[Objectives] Existing reservoir scheduling studies mainly focus on pure hydropower scheduling, with limited consideration of renewable energy integration. Traditional optimal scheduling of hydro-photovoltaic complementary systems typically prioritizes power generation benefits, which fails to meet the requirements of multi-objective comprehensive utilization. Moreover, compared with pure hydropower scheduling, the optimal scheduling of hydro-photovoltaic complementary systems is more complex to solve. This study aims to establish a multi-objective optimal scheduling model for hydro-photovoltaic complementary systems with the objectives of maximizing annual power generation benefits and maximizing the minimum output during specific periods. [Methods] To overcome the local optimum issue in the Moth-Flame Optimization (MFO) algorithm, improvements were made to the multi-objective MFO from three aspects: update formula, inspiration from moths’ linear flight paths, and flame population update strategy. To distinguish individuals that are mutually non-dominated under Pareto dominance, R-domination incorporating reference points was introduced. The combination of these two led to the development of a new high-performance multi-objective evolutionary algorithm: R-IMOMFO. A multi-objective optimization scheduling model for hydro-photovoltaic complementary systems was established, considering both power generation benefits and capacity benefits, and the model was solved using the R-IMOMFO algorithm. [Results] The R-IMOMFO algorithm demonstrated fast convergence, strong resistance to premature convergence, and high accuracy, proving to be an effective method for solving complex multi-objective optimization problems. Using the R-IMOMFO algorithm, non-dominated scheduling solution sets were obtained under three runoff scenarios—wet year, normal year, and dry year—for both power generation and capacity benefits. For each typical year, two extreme schemes and one intermediate scheme were selected for comparative analysis. This enabled scheduling operators to select more appropriate solutions based on their prioritization of different objectives. [Conclusions] The proposed multi-objective optimization model effectively coordinates the relationship between power generation benefits and capacity benefits in hydro-photovoltaic complementary systems, providing data support for decision-making in multi-objective optimal scheduling.