PI-NSGA-II for Multi-Objective Optimization of SWMM Calibration Parameters

Calibration of SWMM commonly involved multiple, competing performance criteria, as improvements in one hydrograph characteristic could entail trade-offs in others. This study presented a preference-informed calibration framework based on PI-NSGA-II to support systematic exploration and selection of practically viable parameter sets. The algorithm preserved the core evolutionary structure of NSGA-II, including elitist non-dominated sorting, crowdingdistance diversity preservation, and genetic variation, while extending it through the incorporation of a Preference Index (PI) that reflected decision-maker intent, regulatory tolerances, or target performance levels. In this way, mathematically non-dominated solutions were differentiated according to their consistency with user-defined priorities, addressing a key limitation of conventional NSGA-II in applied calibration contexts. Calibration was formulated using three normalized objective functions, expressed as percentages, to minimize errors in peak discharge, runoff volume, and lag time. Normalization promoted balanced trade-off exploration and limited dominance by any single response characteristic. The framework was implemented for an urban drainage catchment located along Matthew Brady Boulevard in Windsor, Ontario (Canada), using an event-based calibration and independent event-based validation to evaluate robustness. Model performance was additionally assessed using Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), and Kling-Gupta Efficiency (KGE) as diagnostic indicators. The optimal solution achieved strong calibration performance (NSE = 0.91, KGE = 0.86, RMSE = 0.0015 m³/s), with minimal peak magnitude, timing, and runoff volume errors within acceptable limits (≤ 7%). Validation results demonstrated good generalization (NSE = 0.80, KGE = 0.90), although increased sensitivity in peak reproduction was observed. Overall, the results indicated that PINSGA-II yielded a more decision-relevant Pareto set than conventional NSGA-II by explicitly guiding the search toward target-consistent regions of the trade-off space, thereby reducing subjectivity in solution selection and enhancing the practical applicability of SWMM calibration for urban flood management and water-resources decision-making.