Automatic calibration of hydrologic models with multi-objective evolutionary algorithm and Pareto optimization

In optimization problems with at least two conflicting objectives, a set of solutions rather than a unique one exists because of the trade-offs between these objectives. A Pareto optimal solution set is achieved when a solution cannot be improved upon without degrading at least one of its objective criteria. This study investigated the application of multi-objective evolutionary algorithm (MOEA) and Pareto ordering optimization in the automatic calibration of the Soil and Water Assessment Tool (SWAT), a process-based, semi-distributed, and continuous hydrologic model. The nondominated sorting genetic algorithm II (NSGA-II), a fast and recent MOEA, and SWAT were called in FORTRAN from a parallel genetic algorithm library (PGAPACK) to determine the Pareto optimal set. A total of 139 parameter values were simultaneously and explicitly optimized in the calibration. The calibrated SWAT model simulated well the daily streamflow of the Calapooia watershed for a 3-year period. The daily Nash-Sutcliffe coefficients were 0.86 at calibration and 0.81 at validation. Automatic multi-objective calibration of a complex watershed model was successfully implemented using Pareto ordering and MOEA. Future studies include simultaneous automatic calibration of water quality and quantity parameters and the application of Pareto optimization in decision and policy-making problems related to conflicting objectives of economics and environmental quality.