Design optimization of mooring systems of offshore floating structures is a challenging task, partly because of the large number of design variables, complicated design constraints, nonlinear system behavior, and time-consuming numerical simulations. For engineering designs, efficient yet accurate approaches are needed. This paper proposes an integrated optimization methodology for design of mooring systems. The methodology integrates the design of experiments, screening analysis, time-domain simulations, and a metamodel-based optimization procedure. To demonstrate the methodology, the mooring system of a vessel-shaped offshore fish farm was designed considering the ultimate limit state. The fully-coupled numerical model includes a floater, flexible fish cages and a single-point mooring system. The Kriging metamodels were applied as surrogates for the responses of time-domain simulations. The optimal solutions were found by exploring the design space using a gradient-based search algorithm. Validations were performed on the metamodels and the global optimal solutions. The proposed methodology is also applicable to design optimization of other marine structures.