A Modified linearized orthogonal progressive optimization algorithm coordinates hydropower generation and ecological flow requirements in cascade reservoirs

Coordinating hydropower generation and ecological conservation remains a significant challenge in the operation of cascade reservoirs. Conventional operational strategies often prioritize power generation while neglecting downstream ecological flow requirements (EFRs), thereby disrupting hydrological regimes and causing ecological degradation. This study proposes a multi-objective optimization model for cascade reservoirs that simultaneously maximizes power generation and minimizes ecological water deficits. An Improved Intra-annual Distribution Flow Method (IDFM) is introduced to characterize intra-annual ecological baseflow processes. A Modified Linearized Orthogonal Progressive Optimization Algorithm (MLOPOA) based on MILP is developed to improve solution quality, convergence rate, and computational efficiency. The proposed approach is applied to the cascade system from the lower Jinsha River to the Three Gorges in China. In representative wet, normal, and dry years, MLOPOA maintained zero ecological water deficit and zero constraint violation. Compared with the best benchmark solution satisfying both conditions, MLOPOA increased hydropower generation by 0.80%, 0.27%, and 0.92%, respectively. By integrating dynamic EFR constraints into a hybrid optimization framework, the proposed method provides robust technical support for the sustainable operation of large-scale cascade reservoir systems.