Robust design optimization (RDO) has been eminent in determining the optimal design of real-time complex systems under stochastic environment. Unlike conventional optimization, RDO involves uncertainty quantification which may render the procedure to be computationally intensive, if not prohibitive. In order to deal with such issues, an efficient approximation-based generalized RDO framework has been proposed. Since RDO formulation comprises of statistical terms of the performance functions, the proposed framework deals with approximation of those statistical quantities, rather than the performance functions. Consequently, the proposed framework allows transformation of the RDO problem to an equivalent deterministic one. As a result, unlike traditional surrogate-assisted RDO, the proposed framework yields desirable results in significantly less number of functional evaluations. For performing such response statistical approximation, two adaptive sparse refined Kriging-based computational models have been proposed. However, the generality of the proposed methodology allows any surrogate models to be employed within this framework, provided it is capable of capturing the functional non-linearity. Implementation of the proposed framework in three test examples and two finite element-based practical problems clearly illustrates its potential for further complicated applications. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.