Uncertainty is inevitable in real world. It has to be taken into consideration, especially in engineering optimization; otherwise the obtained optimal solution may become infeasible. Robust optimization (RO) approaches have been proposed to deal with this issue. Most existing RO algorithms use double-looped structures in which a large amount of computational efforts have been spent in the inner loop optimization to determine the robustness of candidate solutions. In this paper, an advanced approach is presented where no optimization run is required to be performed for robustness evaluations in the inner loop. Instead, a concept of Utopian point is proposed and the corresponding maximum variable/parameter variation will be obtained by just solving a set of linear equations. The obtained robust optimal solution from the new approach may be conservative, but the deviation from the true robust optimal solution is very small given the significant improvement in the computational efficiency. Six numerical and engineering examples are tested to show the applicability and efficiency of the proposed approach, whose solutions and computational time are compared with those from a similar but double-looped approach, SQP-RO, proposed previously.

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