*Result*: An adaptive hybrid kriging–RSM approach to enhance the surrogate-based MDO accuracy for re-entry bio-capsules.

*This paper presents an adaptive hybrid kriging-response surface methodology to enhance the accuracy of surrogate-based single- and triple-objective Multi-Disciplinary Design Optimization (MDO) for re-entry bio-capsules. The main goal of surrogate modeling is to produce accurate models while reducing the number of expensive, detailed simulations. This paper presents an adaptive sampling criterion to identify the most valuable new point to add to the existing Design of Experiments (DOE) data. It focuses on regions where the model exhibits high uncertainty and where the global trend is a poor predictor. The hybrid model is then updated with this new point, and this process is repeated until the desired accuracy is achieved. Then, surrogate models are employed to optimize nine single-objective problems and three triple-objective problems related to a re-entry bio-capsule using single-objective and multi-objective genetic algorithms, respectively. In the optimization process, all design disciplines, particularly the structural discipline, as well as objectives such as minimizing deformation, maximizing the buckling resistance, and maximizing the structural frequency, are taken into consideration. Therefore, all geometric parameters of the capsule, including its shape, participate in optimization with structural objectives. The results show that the adaptive hybrid method significantly improves the accuracy of surrogate models, achieving a Coefficient of Determination (R 2) over 0.97 and a Relative Root Mean Square Error (RRMSE) under 9.42 % for all models. This method reduces the RRMSE by up to 28 % compared to non-adaptive approaches, while achieving a higher level of accuracy using the same number of experimental design points. Finally, the results obtained from the single-objective approaches have been compared with those obtained from telemetry in the spaceflight test of the native bio-capsule. The results of the present paper are in close agreement with the spaceflight test results of the native bio-capsule. [ABSTRACT FROM AUTHOR]*