Recently symmetric multi processing (SMP) has become available at a reasonable cost. In this paper, we propose several types of parallel ACO algorithms with SMP for solving the quadratic assignment problem (QAP). These models include the master-slave models and the island models. We evaluated each parallel algorithm with a condition that the run time for each parallel algorithm and the base sequential algorithm are the same. The results suggest that using the master-slave model with increased iteration of ACO algorithms is promising in solving QAPs.