A rule-based multi-objective optimization framework for flood control in coastal urban river networks under extreme rainfall and tidal backflow.

Coastal urban river networks are increasingly exposed to severe flood risk from extreme rainfall and tidal backflow. To mitigate this risk, this study proposes a rule-based multi-objective optimization framework to derive operating rules for hydraulic infrastructure. Within this framework, Storm Water Management Model (SWMM) is coupled with the NSGA-II algorithm to form a multi-objective model to minimize overflow risk and operational cost. Performance metrics evaluate convergence, adaptability under diverse hydrological conditions, and identify optimal water-level rule-based control (WL-RBC) schemes. The framework is applied to a complete river network in Fuzhou City under six representative rainfall-tide scenarios. Optimization results show high-quality solutions across all scenarios. Compared with the original scheme, the dominating solutions reduce exceedance depth at control cross-sections by an average of 48.99 %-77.22 % and lower energy consumption by more than 92 %. Under matched rainfall conditions, the WL-RBC schemes remain adaptable, with Dominance Coverage Rate (DCR) values of 0.74-1.0. Hydraulic performance of the river network is enhanced, with higher storage utilization, smaller water-level fluctuation, shorter inundation duration, and a smaller number of surcharged channels. At control cross-sections, peak water levels and overflow durations are reduced, shifting operations from pump-dominated to gate-prioritized modes and saving energy by factors of 7-848. Overall, the proposed framework can enhance resilience, adaptability, and energy efficiency in coastal cities facing compound flood challenges.