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Particle swarm optimization with penalty mechanism is used in coping with constrained problems. Quantum behaved PSO has been proved efficient compared with PSO. In this paper, three mutation operators including Gaussian, Chaotic, Cauchy and Levy combined with PSO are studied. And three mechanisms are adopted as approach for constraints which are H, J and P strategy. Turbulence operations are come up in PSO which improves the exploratory capabilities. Self-adaptive parameters are adopted in improved H strategy and constraints violates sum is used instead of minimum and maximum fitness values is brought up in improved P strategy, both of the two improved strategies achieved better performances compared with GA in optimizing benchmark functions. Finally convergence and algorithm complexity of adopted algorithms are analyzed.