Determining Robust Optimal Pumping Solutions in a Heterogeneous Coastal Aquifer Using a Robust Decision-Making Approach and Bargaining Theory to Resolve Multiple Sources of Uncertainty

Abstract This paper analyses the impact of heterogeneity in the horizontal hydraulic conductivity field ( $${K}_{hf}$$ ) on the optimal pumping scenarios in a coastal aquifer and presents a multi-objective management framework to select robust optimal scenarios under high levels of uncertainty. Model speed is significantly improved by training an M5 Decision Tree (MDT) algorithm as a fast surrogate model for the density-dependent flow (DDF) in the SEAWAT code. The developed Tree model was linked to a non-dominated genetic algorithm (NSGAII) to determine Pareto optimal solutions, with the aim of maximizing total pumping volume and minimizing saltwater intrusion in a real case study, i.e., the Qom-Kahak aquifer, Iran. A linear sensitivity analysis explores the relationship between Pareto curves in response to variations in calibrated values of $${K}_{hf}$$ to quantify robust scenarios by a robust decision-making technique. Finally, the conflict resolution between minimum saltwater intrusion length, maximum pumping rate and robustness values is solved using a non-cooperative Nash bargaining theory. Results indicate that maintaining discharge from the pumping wells located far from 3 observation points in the case study, especially near the Salt Lake boundary, increases uncertainty in the Pareto solutions, where increasing $${K}_{hf}$$ by up to 30% of calibrated values induces a maximum 12% shift in the Pareto front for the scenario which led to high saltwater intrusion lengths. Moreover, the non-robust scenario causes the saltwater intrusion $$\overline{SWI }$$ zone to sharply advance to the area with a large number of pumping wells, while the scenario with high Nash product values led to a relatively uniform salinized zone which satisfies the allowed SWI length in 5 agricultural zones. In total, the developed MDT-NSGAII model is a computationally effective simulation–optimization model to find the Pareto front with 55 decision variables while achieving a 95% reduction in CPU time compared to the SEAWAT-NSGAII technique.