TITLE: practical algorithms for np complete problems
QUESTION [5 upvotes]: Inspired by:
Conjecture on NP-completeness of tesselation of Wang Tile up to finite size
And the practicality of this topic (solving tessellation on a lattice):
coloring in lattice
Computational approach deciding whether a set of Wang Tile could tile the space up to some size
Reference for Wang Tile
I want to ask for practitioner what kind of software/programmes/algorithms that are usually used to tackle NP complete problems?

REPLY [2 votes]: I want to add to the other good answers the following interesting article explaining the successful use of SAT solvers in the work of Konev and Lisitsa on the Erdos Discrepancy problem. 
http://rjlipton.wordpress.com/2014/02/28/practically-pnp/