**5. Conclusions**

Clustering is a common data analysis and data mining problem. It aims to group similar data objects into sets of disjoint classes. Symmetry can be considered as a preattentive feature which that improves the shapes and objects, as well as reconstruction and recognition. The symmetry-based clustering methods search for clusters that are symmetric with respect to their centers. In addition, the K-M algorithm is one of the most common clustering methods. It can be easily implemented and works faster in most conditions. However, it is sensitively initialized and it can be easily trapped in the local targets. The TS algorithm is a stochastic global optimization technique. A new algorithm using the TS with K-M clustering, called MHTSASM, was presented in this paper. The MHTSASM algorithm fully uses the merits of both TS and K-M algorithms. It uses TS to make economic exploration for data with the help of ASM. It uses different strategies of TS, such as the intensification and diversification. The proposed MHTSASM algorithm performance is compared with multiple clustering techniques based on both optimization and meta-heuristics. The experimental results ensure that the MHTSASM overcomes initialization sensitivity of K-M and reaches the global optimal effectively. However, dealing and identifying clusters with non-convex shapes is one of the paper's limitation, and it will be one of the future research direction.

**Funding:** This research is funded by Deanship of Scientific Research at Umm Al-Qura University, Grant Code: 22UQU4281768DSR02.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The study did not report any data.

**Acknowledgments:** The author would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4281768DSR02).

**Conflicts of Interest:** The author declares no conflict of interest.
