Research on joint optimization scheduling of water, sediment, and power in Xiaolangdi Reservoir based on non-dominated genetic algorithm

Sediment discharge scheduling in reservoirs often requires lowering water levels, which conflicts with the higher levels needed for power generation. Therefore, a reasonable scheduling scheme is essential to ensure long-term operation and maximize benefits. This study focuses on the Xiaolangdi Reservoir, aiming to enhance its siltation reduction and power generation benefits. By integrating a one-dimensional hydrodynamic and sediment transport model with the Non-Dominated Sorting Genetic Algorithm III (NSGA-Ⅲ), an optimization scheduling model for water, sediment, and power generation was developed. The model simultaneously considers sediment and power generation objectives, employing a refined one-dimensional hydrodynamic and sediment transport model that offers more accurate sedimentation calculations than empirical sediment discharge efficiency formulas. The Preissmann scheme discretizes the governing equations, solved via the double-sweep method. The hydro-sediment model calibration involved analyzing the effects of parameters in the sediment transport capacity formula on predicted sedimentation. In the NSGA-III algorithm, an individual represents a series of daily-averaged outflow discharges from the reservoir, which serve as outlet boundary conditions driving the hydro-sediment model. Predicted water levels and updated bed elevations at each cross-section evaluate the objective functions of power generation and siltation reduction. Initial population generation was improved by considering total released water volume. Uniform crossover and polynomial mutation are applied, with mutation amplitude constrained by reservoir discharge capacity. Results show the hydro-sediment model accurately simulates water levels at multiple stations, with Nash-Sutcliffe efficiencies from 0.77 to 0.99. Predicted outflow sediment concentration aligns well with measurements, and sedimentation volume error is within 4.3%. The proposed model optimized Xiaolangdi Reservoir outflow discharge from April 20 to October 20, 2012. Initial crossover and mutation probabilities were set at 0.4 and 0.02, respectively, dynamically reduced to 0.2 and 0.01 over iterations. The target pool level matched the actual level at the operation period's end. Population distribution in objective space was observed across generations. The Pareto optimal solutions from NSGA-Ⅲ highlight the conflict between siltation reduction and power generation, with Pareto front solutions outperforming the original plan. Holding sedimentation constant, power generation increased by 11.4%; conversely, with constant power generation, sedimentation volume reduced by 48%. Keeping the ratio of objectives constant, power generation increased by 13%, and siltation reduction by 50%. The minimum siltation plan and the turning point on the Pareto front were compared with actual operations regarding pool level processes. All optimal solutions converge to states maintaining pool levels below the flood-limited water level, satisfying flood control constraints. The minimum achievable siltation is 0.74×10⁸ m³ and the maximum power generation is 5.82×10⁹ kW·h. This model enables quantitative analysis of trade-offs between power generation and siltation reduction, supporting multi-objective optimal scheduling of reservoirs in heavily sediment-laden rivers.