# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 6 Conclusions  
By analyzing the deficiencies of optimization strategy in the standard equilibrium optimizer (EO), a dynamic heterogeneous search-mutation structure-based equilibrium optimizer (DHSMEO) has been developed to address the issues of population diversity attenuation, insufficient search efficiency, and susceptibility to a local optimum in the EO. Firstly, a dynamic dual-subpopulation adaptive grouping strategy was constructed to form the construction mode of a dual-subpopulation structure, which can improve population diversity and provide an effective information-exchange structure for the heterogeneous hybrid search strategy. Then, a heterogeneous hybrid search-based concentration-updating strategy was introduced into the formed dual-subpopulation structure to form a differentiated population search strategy, which can enhance search efficiency. Finally, a dynamic Levy mutation was applied in the optimal equilibrium candidate, serving as the central hub of the algorithm guidance strategy to leverage the unique randomness of dynamic Levy mutation in refining the optimal equilibrium candidate, which can strengthen the ability of escaping local optima. Three sets of comparative experiments were conducted on 39 typical benchmark functions and a UAV mountain path-planning problem to evaluate the overall optimization capability of DHSMEO. The effectiveness analysis results for improvement strategies suggest that the dynamic dual-subpopulation adaptive grouping strategy, the heterogeneous hybrid search-based concentration-updating strategy, and the dynamic Levy mutation-based optimal equilibrium candidate-refining strategy constructed in DHSMEO all contribute to enhancing the optimization capability. And DHSMEO obtained by combining these three improvement strategies simultaneously to form the dynamic heterogeneous search-mutation structure achieves the best optimization performance. In further comparative experiments with other algorithms, DHSMEO achieved a better optimization capability across most benchmark functions than other algorithms, and it showed superiority in overall optimization performance. Additionally, in the comparison experiments for the UAV mountain path-planning problem, DHSMEO effectively solved the UAV mountain path-planning problem, and it exhibited superiority compared to other algorithms, which shows both practicality and competitiveness in addressing the UAV mountain path-planning problem. With the achievements of DHSMEO, future research on DHSMEO will focus on further enhancing its optimization performance and expanding its applicability. Firstly, improving its adaptability to large-scale optimization problems will be a key direction, which will ensure its efficiency in searching high-dimensional complex optimization space. Moreover, extending DHSMEO to address discrete and multi-objective optimization problems will be studied, which will make it applicable to broader application challenges. Additionally, the application of DHSMEO in more kinds of practical optimization problems will be further investigated, including smart grid scheduling, building structure optimization, and medical image processing, etc. DHSMEO is expected to provide more efficient and reliable solutions in various engineering and scientific domains. Conceptualization, X.W. and K.H. ; methodology, X.W. ; software, X.W. and S.S.; validation, X.W. and S.S.; investigation, X.W. and Y.D. ; writing--original draft preparation, X.W. ; writing--review and editing, X.W., K.H. and Y.D. ; supervision, K.H. and Y.D. ; project administration, K.H, Y.D. and S.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the Systematic Major Project of the China Railway Group under Grant No. P2021T002 and the National Natural Science Foundation of China under Grant No. 82201753. **Informed Consent Statement:** Not applicable.