The growing reliance on high-fidelity, state-of-the-art machine learning based models for engineering decision-making necessitates robust and systematic approaches for model selection. While high predictive accuracy at untrained points is a necessary trait in the final model, other attributes such as model complexity, forecastability, explainability, scalability, and physics-awareness may be equally important or relevant criteria depending on application context and user requirements. In this work, we propose a novel composite performance metric, Surrogate Quality Score (SQS) for model selection based on predictive accuracy and model complexity simultaneously. SQS heuristically integrates these two attributes through a weighted product of normalized measures, yielding a unified score to reflect overall model quality. A user-specified parameter in SQS enables explicit control over the accuracy-complexity trade-off, thereby incorporating human judgement and preference in the model selection process. We extensively discuss and justify the formulation of SQS and demonstrate its utility through an illustrative example. By combining predictive accuracy and model complexity, SQS offers a systematic and objective approach for model selection based on both attributes.
Global optimization of large-scale, complex systems such as multi-physics black-box simulations and real-world industrial systems is important but challenging. This work presents a novel Surrogate-Based Optimization framework based on Clustering, SBOC for global optimization of such systems, which can be used with any surrogate modeling technique. At each iteration, it uses a single surrogate model for the entire domain, employs k-means clustering to identify unexplored domain, and exploits a local region around the surrogate optimum to potentially add three new sample points in the domain. SBOC has been tested against sixteen promising benchmarking algorithms using 52 analytical test functions of varying input dimensionalities and shape profiles. It successfully identified a global minimum for most test functions with substantially lower computational effort than other algorithms. It worked especially well on test functions with four or more input variables. It was also among the top six algorithms in approaching a global minimum closely. Overall, SBOC is a robust, reliable, and efficient algorithm for global optimization of box-constrained systems.