## 5 Conclusions  
In this paper, the GPSC was used with a random hyperparameter search method and 5-fold cross-validation to obtain symbolic expressions for the detection of hepatitis C patients as well as determining the hepatitis C stage (Hepatitis C, Fibrosis, and Cirrhosis) using a dataset containing blood samples. However, the original dataset was highly imbalanced so before using GPSC the dataset balancing techniques had to be applied such as random oversampling, SMOTE, ADASYN, and BorderlineSMOTE. Unfortunately due to a large class imbalance in both binary and especially the multiclass case of the original dataset was not used for generating symbolic expressions using the GPSC method. The original dataset was used to perform final tests on the best symbolic expressionsobtained on datasets balanced with other methods. Based on the conducted investigations, the following conclusions are:  
* using GPSC with random hyperparameters search and 5-fold cross-validation the symbolic expression can be obtained which can detect the Hepatitis-C patients with high classification accuracy,
* using GPSC with One Versus Rest Classifier, random hyper-parameter search method and 5-fold cross-validation it is possible to obtain the symbolic expressions that can detect the hepatitis C patients and their disease progression (Hepatitis-C, Fibrosis and Cirrhosis). However, required average CPU execution time is quite long but this is relative since the execution times mostly depends on the used computational resources,
* the application of different balancing methods can synthetically balanced the class samples which in the end can improve the classification accuracy of obtained symbolic expressions.  
This investigation showed how imbalanced dataset can be balanced using over-sampling methods and used in GPSC algorithm with which symbolic expression can be obtained. To achieve higher classification accuracies in terms of hepatitis C detection and the stage of the disease the random hyperparameter search method for GPSC with 5-fold cross-validation was employed. The used method also addresses the issue of the so-called black-box models, by providing a possibility of interpreting the generated classification models.  
In future investigations, the original dataset will be enlarged if possible. The idea is to achieve an equal number of samples through all the dataset classes. The enlarged dataset could be a good starting point to develop a system of symbolic expressions for detecting Hepatitis C patients and the possible disease progression. Further investigation and tuning of GPSC hyperparameters are required to obtain very small symbolic expressions that have high classification accuracy. One of the limitations of this approach is the parsimony coefficient which has a large impact on the performance of GPSC. The influence of this hyperparameter will be reduced by ensuring that the dataset used is balanced and that correlation between variables is reasonably high.  
Conceptualization, N.A. and Z.C.; methodology, N.A., Z.C. and I.L.; software, N.A. and S.B.S.; validation, N.A., I.L. and S.B.S.; formal analysis, N.A., I.L. and S.B.S.; investigation, N.A., I.L. and S.B.S.; resources, N.A., Z.C. and S.B.S.; data curation, I.L. and S.B.S.; writing--original draft preparation, N.A., I.L. and S.B.S.; writing--review and editing, N.A., I.L. and S.B.S.; visualization, I.L. and S.B.S.; supervision, Z.C.; project administration, Z.C.; funding acquisition, Z.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
This research has been (partly) supported by the CEEPUS network CIII-HR-0108, European Regional Development Fund under the grant KK.01.1.1.01.0009 (DATACROSS), project CEKOM under the grant KK.01.2.2.03.0004, Erasmus+ project WICT under the grant 2021-1-HR01-KA220-HED-000031177, and University of Rijeka scientific grant uniri-ethnic-18-275-1447.  
The authors declare no conflict of interest.