4.4.3. Structural optimization

Jafari et al. [169] combined the advantage of elephant herding optimization (EHO) and the cultural algorithm (CA) and proposed a hybrid algorithm (EHOC). In EHOC, EHO was improved by using the belief space defined by the cultural algorithm. The performance of the EHOC algorithm was evaluated on eight mathematical optimization problems and four truss weight minimization problems. The solution results showed that EHOC was capable of accelerating the convergence rate e ffectively compared with the CA and EHO.

#### **5. Conclusions and Future Directions**

In this paper, tens of research articles related to the EHO algorithm were reviewed. We also discussed the application of the EHO variants in continuous optimization, combinatorial optimization, constrained optimization, and multi-objective optimization. Researchers improved the EHO algorithms

and successfully applied them to various optimization fields. This algorithm has proved to be a promising tool for many optimization problems and engineering applications. However, several aspects of the EHO method that should be further studied, and are as follows:

(1) Most researchers have merely focused on the optimization e ffects of EHO. There is not su fficient explanation for theoretical analysis. Therefore, strengthening the theoretical analysis of EHO and the mathematical model will remain a challenge in future research.

(2) Employing EHO to solve unsolved optimization problems, especially multi-objective optimization problems, needs to be studied in more depth.

(3) Hybridizing EHO with other algorithm components, such as di fferential evolution and hill climbing, is another interesting topic for future research [170].

(4) EHO has achieved some notable accomplishments in solving discrete and continuous optimization problems. Therefore, expanding the application scope of EHO and designing suitable optimization operators should be considered in future research.

(5) EHO has a lower level of constrained optimization than similar methods. This is undoubtedly a shortcoming of EHO. Therefore, more research should be carried out to expand EHO for more constrained optimization applications.

**Author Contributions:** Conceptualization, J.L.; research literature, H.L.; literature search, G.-G.W. and A.H.A.; writing—original draft preparation, J.L.; writing—review and editing, H.L.; funding acquisition, G.-G.W. and A.H.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by an Industry–University Cooperative Education Project (Grant No. 201802046038), Doctoral Foundation of Wuhan Technology and Business University (No. D2019010), and National Natural Science Foundation of China (No. 41576011, No. U1706218, No. 41706010, and No. 61503165).

**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 conflict of interest.
