Optimal management of mixed hydraulic barriers in coastal aquifers using multi-objective Bayesian optimization

Abstract

• Optimum mixed hydraulic barriers location and rate obtained by Bayesian optimization. • Constrained multi-objective Bayesian optimization solved coastal management problem. • BO with few evaluations outperforms NSGA-II with a large number of evaluations. • Injection barriers have higher control over the remediation system. • Abstraction barriers useful as an alternative source of water. Mixed hydraulic barriers is an effective method to control seawater intrusion (SWI), particularly in regions that suffer from water shortages. However, determining the optimal well locations and rates for injection and abstraction is challenging due to the computational burden resulting from the huge number of calls for the high-fidelity hydrogeological simulation model. To alleviate this issue, we utilized a constrained multi-objective Bayesian optimization (BO) approach to optimize rates and locations of the hydraulic barriers to minimize total cost, aquifer salinity, and salt-wedge intrusion length, while satisfying regional abstractions with acceptable salinity levels. BO is useful for optimizing computationally expensive problems in few iterations by using a surrogate model and an acquisition function. Despite being an efficient optimization tool, the use of BO in the field of coastal aquifer management has not been explored. The proposed framework was evaluated on an unconfined aquifer subjected to three management scenarios considering different physical and technical constraints and was benchmarked against the widely used robust NSGA-II (Non-dominated Sorting Genetic Algorithm II) method. The results proved the effectiveness of BO in achieving an optimum mixed hydraulic barriers design in much fewer runs of the variable density aquifer model. BO with 350 evaluations yielded comparable results to 4150 evaluations using NSGA-II. BO solutions were spatially well-distributed along the approximated Pareto front. For the same number of evaluations, the hypervolume obtained by BO was larger by 30%. Based on different scenarios, the average amount of water required for abstraction ranged from 1.5% to 25% of that for injection. The injection has a significant impact on SWI management, but the abstracted water provides an alternative source of water. A sensitivity analysis was conducted on the optimization problem to illustrate its efficiency by omitting the barriers one at a time and assessing impacts on objective and constraint functions.