A multi-criteria surrogate-assisted framework for preliminary design optimization of steel gridshells

The paper proposes a surrogate-assisted framework for the preliminary design optimization of steel gridshells, in which the cross-section size of the members is determined by separately considering three design criteria: member axial resistance, global structural deformability, and global elastic buckling. The reference datasets are generated through an automatic parametric procedure implemented in MATLAB and coupled with the structural analysis software OpenSees and SAP2000. For each combination of the design parameters, the numerical procedure automatically updates the member cross-section until the selected design criterion is satisfied. The resulting optimized solutions are then used to train surrogate models. To this end, three dedicated feed-forward neural networks are developed to predict the optimized cross-section size associated with each design criterion, while Gaussian Process Regression, Regression Tree Ensemble, and fitrnet models are adopted as benchmark regression approaches. The results obtained on independent check datasets show a good prediction accuracy for all the considered criteria, with particularly stable performance for member axial resistance and global buckling, whereas a higher sensitivity is observed for the deformability-based criterion. The framework is applied to a regular barrel-vault steel gridshell through two preliminary optimization problems aimed at minimizing the required member diameter and the total structural mass. In both cases, global elastic buckling governs the final sizing. Direct finite-element checks and geometrically nonlinear analyses of perfect and imperfect configurations support the consistency of the surrogate-assisted solutions, while showing a greater sensitivity to initial imperfections for the minimum-mass configuration. By transferring the iterative sizing analyses to the offline phase, the proposed approach enables a rapid exploration of alternative multi-criteria solutions during preliminary design.