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Parallel and adaptability are introduced in the algorithm of quantum-behaved PSO in this paper, which is named PAQPSO and used to solve the CO problem. The PAQPSO outperforms QPSO and AQPSO in global search ability and local search ability, because the parallel and adaptive method is more approximate to the learning process of social organism with high-level swarm intelligence and can make the population evolve persistently. We adopt a non-stationary multi-stage assignment penalty in solving constrained problem to improve the convergence and gain more accurate results. This approach is tested on several accredited benchmark functions and the experiment results show much advantage of PAQPSO to AQPSO, QPSO and the traditional PSO (Particle Swarm Optimization). And the running time is also decreased in proximity linear.