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There are two main issues with a simulation-optimization framework that couples a high-fidelity numerical model with an optimization algorithm. First, the numerical models are often computationally expensive and second, the optimization algorithm requires the numerical model to run several thousands of times which makes the whole process overly time-consuming. In addition, the computational complexity can increase further if the considered optimal management problem has multiple criteria and/or a high number of decision variables (see Table 1). This computational burden can be reduced significantly by using different surrogate modeling techniques (Rao et al. 2004; Bhattacharjya & Datta 2009; Dhar & Datta 2009; Papadopoulou et al. 2010; Sreekanth & Datta 2011, 2015; Ketabchi & Ataie-Ashtiani 2015). A surrogate model is an empirical or lower-fidelity alternative to either (A) the response of the high-fidelity numerical simulation model itself or (B) the objective function of the considered optimization problem or (C) the operating policy model in case of optimal control problems (Ratto et al. 2012). A surrogate model is simpler, considerably faster to run, and is generally derived through a training framework from the original simulation model (Razavi et al. 2012b).

Table 1

Recent studies on groundwater management models for coastal groundwater systems

ReferenceModelaProblembObjective functionc#DVdSMeOAfSTgTDhCEi
Bhattacharjya & Datta (2009)  3D DA-GW GW (q) max(Qout), min(C), min(Qinj33 MLP NSGA-II HC TR3 1,000 × 2,500 
Bray & Yeh (2008)  FEMWATER GW (q,x,y) min(Qinj215 – GA RC TR5 Parallel 
Dhar & Datta (2009)  FEMWATER GW(q) max(Qout), min(Qinj33 MLP NSGA-II HC TR3 24 × 1,800 
Haddad & Marino (2011)  3D DA-GW GW(q) max(C26 – HBMO HC, RC TI 6,000 
Kourakos & Mantoglou (2010)  SEAWAT (2D) GW(q) min(Cök), min(Cumw– NSGA-II HC TI ? × 400 
Papadopoulou et al. (2010)  PTC GW(q) max(QoutRBF DE RC TI 20 × 200 
Rao et al. (2004)  SEAWAT GW(q) max(Qout), min(Qinj27 MLP SA HC TR3 10,000 
Sreekanth & Datta (2011)  FEMWATER GW(q) max(Qout), min(Qinj33 GP NSGA-II HC TR3 200 × 750 
ReferenceModelaProblembObjective functionc#DVdSMeOAfSTgTDhCEi
Bhattacharjya & Datta (2009)  3D DA-GW GW (q) max(Qout), min(C), min(Qinj33 MLP NSGA-II HC TR3 1,000 × 2,500 
Bray & Yeh (2008)  FEMWATER GW (q,x,y) min(Qinj215 – GA RC TR5 Parallel 
Dhar & Datta (2009)  FEMWATER GW(q) max(Qout), min(Qinj33 MLP NSGA-II HC TR3 24 × 1,800 
Haddad & Marino (2011)  3D DA-GW GW(q) max(C26 – HBMO HC, RC TI 6,000 
Kourakos & Mantoglou (2010)  SEAWAT (2D) GW(q) min(Cök), min(Cumw– NSGA-II HC TI ? × 400 
Papadopoulou et al. (2010)  PTC GW(q) max(QoutRBF DE RC TI 20 × 200 
Rao et al. (2004)  SEAWAT GW(q) max(Qout), min(Qinj27 MLP SA HC TR3 10,000 
Sreekanth & Datta (2011)  FEMWATER GW(q) max(Qout), min(Qinj33 GP NSGA-II HC TR3 200 × 750 

a3D DA-GW = 3D density driven groundwater model, FEMWATER, SEAWAT, PTC = see reference.

bGW = groundwater management, q = abstraction (injection) rate, x = x-coordinate, y = y-coordinate of the well.

cQout = pump volume, Qinj = injection volume, C= costs.

dNumber of decision variables.

eSurrogate model: GP = genetic programming, MLP = multilayer perceptron, RBF = radial basis function network.

fOptimization algorithm: GA = genetic algorithm, HBMO = honey-bee mating algorithm, NSGA-II = nondominated sorting genetic algorithm II, DE = differential evolution, SA = simulated annealing.

gType of study: HC = hypothetical case, RC = real case.

hTime dependence of decision variables: TI = time-invariant, TR <x> transient over x periods.

iComputational effort: <population size > x < nr. of generations > .

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