Set-based design (SBD) enables systematic exploration of complex engineering design spaces by preserving sets of feasible solutions rather than converging prematurely to a single design. However, identifying and refining end-state sets in high-dimensional spaces remains computationally prohibitive when exhaustive evaluation or dense sampling is required. This paper proposes an active learning–based framework to support scalable end-state exploration within the set-based design paradigm. Instead of directly optimizing end-states, the proposed approach iteratively learns a reliable representation of the feasible design space through selective sampling, surrogate modeling, and probabilistic feasibility assessment. A surrogate regression model is trained and validated using cross-validated accuracy thresholds to ensure predictive reliability before downstream use. Kernel density estimation is then employed to characterize the distribution of feasible end-states and to define acceptance regions for newly sampled candidates. New end-states are adaptively accepted or rejected based on their likelihood under the learned density model, allowing computational effort to focus on informative and feasible regions of the design space. Accepted samples are used to update geometric and probabilistic representations of the feasible end-state set, enabling progressive refinement consistent with set-based design principles. By replacing exhaustive end-state evaluation with selective learning, the proposed framework significantly reduces computational burden while preserving the exploratory nature of set-based design, making it well suited for high-dimensional engineering design problems.

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Dr. Neda Masoud