Abstract: The multi-objective optimization problem of cascade reservoirs involves high factor dimensions and complicated inter-objective relationships. Traditional statistical methods are difficult to consider the target information contained in different indicators comprehensively, and can give only qualitative analysis of their mutual feedback relationships. Aiming at the problem, this paper constructs a power generation-water supply-ecology multi-objective optimal scheduling model for cascade reservoirs, solves it using a fast non-dominated sorting genetic algorithm (NSGA-Ⅱ), and formulates a preliminary hypothesis of mutual feedback relationships among the three objectives. And we apply a structural equation modeling (SEM), conduct a high-dimensional confirmatory factor analysis using the index values given by the multi-objective non-inferior solution set of cascade reservoirs, and present visual and quantitative calculation results for the mutual feedback relationships among the objectives. The results of the Xiluodu-Xiangjiaba cascade reservoirs show that under different inflow frequencies, the power generation-water supply conflict is the most severe, followed by power generation-ecology; while compared with these conflicts, the water supply-ecology feedback relationship is insignificant. As the frequency of inflow increases, the conflict between power generation and water supply sharpens rapidly.

Key words: structural equation modeling, cascade reservoirs, multi-objective optimal scheduling, mutual feedback relationship