**7. Conclusions**

In this paper, a relatively simple and direct method using turning-based mutation was proposed and tested on Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions against the SHADE, L-SHADE, and jSO algorithms. The basic thought of the proposed method is to change the direction of mutation under certain conditions to maintain the population diversity and a longer exploration phase. It can thus avoid premature convergence and escape the local optimum to ge<sup>t</sup> better optimization results. The results of experiments showed that this method is e ffective on CEC2020 benchmark sets in 10, 15, and 20 dimensions. The strong point of the proposed method is that it can be applied to variants of SHADE easily. A disadvantage is that it increases the time complexity and its e ffectiveness lacks theoretical proof. Our future research in the area will focus on further experiments, and on applying the proposed method to more algorithms. For example, the improved method may be useful for some practical problems featuring constraints.

**Author Contributions:** Conceptualization, H.K.; methodology, H.K.; project administration, L.J. and Y.S.; software, X.S.; validation, X.S. and Q.C.; visualization, L.J. and Q.C.; formal analysis, H.K.; investigation, Q.C.; resources, Y.S.; data curation, L.J.; writing—original draft preparation, L.J.; writing—review and editing, H.K. and X.S.; supervision: X.S.; funding acquisition: Y.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, gran<sup>t</sup> number 61663046, 61876166. This research was funded by Open Foundation of Key Laboratory of Software Engineering of Yunnan Province, gran<sup>t</sup> number 2015SE204.

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