The HP model can be expressed in both two and three dimensions, generally with square lattices, although triangular lattices have been used as well.
Randomized search algorithms are often used to tackle the HP folding problem. This includes stochastic, evolutionary algorithms like the Monte Carlo method, genetic algorithms, and ant colony optimization. While no method has been able to calculate the experimentally determined minimum energetic state for long protein sequences, the most advanced methods today are able to come close.
Even though the HP model abstracts away many of the details of protein folding, it is still an NP-hard problem on both 2D and 3D lattices.
Recently, a Monte Carlo method, named FRESS, was developed and appears to perform well on HP models.