Abstract: One challenge of climate change adaptation is to design watershed-based stormwater management plans that meet current total maximum daily load targets and also take into consideration anticipated changes in future precipitation patterns. We present a multi-scale, multiobjective framework for generating a diverse family of stormwater best management practice (BMP) plans for entire watersheds. Each of these alternative BMP configurations are non-dominated by any other identified solution with respect to cost of the implementation of the management plan and sediment loading predicted at the outflow of the watershed; those solutions are then pruned with respect to dominance in sensitivity to predicted changes in precipitation patterns. We first use GIS data to automatically precompute a set of cost-optimal BMP configurations for each subwatershed, over its entire range of possible treatment levels. We then formulate each solution as a real-valued vector of treatment levels for the subwatersheds and employ a staged multiobjective optimization approach using differential evolution to generate sets of non- dominated solutions. Finally, selected solutions are mapped back to the corresponding preoptimized BMP configurations for each subwatershed. The integrated method is demonstrated on the Bartlett Brook mixed-used impaired watershed in South Burlington, VT, and patterns in BMP configurations along the non-dominated front are investigated. Watershed managers and other stakeholders could use this approach to assess the relative trade-offs of alternative stormwater BMP configurations.
Abstract: Important progress has been made by many researchers in extracting fundamental designprinciples from patterns in design parameters along the nondominated front generated by evolutionary algorithms in biobjective optimization problems. However, to the best of our knowledge, no attention has been given to discovering design principles from the wealth of additional information available from patterns in dominated solutions. To explore the same, we use heatmaps of dominated solutions to visualize how relevant variables self-organize with respect to the objectives throughout the feasible region. We overlay ceteris paribus lines on these heatmaps to show how the objective values change when a given design variable is varied while all others are held constant. We use three biobjective optimization problems to demonstrate various ways in which these visualization techniques can provide additional useful information beyond that which can be determined from the nondominated front. Specically, we investigate a simple two-member truss design problem, a simple welded beam design problem, and a real-world watershed management design problem to illustrate: 1) how principles derived from the nondominated front alone can be misleading; 2) how new principles can be derived from the dominated solutions; and 3) how nondominated solutions can often be fragile with respect to assumptions about uncertain external forcing conditions, whereas solutions a short distance inside the front are often much more robust.
Abstract: We introduce a new synergistic combination of features, some of which have previously been used individually but not together, to improve uniformity of spacing in evolved non-dominated sets, especially in biobjective problems. On five standard biobjective benchmark tests, these features are shown to enhance performance in distinct and complementary ways.