In this paper, we propose the island model parallel memetic algorithm with diversity-based dynamic adaptive strategy (PMADLS) for controlling the local search frequency and demonstrate its utility in solving complex combinatorial optimization problems, in particular large-scale quadratic assignment problems (QAPs). The empirical results show that PMA-DLS converges to competitive solutions at significantly lower computational cost when compared to the canonical MA and PMA. Furthermore, compared to our previous work on PMA using static adaptation strategy, it is found that the diversity-based dynamic adaptation strategy displays better robustness in terms of solution quality across the class of QAP problems considered without requiring extra effort in selecting suitable parameters. Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control