  In this study, we investigate a recent finding based on strong lensing
observations, which suggests that the sub-halos observed in clusters exhibit
greater compactness compared to those predicted by $\Lambda$CDM simulations. To
address this discrepancy, we performed a comparative analysis by comparing the
cumulative mass function of sub-halos and the
$M_{\text{sub}}$-$V_{\text{circ}}$ relation between observed clusters and 324
simulated clusters from The Three Hundred project, focusing on re-simulations
using GADGET-X and GIZMO-SIMBA baryonic models. The sub-halos' cumulative mass
function of the GIZMO-SIMBA simulated clusters agrees with observations, while
the GADGET-X simulations exhibit discrepancies in the lower sub-halo mass range
possibly due to its strong SuperNova feedback. Both GADGET-X and GIZMO-SIMBA
simulations demonstrate a redshift evolution of the sub-halo mass function and
the $V_{max}$ function, with slightly fewer sub-halos observed at lower
redshifts. Neither the GADGET-X nor GIZMO-SIMBA(albeit a little closer)
simulated clusters' predictions for the $M_{\text{sub}}$-$V_{\text{circ}}$
relation align with the observational result. Further investigations on the
correlation between sub-halo/halo properties and the discrepancy in the
$M_{\text{sub}}$-$V_{\text{circ}}$ relation reveals that the sub-halo's half
mass radius and galaxy stellar age, the baryon fraction and sub-halo distance
from the cluster's centre, as well as the halo relaxation state play important
roles on this relation. Nevertheless, we think it is still challenging in
accurately reproducing the observed $M_{\text{sub}}$-$V_{\text{circ}}$ relation
in our current hydrodynamic cluster simulation under the standard $\Lambda$CDM
cosmology.
