An improved quantum-behaved particle swarm optimization with perturbation operator and its application in estimating groundwater contaminant source

Tian, Na, Sun, Jun, Xu, Wenbo and Lai, Choi-Hong (2011) An improved quantum-behaved particle swarm optimization with perturbation operator and its application in estimating groundwater contaminant source. Inverse Problems in Science and Engineering, 19 (2). pp. 181-202. ISSN 1741-5977 (Print), 1741-5985 (Online) (doi:10.1080/17415977.2010.531470)

Abstract

In this study, a heuristic method known as quantum-behaved particle swarm optimization (QPSO) is used to solve the inverse advection–dispersion problem of estimating the strength of a time-varying groundwater contaminant source from the knowledge of forensic observations. No prior information of the functional form is given in this study. The implicit upwind finite difference method is used in the governing advection–dispersion equation. The least squares method is used to model the inverse problem, which transforms to an optimization problem. Considering the ill-posedness of the inverse problem, the Tikhonov regularization method is used to stablize the inverse solution. To ensure the global convergence properties of the QPSO, an improved version with the perturbation operator is proposed and its performance is tested by several well-known benchmark functions. Finally, the proposed method is applied to reconstruct the contaminant source history and comparisons with other methods are also presented in this article. The numerical experiments demonstrate the efficiency and validity of our proposed method.

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