1. Introduction:
River-aquifer (R-A) exchange influences both quantity and quality
aspects of groundwater and river water systems significantly.
Consequently, proper and effective quantification and representation of
river-aquifer exchange are very important for the management of water
resources and aquatic ecosystems. Climate and groundwater pumping for
irrigation has caused rapid groundwater depletion in India (Dangar et
al.,2021). Several works have been carried out about the identification
and the quantification of groundwater and surface water interactions
i.e. R-A exchanges (Constanzt, 1998; Sophocleous, 2002; Becker et al.,
2004; Anderson, 2005; Kalbus et al., 2006; Keery et al., 2007; Lowry et
al., 2007; Yang et al., 2017). Some studies on R-A exchanges also
demonstrate the effect of it on river temperature (Westhoff et al.,
2007; Burkholder et al., 2008; Hebert et al., 2011) along with the
emphasis on exchanges in hyporheic zone (Burkholder et al., 2008).
Simulation-optimization (S-O) techniques are often used in identifying
the optimal management practices of groundwater for the selected region.
Many challenges are associated with this S-O technique like the
selection for proper simulation or optimization algorithm and comparison
of the results of various techniques used. In the multi-objective
optimization problems, comparison of results becomes more significant as
Pareto fronts generated in this approach can have some similarities with
some diversity. Jha et al. (2020) statistically evaluated the
relationship between groundwater pumping rates and groundwater levels
during pre-monsoon and post-monsoon seasons using a numerical
groundwater-flow simulation model. The simulation-optimization (S-O)
model used linear programming (LP) optimization to handle groundwater
hydraulic optimization management problems after convolution techniques
were employed to integrate the simulation model with an optimization
method. Kamali Asghar (2017) used a mathematical simulation optimization
programming model to handle the issue of aquifer management, relying on
the stability of water quality and quantity. The simulation-optimization
models and the construction of the sustainability index for determining
the best point of the Pareto front were used in the study’s modeling.
Abd-Elmaboud et al. (2021) introduced a new model that connects
geomorphological and hydrogeological data with recharge rates. The
MFUSG-PSO model with an indirect simulation-optimization technique for
the inversion of the groundwater flow problem was used to calibrate the
recharge rates. The second phase involved training a CFNN model to
connect the calibrated recharge rates with freely available
geomorphological and hydrogeological data to construct
interrelationships. For the best possible conservation of water
resources, Conant et al. (2019) suggested that it is critical to
understand and quantify exchange activities between rivers and
groundwater. The exchange between rivers and groundwater is significant
in a variety of current concerns, including providing drinking water,
characterizing and managing environmental flow regimes, preserving or
restoring riverine ecosystem health and functioning, and alleviating
toxins. For reaches in plains with flow monitoring data. Li et al.
(2020) introduced a cumulative exchange fluxes method based on surface
water balance to study GW-SW interactions. The dynamic change processes
of GW-SW interactions can be qualitatively and quantitatively judged
through a curve of cumulative exchange fluxes by this method. The
hyporheic zone, which is usually regarded as a biogeochemical hotspot,
is where surface-groundwater interactions are most frequent and
according to McClain et al. (2003), these hotspots are the key to manage
water resources effectively.
Calandra et al. (2014) proposed an approach to make full use of the
simulation algorithms developed by Bayesian Optimization to analyze the
quality of Pareto fronts, unlike the existing algorithms which only
returned the Pareto solution sets without considering the qualitative
assessment. The approach was able to delineate the actual Pareto fronts
better in presence of noise and at the same time can also perform
sensitivity analysis of the parameters concerning the quality of model
output. Lobato et al. (2016) have presented a Bayesian method called
PESMO to identify Pareto solution set to Multi-Objective optimization
problems. The evaluation points were chosen as such to minimize the
entropy of the Pareto set. When compared with existing techniques, PESMO
was found to produce better results with a smaller count of evaluations,
while the decoupled estimation led to an improved performance
particularly when the existing techniques lose efficiency with an
increase in objectives. Emmerich et al. (2018) have also discussed the
fundamentals and evolutions in the field of Multi-objective
optimization. The topics covered in their article include-
order-theoretical foundations, scalarization approaches, and optimality
conditions. In context to the evolutionary methods, three
state-of-the-art techniques were discussed namely NSGA-II, SMS-EMOA, and
MOEA/D. NSGA-II representing the Pareto-based approach, SMS-EMOA
exemplifies the Indicator-based approach while MOEA/D is an example of a
decomposition-based approach. The choice of the correct technique
depends on the number of objectives, count of solution sets, desired
distribution of the solutions along with the location and shape of the
Pareto front. Belakaria et al. (2019) have addressed the optimization of
the Multi-Object (MO) black box to determine true solutions of
Pareto-set by reducing the count of function evaluations. The study
proposed a new algorithm called Max-value Entropy Search for
Multi-objective Optimization (MESMO) to ascertain an optimized design
that efficiently trades off among performance, power requirement, and
area overhead. Their approach used the output matrix entropy function to
efficiently select the input parameters, to obtain highly accurate
Pareto-set solutions. The algorithm was found to be constantly
outperforming the existing state-of-the-art algorithms in computing
Pareto set solutions.
Binois et al. (2014) have taken into account Kriging metamodel for
estimating the Pareto front and also to quantify bias associated with
the solution set at any phase of the multi-objective optimization. The
approach taken by them assumed the original dataset to be having
Gaussian distribution. The concept of random set theory has been used to
compute Vorob’ev deviation to capture the variability of the dataset
with non-dominated points. This method applied on several numerical
problems yielded satisfactory output in accurately determining of Pareto
front. Horn et al. (2016) proposed a model based on Random Forests for
model-based multi-objective optimization to determine the Pareto front
for mixed hierarchical configuration problems. A two-phase parameter
experiment was carried out. The results of the single model experiment
were quite promising, however, the solution derived through a
multi-model approach could be improved further. Especially, the bias
estimation associated with the Random Forest model needed to be
resolved.
Cao et al. (2017) have tried to quantify the bias of the estimated
solution of multi-objective problems using two versions of the
normalized hypervolume. A case study was carried out in a chemical
process with three sets of solutions, each having a different
optimization goal. Results showed that the normalized hypervolume showed
great accordance to the ideal situations while taking into account the
degree of the trade-offs between the possibilities considered to compute
the front. Bassi et al. (2018) have considered a new approach to
evaluate statistical parameters for a set of objects equivalent to
surfaces and arcs. Their approach is based on the identification of the
most representative member of a family tree and was found useful to
address the uncertainties associated with Pareto fronts. The Pareto
front was ascertained by minimizing the hypervolume between the front
and the reference points. The algorithm was tested on a complex 5 bar
truss structure with satisfactory outputs being obtained. Avent et al.
(2019) proposed a new approach called DPARETO, to determine the
trade-off among various differentially cloistered algorithms. Bayesian
Optimization (BO) was used to concurrently optimize both privacy and
utility parameters of a Pareto front. Moreover, they also established
the effectiveness of BO in creating visualization interfaces helpful in
decision making. Bionis et al. (2019) have designed a GPareto library
for R which enables the optimization of multi-objective algorithms for
functions associated with a black box. Moreover, the package also
contained several algorithms for the accurate assessment of the
associated bias. The study also proposed several infill criteria in
minimizing the bias associated with several optimization models such as
efficient global optimization technique.
Marjit R. (2009) has made a noble attempt to increase the efficiency of
the Building performance simulation (BPS) tool by combining it with a
robust multi-objective optimization algorithm. The thesis aimed at
developing a multi-objective algorithm with a meta-model to optimize the
simulation of a Pareto front. Asadzadeh et al. (2014) on the other hand,
have developed a new technique called Convex Hull Contribution (CHC) to
address multi-objective (MO) optimization functions associated with
Pareto fronts. They demonstrated the effectiveness of CHC in enhancing
the accuracy of Pareto archived multi dimensioned search while
addressing the multi-objective problems. Audet et al. (2018) have
presented a review of the algorithms devised so far to address the
multi-objective-based optimization in the determination of Pareto
fronts. An assessment of a large number of performance indicators was
carried through various algorithms. Total 57 performance indicators were
grouped into four categories by their properties, viz. cardinality,
convergence, distribution, and spread. Hollermann et al. (2019) have
proposed a new flexible method to automatically identify one optimum
design for multi-objective decision-making. Their approach addresses
both economic and environmental aspects to identify a viable design. The
bias associated with the parameters while predicting a future event
could be handled easily by developing an extension of this algorithm.
Present work was carried out to address the challenging issue of R-A
exchanges which can be analyzed through numerical models. The output of
the numerical models depends on the model domain considered, different
hydrogeological parameters used and boundary conditions applied.
Considering the R-A exchanges in groundwater resource management
problems can help in finding out more efficient and river health
inclusive management practices through simulation-optimization models.
Meanwhile, selection of the optimization algorithm, model domain
demarcation and the comparison of optimum results to provide a
physically meaningful management strategy is still a bottleneck in the
groundwater management problems. Therefore, different model domain
demarcations for the same river system were considered for the
development of the groundwater model, and their impact on R-A exchanges
was analyzed. In addition, different optimization techniques were also
used and their outputs i.e. Pareto fronts were compared. Finally, this
set of optimal results were interpreted in terms of groundwater
management.