This article presents an implementation of a cellular parallel genetic algorithm and a local optimization heuristic to solve the Quadratic Assignment Problem (QAP). First, we implemented a cellular model that combines the most representative characteristics of the population in the Genetic Algorithm, later, we resort to a greedy 2-opt heuristic optimization which performs a meticulous genetic exploitation of the spaces previously explored by the Genetic Algorithm. Our algorithm was completely implemented with CUDA on a Graphical