Fully stressed design is a classical principle in structural optimization that seeks minimum-weight structures by ensuring uniform stress utilization. Generally, parametric models are used as inputs, but they are confined to a particular type of design. To enable more robust and diverse designs within a single machine learning model, a voxel-based representation can be adopted. However, the drawback of this approach is the increased dimensionality of the problem. In this work, a depth-encoded 2D representation is adopted, where grayscale intensity encodes the local through-thickness extent of material, thereby reducing the dimensionality. This work presents a surrogate-assisted multi-objective optimization framework for fully stressed beam design, combining exact mechanics with machine learning. A cantilever Euler–Bernoulli beam with spatially varying cross-sectional height is employed as the canonical benchmark. Bending stress distributions and tip deflections are approximated using data-driven surrogate models trained on a diverse dataset of mechanically admissible geometries. Two surrogate strategies are investigated: Random Forest regressors are selected for their robustness, resistance to overfitting, and reliable performance on moderately sized datasets with localized nonlinearities. In contrast, multilayer perceptron networks are adopted for their superior expressive capacity and ability to capture smooth, high-order nonlinear relationships, enabling a comparative assessment of surrogate impact on optimization outcomes. The MLP surrogate achieved R^2scores of 0.867 and 0.944 for stress ratio and deflection prediction, respectively, while the RF surrogate attained R^2scores of 0.884 and 0.971, demonstrating higher accuracy in deflection estimation. Numerical results shows that this framework achieves near-uniform stress distributions and substantial material reduction relative to uniform designs, while satisfying deflection limits.