How to compute AUC in gridsearchSV (multiclass problem)
Metrics are independent from ML algorithms, so it doesn't matter which algorithms did you use. 

To calculate multiclass AUC you could use lib pRoc in R or use code this link(in Python).  

Sources:


https://web.expasy.org/pROC/
https://medium.com/@plog397/auc-roc-curve-scoring-function-for-multi-class-classification-9822871a6659