Saltwater intrusion, commonly associated with extensive groundwater extraction, is an important problem for coastal regions. In this study, we present a multi-objective optimization approach to determine pumping rates and well locations to prevent saltwater intrusion, while satisfying desired extraction rates in coastal aquifers. The proposed method is an iterative sub-domain method, in which the proposed algorithm searches for the optimal solution by perturbing the well locations and pumping rates simultaneously. The decision variables of the optimization problem are modeled as continuous independent variables. Sharp interface solution for homogenous steady state problem is used along with the Dupuit and Ghyben-Herzberg assumptions. Using this approach, the direct method of searching for saltwater intrusion points is formulated by comparing the location of the stagnation points of the flow field, and the saltwater intrusion profiles obtained from the single-potential theory solution. The search for the optimal solution, within each sub-domain, is conducted using genetic algorithm. The multiobjective problem is formulated to maximize pumping rates while minimizing the distance between critical stagnation point and the reference coastline location, such that the wells are placed as closely to the coast as possible. Several numerical experiments are conducted to evaluate the effectiveness of the proposed method. As a case study, the numerical results obtained from the proposed method are compared with the work of Cheng et al. [Water Resour. Res. 36 (2000) 2155]. This comparison yielded higher pumping rates than what was reported in their study. The sequential use of multi-objective criteria, with preselected weights, successfully demonstrated the capability of the model to achieve two objectives simultaneously. The proposed approach provides a cost effective solution to an important management problem in coastal aquifers. q

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Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA).Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function.The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods.

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