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A novel Cultural Quantum-behaved Particle Swarm Optimization algorithm (CQPSO) is proposed in this paper to improve the performance of the Quantum-behaved PSO (QPSO). The cultural framework is embedded in our QPSO, and the knowledge stored in the belief space can guide the evolution of the QPSO. A total of 15 high-dimensional and multi-modal functions as well as an optimal pressure vessel design problem are employed to investigate the proposed algorithm. Numerical simulations results demonstrate that the CQPSO can indeed outperform the QPSO.