Improved non-dominated sorting genetic algorithm III for efficient of multi-objective cascade reservoirs scheduling under different hydrological conditions

Reservoir scheduling is becoming increasingly critical in natural, cultural, and ecological contexts. Nevertheless, with the proliferation of interests and constraints, the complexity of scheduling problems rises, and the scope of scheduling expands significantly. To tackle multi-objective and multi-constraint reservoir scheduling problems, practical and highly efficient optimization methods are urgently warranted to offer scientific and rational management solutions. To address these challenges, a long-term multi-objective model is hereby established, focusing on power generation (production of electrical energy through hydropower stations), output (the minimum generating capacity or output that the reservoir can provide during operation), and flow (the lowest stream flow within the reservoir and through the turbine). An improved non-dominated sorting genetic algorithm III (INSGA-III) is proposed to determine the optimal scheduling scheme for a cascade reservoir group. INSGA-III employs a more comprehensive initialization of the population using the Pareto set, adopts elite crossover to ensure the ability to converge to the optimal solution later, and incorporates Le<acute accent>vy flights to explore a wider range in the early stages. Performance testing is conducted using a set of benchmark functions, and its efficient performance on various benchmark functions is verified through the IGD indicator and runtime. This study examines a cascade reservoir group of the Jinsha River. Firstly, the analysis of the Pareto front, distribution, and averages confirms the reliability and efficacy of INSGA-III in solving reservoir problems. Subsequently, incorporating both subjective and objective data, the rank-sum ratio method is employed to select optimal solutions from the INSGA-III Pareto front across different scenarios. Following that, the power generation situation of each hydropower station and the trend of reservoir water level changes are analysed. The case study of the Jinsha River cascade reservoirs demonstrates that this model achieves a balance between power generation and hydropower station stability while also safeguarding downstream ecological integrity. Compared to other algorithms, INSGA-III demonstrates superior stability and performance. The model established in this study integrates multiple demands, and the proposed method effectively addresses these complexities, offering a valuable reference for regional scheduling.