Optimal design of groundwater remediation systems using fuzzy set theory

In this study we use fuzzy sets to describe uncertainty in aquifer parameters and demonstrate the use of this information in optimal design of pump‐and‐treat systems. On the basis of uncertainty in aquifer parameters, two optimization models are formulated, where pumping rates are represented as either deterministic or fuzzy decision variables. Both models with fuzzy constants and fuzzy variables are then transformed into computationally efficient algorithms through the application of fuzzy set theory. The resulting models are solved by optimization algorithms such as golden section search, genetic algorithm (GA), and direct comparison methods. Several examples are given to demonstrate the effectiveness of the models and algorithms presented in this study. The numerical results, which are also compared with the results obtained from probabilistic analysis, show that the optimal solutions obtained from both models provide flexible and reliable pump‐and‐treat strategies and may increase the effectiveness of the remediation system under uncertainty.