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In this article, a novel stable deviation quantum-behaved particle swarm optimization for solving global optimization problem is presented. The proposed stable deviation quantum-behaved particle swarm optimization algorithm uses interpolation and stable deviation function. The method of recombination operator is employed to generate a new solution vector in the search space. Therefore, the chance of fast converging can be improved. The performance of the proposed stable deviation quantum-behaved particle swarm optimization algorithm is compared with a quantum-behaved particle swarm optimization and a quantum-behaved particle swarm optimization with quadratic interpolation recombination operator, which is an advanced variant of quantum-behaved particle swarm optimization. Finally, the proposed stable deviation quantum-behaved particle swarm optimization algorithm is applied to constrained optimal piezoelectric actuator and sensor location for active vibration control of a simply supported plate under the different periodic loads.