Algorithmic funnel-and-gate system design optimization

Funnel-and-gate systems ( FGSs), which constitute a common variant of permeable reactive barriers used for in situ treatment of groundwater, pose particular challenges to the task of design optimization. Because of the complex interplay of funnels and gates, the evolutionary algorithms applied have to cope with multimodality, nonseparability, and nonlinearity of the optimization task. We analyze these features in a test case, introducing an objective function for design cost and constraints to account for plume capture and detention time in the gate reactors. We show that the derandomized evolution strategy with covariance matrix adaptation (CMA-ES) does solve the given design optimization problem with high success rates. We further examine the performance of the algorithm for the example of four-gate systems in three heterogeneous template aquifers. Here a special focus is set on the parameterization of the FGS (i.e., the problem encoding). The comparison of three different encodings reveals their significance concerning the search progress and its success. Among the found optimal and near-optimal design solutions, mutual patterns were recognized. In particular, a large central barrier seems to be a superior feature.