Categorical optimization via Bayesian anchored latent trust-regions for structural design under high-dimensional uncertainties

Categorical structural optimization under aleatoric uncertainties presents significant challenges due to the requirement of selecting each design variable from a finite catalog of allowable instances. Moreover, each candidate design necessitates costly stochastic finite-element evaluations. Existing latent-space optimization methods, while capable of reducing the dimensionality of catalog attributes, typically treat the resultant space as a continuous search domain. This approach necessitates rounding off the continuous optimum to the nearest catalog instance, potentially altering the objective value, constraint status, or physical interpretation of the design. To mitigate this issue, this paper introduces the Categorical Optimization with Bayesian Anchored Latent Trust-Regions (COBALT) framework, designed for high-dimensional categorical optimization under uncertainties (OUU). COBALT initially embeds the physical catalog into a low-dimensional latent representation, locking the mapped instances as a discrete anchored graph. Subsequently, a data-independent random tree decomposition is employed to offer bounded-complexity additive modeling for high-dimensional categorical variables. On this anchored domain, an additive Sparse Axis-Aligned Subspace Gaussian Process (SAAS-GP) surrogate is fitted to heteroscedastic Monte Carlo-based Finite Element Analysis (MC-FEA) observations. A trust-region discrete graph acquisition search is then used to select the next admissible catalog configuration, avoiding continuous relaxation or rounding-off. The proposed strategy is demonstrated in the robust design optimization of complex beam structures, considering factors such as structural weight, strain energy, and local buckling performance. Numerical examples indicate that evaluating only valid catalog designs through the MC-FEA oracle preserves physical admissibility throughout the active learning loop. Furthermore, it can enhance the efficiency of robust categorical structural optimization when compared to relaxation-based and non-surrogate search strategies under equivalent conditions.