Intelligent design interfaces that rely on preference-based optimization are most useful when their suggestions are both meaningful to users and feasible within the target domain. Procedural models offer compact and editable design spaces, but their native parameters can be entangled and can generate many invalid outputs, causing human-in-the-loop optimizers to waste comparisons. We propose an interaction-oriented representation-learning pipeline for procedural models and study it in automotive wheel design. The method first screens procedurally generated samples using geometric rules and finite-element analysis, then learns a reduced latent space from the screened subset. We further introduce supervised functional alignment, which reserves selected latent dimensions for stiffness, strength-related stress response, or weight so that search can be biased toward functionally meaningful regions. Simulation experiments show that screened reduction improves target-shape retrieval and the feasibility rate of suggestions, whereas unscreened reduction degrades both. Additional simulations show that constraining search along learned functional dimensions accelerates exploration toward target functional properties. A controlled study with 40 participants further shows that a 5D feasibility-aware space yields higher shape similarity and more feasible suggestions than the original 9D procedural parameterization. These results suggest that, for intelligent user interfaces in engineering design, the representation exposed to the user is a central part of the interaction design, not merely a preprocessing step for the optimizer.

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