optimization

[naash]

does applying constrain in the first two layer of an electrode during optmization affect tranport behavior of a system when we calculate the tranmission properties o0f the same system

[kstokbro]

This is very system dependent, it is not possible to give a general answer.
Check the reference below to see the effect of surface relaxation for a specific system

Theoretical study of the nonlinear conductance of Di-thiol benzene coupled to Au(1 1 1) surfaces via thiol and thiolate bonds

K. Stokbro, Computational Materials Science Volume 27, Issues 1–2, March 2003, Pages 151–160