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.