Developing long term operation rules for multi-reservoir systems is complicated due to the number of decision variables, the non-linearity of system dynamics and the hydrological uncertainty. This uncertainty can be addressed by coupling simulation models with multi-objective optimisation algorithms driven by stochastically generated hydrological timeseries but the computational effort required imposes barriers to the exploration of the solution space. The paper addresses this by (a) employing a parsimonious multi-objective parameterization-simulation-optimization (PSO) framework, which incorporates hydrological uncertainty through stochastic simulation and allows the use of probabilistic objective functions and (b) by investigating the potential of multi-objective surrogate based optimisation (MOSBO) to significantly reduce the resulting computational effort. Three MOSBO algorithms are compared against two multi-objective evolutionary algorithms. Results suggest that MOSBOs are indeed able to provide robust, uncertainty-aware operation rules much faster, without significant loss of neither the generality of evolutionary algorithms nor of the knowledge embedded in domain-specific models.