Optimized Garbled Circuit Algorithmic Description The Garbled Circuit (GC) is now over thirty years old, and many optimization methodologies have been proposed, including point-and-permute, row-reduction, free-XOR, fixed-key blockcipher, half-and. 

But, after Googling papers and forums, I can't find any concrete algorithmic descriptions which includes all of these optimizations. Does anyone know the exact descriptions of optimized GCs? 

I ask because I need to implement the algorithm for personal use.
Not all optimizations of garbled circuits are compatible with each other. Are you interested in implementing all of the different combinations? If not, the Half Gates paper already gives a formal description of the scheme, which includes point-permute, fixed-key block cipher, free-XOR. This should represent the state-of-the-art combination of GC optimizations. There is a good implementation of half-gates in the Ivory project.