Optimal control algorithm and neural network for dynamic groundwater management

Abstract

Abstract:Researchers have found that obtaining optimal solutions for groundwater resource-planning problems, while simultaneously considering time-varying pumping rates, is a challenging task. This study integrates an artificial neural network (ANN) and constrained differential dynamic programming (CDDP) as simulation-optimization model, called ANN-CDDP. Optimal solutions for a groundwater resource-planning problem are determined while simultaneously considering time-varying pumping rates. A trained ANN is used as the transition function to predict ground water table under variable pumping conditions. The results show that the ANN-CDDP reduces computational time by as much as 94Ð5% when compared to the time required by the conventional model. The proposed optimization model saves a considerable amount of computational time for solving large-scale problems.

Integration of Optimal Dynamic Control and Neural Network for Groundwater Quality Management

“…(1) to (5). The following shows the procedure to develop the ANN-CDDP model (Chu and Chang 2009a), explained in more detail:…”

“…(2)), the ANN models (Eqs. (6) and (7)) in this study, are obtained by chain rule (Dimopoulos et al 1995;Chu and Chang 2009a). Derivative of transition equation with respect to x t , u t is:…”

“…For a multilayered network, the derivatives in the transition equation are derived by ANN in the following (Chu and Chang 2009a).…”

“…Previous studies demonstrated an ANN methodology as a groundwater simulator in the optimization model. An ANN embedded within an optimization model can accurately predict ground water state in response to management alternatives (Rogers and Dowla 1994;Rao et al 2005;Becker et al 2006;Coppola et al 2007;Chu and Chang 2009a). Rogers and Dowla (1994) used an ANN-Genetic Algorithm (GA) methodology to replace a traditional simulation-optimization model.…”

“…The ANNs were embedded into a multiobjective linear optimization model to find a compromise pumping policy that effectively balances the two conflicting objectives between water supply and wellfield vulnerability in the nearby contaminant area. Chu and Chang (2009a) integrated the ANNs and constrained differential dynamic programming (CDDP) for a groundwater resource-planning problem. The ANNs were used as surrogates of numerical models in groundwater flow simulation.…”