## 6 Conclusions  
Faced with complex optimization problems, the original WOA algorithm may drive the search to premature convergence or be stuck at the local optimal solutions, etc. To overcome those disadvantages, a multi-strategy ensemble whale optimization algorithm (MSWOA) was developed in this paper. The proposed MSWOA first adopted the chaotic initialization strategy so that the whale swarm could be evenly distributed in the search area. Then, two strategies of the conventional WOA was modified to facilitate its search performance. More precisely, by introducing the best search agent as a reference target, the random searching strategy was enhanced to reduce blindness and accelerate the convergence during optimization. Furthermore, the spiral updating position strategy was improved by the Levy flight, which has a high ability to balance exploration and exploitation. Finally, the enhanced position revising mechanism was designed to strengthen exploration ability further and yields a better MSWOA.  
A large number of comparative experiments were conducted to validate the effectiveness of the MSWOA algorithm. For a start, we performed extensive numerical optimization simulation experiments based on nineteen classical benchmark problems, which were extensively used to test the performance of metaheuristics. Moreover, MSWOA was thoroughly compared with six well-established optimization methods. Comparison results indicated that the proposed MSWOA could achieve good results for the majority of the nineteen benchmark problems. Additionally, to further testify the performances of the MSWOA algorithm, we applied the MSWOA to the fault diagnosis of analog circuits. Empirical studies indicated that the diagnostic accuracy of the SVM optimized by the proposed MSWOA was the highest, which reflects that MSWOA possesses excellent practicability in the circuit fault diagnosis field. Therefore, the proposed MSWOA can be considered as a novel and efficient tool for addressing the numerical optimization problems and analog circuit fault diagnosis tasks.  
However, for a few fixed-dimension multimodal functions, MSWOA had no obvious superiorities compared with other algorithms. Therefore, how to facilitate the MSWOA accuracy and speed for fixed-dimension multimodal functions still deserves further study.  
Conceptualization, X.Y. and Z.M.; Investigation, Z.M. and Z.Y.; Methodology, X.Y., Z.M. and Z.L.; Software, Z.M. and Z.L.; Supervision, X.Y. and F.Z.; Validation, Z.L. and Z.Y.; Writing--original draft, X.Y. and Z.M. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the National Natural Science Foundation of China (Grant No. 61803227, 61973184, 61773242, 61603214), The National Key R & D Program of China (Grant No.2017 YFB1302400), Key Research and Development Program of Shandong Province (Grant No. 2018 GGX101039), Independent Innovation Foundation of Shandong University (Grant No. 2082018 ZQNM005).  
We would like to thank the editors and the anonymous reviewers for their insightful comments and constructive suggestions.  
The authors declare that there is no conflict of interest regarding the publication of this paper  
Figure 21: Fault diagnosis accuracy curves of the three methods optimized SVM.