Enhancing the Solution of Large Monitoring Network Design Problems Using a New Epsilon-Dominance Hierarchical Bayesian Optimization Algorithm

by Joshua B. Kollat,
Patrick M. Reed,

Abstract: Designing long-term monitoring (LTM) networks for contaminated groundwater is a challenging problem that has long been recognized to suffer from the curse of dimensionality. LTM design problems are challenging multiobjective problems that have discrete decision spaces that grow exponentially as the different types of measurements, their locations, and sampling rates are considered. The scaling challenges of LTM network design problems have been discussed in the water resources literature for more than 30 years. Since the late 1990's, evolutionary algorithms (EAs) have shown promise for providing approximately optimal LTM network designs for problems of limited size and complexity. However, recent studies have highlighted that currently available algorithms do not consider that sampling decisions are often correlated due to contaminant plume structure. Current Multi-Objective Evolutionary Algorithms(MOEAs) have at best displayed quadratic computational scaling, which means that as the number of sampling decisions (l) increases linearly, the number of design evaluations required to optimize the problem grows at least quadratically - O(l²). This work is focusing on the development of a next generation MOEA that can learn and exploit the physical linkages between decision variables in LTM design applications with the goals of providing more robust performance for increased problem sizes. The proposed MOEA is termed the Epsilon-Dominance Hierarchical Bayesian Optimization Algorithm (ε-hBOA). ε-hBOA has been tested relative to the best known traditional MOEA, the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (ε-NSGAII) for solving a four-objective LTM problem. A comprehensive performance assessment of the ε-NSGAII and various configurations of the ε-hBOA have been performed for both a 25-well LTM design test case (a relatively small problem with over 33 million possible designs), and a 58-point LTM design test case (a much larger problem with over 2.88 x 1017 possible designs). The results from this comparison indicate that the model building capability of the ε-hBOA greatly enhances its performance relative to the ε -NSGAII, especially on large LTM design problems.

Subject Headings: Algorithms | Groundwater pollution | Fouling | Water resources | Bayesian analysis | Building design | Pollutants | Plumes

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