5. Conclusions:
Three different domain sizes of groundwater model for optimization of withdrawal and gain in the river from the aquifer, by four different optimization algorithms were discussed. The groundwater model development, optimization models, ANN model to reduce evaluation time, performance metrics for Pareto fronts, and the comparison of the distribution of optimal decision variables for different optimization techniques, are also discussed. The ANN model for three domains shows the difference in accuracy, suggesting a change in domain size and consequently boundary conditions can alter the performance of ANN. Results show that boundary conditions and domain size influence the result of simulation-optimization models. Domain-1 was found more efficient and was capable to give a higher value of R-A exchange corresponding to the discharge of pumping wells.
The simulation-optimization model result suggests that GA provided a diverse set of Pareto solutions even for a low number of evaluations but the solution of other algorithms was dominating, with MOPSO being the best. And among the three domains, model 2 consistently implied a greater interrelation between the two costs, i.e. total discharge and river gain. In the ANN-Optimization model, MOPSO showed significant improvement in both diversity and convergence. GA solutions didn’t show major improvement in convergence. This suggested the use of GA to obtain a tentative solution set that can be obtained without the use of the ANN model. The use of ANN can significantly improve the performance of MOPSO by allowing it to have a greater number of evaluations, which was limited in the raw simulation model due to the infeasible computation time.
The distribution of optimal decision variables was well distributed for MOEAD and comparatively limited in other optimization techniques. But the distribution of decision variables didn’t represent the quality of the solution from perspective of performance of optimization algorithm. In case of decision-making problems, this study can be helpful to have good distribution of decision variables, even though they provide a better solution but not the best one. Apart from statistical distribution of solutions, the spatial distribution of optimized decision variables (well discharge) provided a lot of information regarding the physical interpretation and conceptual verification of the solutions. These solutions followed an expected trend of higher discharge at faraway wells and lower discharge at the close wells. From this study, the influence of domain demarcation, boundary conditions, and optimization algorithm has been observed on the Pareto fronts and optimized decision variables. The conceptual verification of the Pareto solutions was also explained. Besides this, the use of ANN and handling the constraints of the optimization problem is also considered for a real-world groundwater problem. Still, several challenges in R-A exchange-related groundwater decision-making exist. Accurate R-A exchange modeling, precise surrogate models to reduce S-O time, and dealing with high heterogeneity of the domain, to name a few.