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During the history of science of computational intelligence, many evolutionary algorithms approaches were proposed having more or less success in solving various optimization problems. In this context, the Particle Swarm Optimization (PSO) is a bio-inspired optimization mechanism based on the metaphor of social behaviour of birds flocking and fish schooling in search for food. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-behaved PSO (QPSO) approach using Gaussian probability distribution function (G-QPSO). Numerical simulations based on optimized proportional-integral-derivative (PID) control of an automatic regulator voltage system for nominal system parameters and step reference voltage input demonstrate the effectiveness and efficiency of G-QPSO approach. Simulation results of G-QPSO to determine the PID parameters are compared with the classical PSO and QPSO.