Display omitted •Propose a coordinated optimization framework for hydro-PV hybrid systems.•Develop a multi-objective optimization model for long-term complementary operation.•Design a parallel GFM-MOEA algorithm to search Pareto optimal solutions.•Propose a novel SMAA-FOS model for robust decision-making.•Make a risk-informed complementary operation strategy with higher reliabilities. Hydropower system is a crucial support for the integration of various renewable energy sources. The integration of dispatchable hydropower and non-dispatchable photovoltaic (PV) power is promising to achieve efficient resource use. This paper proposes a coordinated optimization framework for the long-term complementary operation of large-scale hydro-PV hybrid systems. A multi-objective optimization model is established that simultaneously optimizes the economic benefit and operational safety of the hybrid system, i.e., the quantity and quality of the joint power output. The proposed model decouples hydropower and PV power in time scales to maintain calculation accuracy and reduce problem dimensions. A parallel generic front modeling-based multi-objective evolutionary algorithm (GFM-MOEA) is designed to produce a well-converged and well-distributed set of Pareto optimal solutions. Also, we develop a novel robust decision-making model to evaluate, rank and select the Pareto optimal solutions, which allows potential uncertainties in input data to be considered. The proposed framework is applied to the Longyangxia hydro-PV hybrid power system, which is the largest hydro-PV power plant in the world. Several numerical experiments are conducted to examine the hydrological effect on multi-objective optimization as well as the effect of uncertainty levels on robust decision-making. The results show that: (1) a clear competing relationship exists between total generated power and stability of the joint power output; (2) hydropower can compensate for the PV power, mainly when the solar radiation is limited while the abundant water resource is available due to rainfalls; (3) hydrological regimes have significant impacts on the multi-objective optimization results and the complementary effect; (4) the robust decision-making model enhances the reliability of the risk-informed complementary operation strategy by measuring the robustness and uncertainty of the decision.