**5. Conclusions**

This paper proposed a local density-based abnormal case removal method for the industrial operational optimization problem. Particularly, the reason as to why abnormal cases should be removed from the case set retrieved by traditional method was analyzed in view of the safety and reliability requirements of industrial operational optimization. Then, historical cases whose LOF exceeded the corresponding threshold were removed by the designed local density-based abnormal case removal algorithm. The simulation results showed that, compared with classic CBR, the local density-based abnormal case removal method could improve the performance of operational optimization by 20.3% in the numerical case and 23.5% in the industrial case study, while improving the performance of operational optimization by 8.5% in the numerical case and 13.3% in the industrial case study compared with case-based fuzzy reasoning. In this paper, the calculation of local density increased computation cost, thus, how to obtain the local density of retrieved cases with lower computation burden would be an interesting topic in the future.

**Author Contributions:** Conceptualization, X.P. and Y.W.; Data curation, X.P. and L.G.; Formal analysis, X.P. and Y.X.; Funding acquisition, Y.W.; Investigation, X.P., Y.X. and L.G.; Methodology, X.P. and Y.X.; Project administration, Y.W.; Software, X.P.; Supervision, Y.W.; Validation, X.P. and L.G.; Visualization, X.P. and L.G.; Writing—original draft, X.P.; Writing—review & editing, X.P., Y.W. and Y.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported in part by National Natural Science Foundation of China (NSFC) (U1911401), in part by the National Key Research and Development Program of China (2020YFB1713800), and the Science and Technology Innovation Program of Hunan Province (2021RC4054).

**Data Availability Statement:** The data set used in the numerical case was generated with the MATLAB 2019A.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
