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This paper introduces COBALT, a novel framework for categorical structural optimization under uncertainty that avoids continuous relaxations by embedding the design catalog into a low-dimensional, discrete anchored graph. COBALT uses a data-independent random tree decomposition for bounded-complexity additive modeling over high-dimensional categorical variables, fitting an additive SAAS-GP surrogate to MC-FEA observations. Applied to robust design optimization of bar structures, COBALT demonstrates improved efficiency by only evaluating valid catalog designs, preserving physical admissibility throughout the active learning loop.
COBALT unlocks efficient structural design optimization by treating the design space as a discrete anchored graph, avoiding the pitfalls of continuous relaxation and rounding-off that plague existing methods.
Categorical structural optimization under aleatoric uncertainty is challenging because each design variable must be selected from a finite catalog of admissible instances, while each candidate design may require expensive stochastic finite-element evaluations. Existing latent-space optimization strategies can reduce the dimensionality of catalog attributes, but they often treat the reduced space as a continuous search domain. The resulting continuous optimum must then be rounded off to a nearby catalog instance, which may alter the objective value, constraint status, or physical interpretation of the design. To address this issue, this paper proposes the \textbf{C}ategorical \textbf{O}ptimization with \textbf{B}ayesian \textbf{A}nchored \textbf{L}atent \textbf{T}rust Regions (\textbf{COBALT}) framework for high-dimensional categorical Optimization Under Uncertainty. COBALT first embeds the physical catalog into a low-dimensional latent representation and locks the mapped instances as a discrete anchored graph. A data-independent random tree decomposition is then used to provide bounded-complexity additive modeling over high-dimensional categorical variables. On this anchored domain, an additive SAAS-GP surrogate is fitted to heteroscedastic MC-FEA observations, and a trust-region discrete graph acquisition search selects the next admissible catalog configuration without continuous relaxation or rounding-off. The proposed strategy is applied to robust design optimization of complex bar structures, considering structural weight, strain energy, and local buckling performance. By evaluating only valid catalog designs through the MC-FEA oracle, COBALT preserves physical admissibility throughout the active learning loop and improves the efficiency of robust categorical structural optimization.
