Hybridization of photovoltaic (PV) and pumped hydro storage (PHS) can be a promising renewable energy-based system. In such system, optimal operation with respect to reliability is a vital and challenging issue. This paper proposes a multi-objective framework for optimal operation of an on-grid PV-PHS hybrid energy system (HES).For this aim, as the first stage, a multi-objective model is defined in which operation cost (OC) and loss of power supply probability (LPSP) are considered as objective functions and power purchased from the grid and incentive value (used for demand response) are regarded as decision variables. Multi-objective crow search algorithm (MOCSA) is developed to find a well-distributed and widely spread Pareto front. At the second stage, a multi-criteria decision making (MCDM) method is proposed to evaluate and rank non-dominated solutions from the best to worst. To conduct MCDM, technique for order performance by similarity to ideal solution (TOPSIS) integrated with analytic hierarchy process (AHP) method is utilized. On the case study, simulation results show that a high reliability system is suggested in which LPSP, OC