Uncertainty is inevitable and has to be taken into consideration in engineering optimization; otherwise, the obtained optimal solution may become infeasible or its performance can degrade significantly. 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 for robustness evaluation in the inner loop. Instead, a concept of Utopian point is proposed and the corresponding maximum variable/parameter variation will be obtained just by performing matrix operations. The obtained robust optimal solution from the new approach may be conservative, but the deviation from the true robust optimal solution is small enough and acceptable 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 efforts are compared to those from a previously proposed double-looped approach, sequential quadratic program-robust optimization (SQP-RO).

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