This manuscript presents robust optimization framework with multi-objective approach for day-ahead operation of hybrid power system consisted of photovoltaic (PV) panel, fuel cell (FC) with electrolyzer (Elc) back-up. The multi-objective optimization model of PV/FC/Elc has been developed by combining the physical and operational constraints with mathematical equivalence of affine forms as well as considering the uncertainties occurring in the load demand and PV power generation. As a novel contribution to the literature, three robust optimization approaches for scheduling the hybrid power systems have been presented through the conservatism approach. Moreover, the objective function has been described to integrate the different objectives as aiming to minimize non-supplied load, while maximize the utilization rate of the essential source. By this way, it has been aimed to accelerate the adaptation of the demand response strategies for the proposed system. Moreover, this hybrid scheme provides solutions to meet the power demands for the residential end-users located in off-grid areas or islands. The mixed integer linear programming (MILP) model is tested in GAMS v.24.1.3 using the solver CPLEX v.12 and the developed strategy is analyzed for different load patterns. The results are discussed and commented with some suggestions to prove the contribution of the paper.