Uncertainties in design variables and environmental factors are common in many engineering problems, and they must be taken into account when searching for robust optimal solutions. In robust multi-objective optimization it is common practice to optimize the average performance instead of the nominal objective functions. To compute average performance, and to determine the compliance of the solutions to the constraints, sampling is needed in a neighborhood of each individual and the performance of each sample point must be evaluated. This drives the computational cost of robust optimization up. In this paper we present a repository-based approach that reduces the number of evaluations needed during robust optimization. Unlike most of the approaches available to date, we introduce methods to keep the joint probability density function of the input variables intact when pre-existing points from the repository shall be used. This allows for cheap robust-optimization also in the presence of non-uniform uncertain-variable distributions. The robust optimization of unmanned entry capsules, considering continuous shape-variation models, aerothermodynamics, flight mechanics, and thermal protection system models at the same time is a valuable test-bed for the method presented here. In this paper we discuss the results of minimizing the mass of the capsules while maximizing the internal volume and the re-usability. We demonstrate that using a double-repository archive maintenance scheme it is possible to obtain accurate results and a reduction of the computational cost that is close to 70%, if compared to classical sampling-based methods for robust optimization. The analysis of robust-optimal entry capsules demonstrates that there are design conditions for which small and fully reusable capsules for unmanned entry from low Earth orbits perform as well as capsules with ablative materials, also under uncertainties.
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