Water resource management (WRM) through dams or reservoirs is worldwide necessary to support key human‐related activities, ranging from hydropower production to water allocation and flood risk mitigation. Designing of reservoir operations aims primarily to fulfill the main purpose (or purposes) for which the structure has been built. However, it is well known that reservoirs strongly influence river geomorphic processes, causing sediment deficits downstream, altering water, and sediment fluxes, leading to riverbed incision and causing infrastructure instability and ecological degradation. We propose a framework that, by combining physically based modeling, surrogate modeling techniques, and multiobjective (MO) optimization, allows to include fluvial geomorphology into MO optimization whose main objectives are the maximization of hydropower revenue and the minimization of riverbed degradation. The case study is a run‐of‐the‐river power plant on the River Po (Italy). A 1‐D mobile‐bed hydro‐morphological model simulated the riverbed evolution over a 10 year horizon for alternatives operation rules of the power plant. The knowledge provided by such a physically based model is integrated into a MO optimization routine via surrogate modeling using the response surface methodology. Hence, this framework overcomes the high computational costs that so far hindered the integration of river geomorphology into WRM. We provided numerical proof that river morphologic processes and hydropower production are indeed in conflict but that the conflict may be mitigated with appropriate control strategies.