quantum-inspired differential evolution algorithm with grey wolf optimizer (QDGWO) was proposed to solve the 0-1 knapsack problems. The proposed algorithm combined the superposition principles of quantum computing, differential evolution operations, and the hunting behaviors of grey wolves. The QDGWO used the principles of quantum computing such as quantum superposition states and quantum gates. Furthermore, it contained mutation, crossover, and selection operations of the DE. To maintain a better balance between the exploration and exploitation of searching for the global optimal solution, the proposed algorithm adapted a quantum rotation gate with the adaptive GWO to update the population of solutions. The results of tests performed for resolving the knapsack problems demonstrate that the QDGWO was able to enhance diversity and convergence performance for solving 0-1 knapsack problems. In addition, the QDGWO was effective and efficient in finding the optimal solutions for high-dimensional situations.

Although the QDGWO displays excellent performance in solving 0-1 knapsack problems, there are several directions of improvement for the proposed algorithm. First, to improve the effectiveness of the QDGWO, initial solutions of the quantum population can be generated with metaheuristic methods. In addition, the proposed approaches can be applied to solve other combinatorial optimization problems. Moreover, it is worth studying

how to use the concepts of quantum computing in other novel metaheuristic approaches such as the MPA [22] and AOA [27], as well as multi-objective optimization algorithms.

**Author Contributions:** Conceptualization, Y.W. and W.W.; methodology, Y.W.; software, Y.W.; validation, Y.W.; formal analysis, Y.W.; investigation, Y.W.; resources, Y.W.; data curation, Y.W.; writing— original draft preparation, Y.W.; writing—review and editing, Y.W. and W.W.; visualization, Y.W.; supervision, W.W.; funding acquisition, W.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. 61873240).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank the anonymous reviewers for their constructive comments and suggestions. This work was supported in part by the National Natural Science Foundation of China (No. 61873240).

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