Sensitivity analysis on Gaussian quantum-behaved particle swarm optimization control parameters

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm that falls under the category of nature-inspired algorithms and is similar to evolutionary computing in various ways. Rather than the survival of the fittest, the PSO is driven by a representation of a social psychological model inspired by the group behaviors of birds and other social species. The particle's position is modified in PSO based on its position as well as velocity, while in quantum mechanics, the trajectory idea is absurd; however, the uncertainty principle suggests that a particle's position, as well as velocity, cannot be determined simultaneously. As a result, an advanced version of the quantum mechanics-based PSO method is proposed. The study in this paper is focused on an investigation of a new quantum-behaved PSO (QPSO) method called Gaussian quantum-behaved particle swarm optimization (GQPSO), which uses a mutation operator with a Gaussian distribution and is inspired by classical PSO methods and quantum mechanics concepts. In GQPSO, inadequate control parameter tuning results in poor solutions. To better understand the effect of different control parameters and their implications on GQPSO results, this paper used a full parametric sensitivity analysis on five different problems (the Design of a pressure vessel, Tension/Spring Compression, Rastrigin function, Ackley function, and Constrained Box Volume Problem). By adjusting each parameter one at a time, different optimization problems were used to investigate GQPSO. As a result, to allow particles to change their earliest best solution based on viability, a constraint-handling mechanism was developed. The optimal parameter set for GQPSO is provided based on the analysis of the results. With the help of the proposed optimal parameter set (contraction–expansion coefficient values as (1 = 1.6,2 = 1.3), swarm size as ‘350’, and number of Iterations as ‘500’), GQPSO returned an optimized solution for Rastrigin and Ackley functions. It also performed better in the case of the design of a pressure vessel and tension/spring compression problems in comparison to the existing solution available in related literature. As per the findings of the sensitivity analysis, GQPSO is the most sensitive to the contraction-expansion coefficient in comparison to the maximum number of iterations (itermax) and swarm size (‘n’).