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In a previous paper, we proposed a variant of the ACO algorithm called the cunning ant system (cAS) and evaluated it using TSP instances in the TSPLIB. The results showed that it could be one of the most promising ACO algorithms. In this paper, we applied cAS to solving the QAP and showed cAS has promising performance on the QAP as well. We introduced the entropy measure to evaluate the diversity of pheromone density and to analyze the convergence process of cAS. The results clearly showed evidence that the cunning scheme in cAS is effective in maintaining diversity of pheromone density and leads to successful search. The effectiveness of cAS was also confirmed when it was combined with the taboo local search.