Multi-objective derivation of gated-spillway operating rules under hydrologic uncertainty: A two-stage simulation-optimization framework

Operating gated spillways during floods requires balancing conflicting objectives - dam safety, downstream flood protection, and hydropower generation - under substantial hydrologic uncertainty, a task for which fixed heuristic rules are poorly suited. This paper presents a two-stage simulation-optimization framework that derives a state-dependent gate-operating rule table, mapping the reservoir water-surface elevation and inflow directly to gate opening. The policy is optimized with a multi-objective evolutionary algorithm (NSGA-II) against a scenario-based ensemble of design floods spanning multiple return periods, storm durations, hyetograph shapes, and antecedent moisture conditions, under three objectives: maximizing worst-case freeboard, maximizing mean energy, and minimizing worst-case downstream stage. To keep the computation tractable, Stage 1 explores the decision space with a Muskingum-Cunge surrogate, and Stage 2 refines the Pareto front with a full one-dimensional unsteady HEC-RAS model applied to the most critical hydrographs. Applied to the Pournari I dam on the Arachthos River, Greece, the framework yields a monotone, operator-readable rule table that, across 360 independent validation floods, prevents overtopping in every case, keeps the freeboard above the 2 m operational threshold, and attenuates a 9,060 m3/s inflow to about 4,350 m3/s (52%). The approach provides a transparent, deployable decision-support tool for real-time reservoir flood control.