## 2 Differential Step-Scaling Antilion Algorithm
### Algorithm Idea and Specific Steps
## 5 Conclusions and Future Perspectives

In this paper, an improved ant-lion algorithm called DSALO is proposed to solve the parameter optimization problem of ADRC. Because parameters of ADRC are directly related to the control performance, ulteriorly the economic effectiveness of the controlled object, finding an optimized set of parameters is of great importance. Specific to this work, a parameter set \(\{\omega_{o},\omega_{c}\}\) is optimized with two performance indexes: IAE and IAE + overshoot. These indexes are important because they can reflect the economic effectiveness of a controlled plant in industrial manufacturing. In order to improve search abilities of origin ALO, differential evolution strategy is introduced to improve global search ability and a step scaling method is used to enhance local search ability. Experiments on test functions show that the DSALO algorithm has a significant improvement in accuracy for multimodal functions and a significantly higher convergence speed for unimodal functions, multimodal functions, and composite functions. The experimental results show that the DSALO algorithm has a batter optimization effect, further show that DSALO is capable of an ADRC parameter optimization problem. Since this is the first time using an ant-lion based algorithm to optimize the ADRC parameter, this study can be a basis of future optimization work for different ADRC varieties and nonlinear ADRC. It should be noted that, however, some aspects can be studied in future work. One aspect is that DSALO does not show significant accuracy improvement, though a small improvement exists, for unimodal functions and composite functions. This phenomenon needs more study and DSALO may need modification at a deeper level. On the other hand, the convergence speed of DSALO still needs further improvement. As stated in this paper, an industrial application of optimization algorithms usually inherently compromises between computation time and accuracy. It means that reducing computation time is of great importance. Additionally, a parallel version of DSALO should be developed for future work to deal with some complex cases, which can save the costs of computation time. Conceptualization, Q.J. ; methodology, Y.Z. ; software, Y.Z. ; validation, Q.J. ; formal analysis, Y.Z. ; investigation, Y.Z. ; resources, Q.J. ; data curation, Q.J. ; writing--original draft preparation, Y.Z. ; writing--review and editing, Q.J. ; visualization, Y.Z. ; supervision, Y.Z. ; project administration, Q.J. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. ## References

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