A comparative study of Monte Carlo simple genetic algorithm and noisy genetic algorithm for cost-effective sampling network design under uncertainty

This study evaluates and compares two methodologies, Monte Carlo simple genetic algorithm (MCSGA) and noisy genetic algorithm (NGA), for cost-effective sampling network design in the presence of uncertainties in the hydraulic conductivity (K) field. Both methodologies couple a genetic algorithm (GA) with a numerical flow and transport simulator and a global plume estimator to identify the optimal sampling network for contaminant plume monitoring. The MCSGA approach yields one optimal design each for a large number of realizations generated to represent the uncertain K-field. A composite design is developed on the basis of those potential monitoring wells that are most frequently selected by the individual designs for different K-field realizations. The NGA approach relies on a much smaller sample of K-field realizations and incorporates the average of objective functions associated with all K-field realizations directly into the GA operators, leading to a single optimal design. The efficacy of the MCSGA-based composite design and the NGA-based optimal design is assessed by applying them to 1000 realizations of the K-field and evaluating the relative errors of global mass and higher moments between the plume interpolated from a sampling network and that output by the transport model without any interpolation. For the synthetic application examined in this study, the optimal sampling network obtained using NGA achieves a potential cost savings of 45% while keeping the global mass and higher moment estimation errors comparable to those errors obtained using MCSGA. The results of this study indicate that NGA can be used as a useful surrogate of MCSGA for cost-effective sampling network design under uncertainty. Compared with MCSGA, NGA reduces the optimization runtime by a factor of 6.5.