Comparison of parallel optimization algorithms on computationally expensive groundwater remediation designs

Abstract

Contaminated groundwater resources threaten human health and destroy ecosystems in many areas worldwide. Groundwater remediation is crucial for environmental recovery; however, it can be cost prohibitive. Planning a cost-effective remediation design can take a long time, as it may involve the evaluation of many management decisions, and the corresponding simulation models are computationally demanding. Parallel optimization can facilitate much faster management decisions for cost-effective groundwater remediation design using complex pollutant transport models. However, the efficiency of different parallel optimization algorithms varies depending on both the search strategy and parallelism. In this paper, we show the performance of a parallel surrogate-based optimization algorithm called parallel stochastic radial basis function (p-SRBF), which has not been previously used on contaminant remediation problems. The two case problems involve two superfund sites (i.e., the Umatilla Aquifer and Blaine Aquifer), and one objective evaluation takes 5 and 30 min for the two problems, respectively. Exceptional speedup (superlinear) is achieved with 4 to 16 cores, and excellent speedup is achieved using up to 64 cores, obtaining a good solution at 80 % efficiency. We compare our p-SRBF with three different parallel derivative-free optimization algorithms, including genetic algorithm, mesh adaptive direct search, and asynchronous parallel pattern search optimization, in terms of objective quality, computational reduction and robust behavior across multiple trials. p-SRBF outperforms the other algorithms, as it finds the best solution in both the Umatilla and Blaine cases and reduces the computational budget by at least 50 % in both problems. Additionally, statistical comparisons show that the p-SRBF results are better than those of the alternative algorithms at the 5 % significant level. This study enriches theoretical real-world groundwater remediation methods. The results demonstrate that p-SRBF is promising for environmental management problems that involve computationally expensive models.

Keywords: Groundwater remediation; Parallel optimization; Surrogated-based optimization.