Enhanced Nonlinearity Interval Mapping Scheme for High Performance Simulation-Optimization of Watershed-Scale BMP Placement

Water Resources Research

Rui Zou , John Riverson, Yong Liu, Ryan Murphy, Youn Sim

ABSTRACT: Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly-used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 minutes) to complete with the resulting optimal solution having a total cost of $67.2 million, while each of the multiple GA executions took 21 to 38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of $67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

KEYWORDS: Best Management Practice; Placement; Simulation-Optimization; Nonlinearity Interval Mapping Scheme; Interval Response Coefficient; Genetic Algorithms