Why compare to COBYLA instead of BOBYQA?

The FOP formulation used is shown in (2) below. The situation for equality constraints is similar. For example, this is a common assumption in robust optimization [Zhen et al., 2018]. There are three practical issues with (3): 1. Details are beyond the scope of this manuscript.

Designing shape memory alloys (SMAs) that meet performance targets while remaining affordable and sustainable is a complex challenge. In this work, we focus on optimizing SMA compositions to achieve a desired martensitic start temperature (Ms) while minimizing cost. To do this, we use machine learning models as surrogate predictors and apply numerical optimization methods to search for suitable alloy combinations. We trained two types of machine learning models, a tree-based ensemble and a neural network, using a dataset of experimentally characterized alloys and physics-informed features. The tree-based model was used with a derivative-free optimizer (COBYLA), while the neural network, which provides gradient information, was paired with a gradient-based optimizer (TRUST-CONSTR). Our results show that while both models predict Ms with similar accuracy, the optimizer paired with the neural network finds better solutions more consistently. COBYLA often converged to suboptimal results, especially when the starting guess was far from the target. The TRUST-CONSTR method showed more stable behavior and was better at reaching alloy compositions that met both objectives. This study demonstrates a practical approach to exploring new SMA compositions by combining physics-informed data, machine learning models, and optimization algorithms. Although the scale of our dataset is smaller than simulation-based efforts, the use of experimental data improves the reliability of the predictions. The approach can be extended to other materials where design trade-offs must be made with limited data.

The global optimization of a high-dimensional black-box function under black-box constraints is a pervasive task in machine learning, control, and engineering. These problems are difficult since the feasible set is typically non-convex and hard to find, in addition to the curses of dimensionality and the heterogeneity of the underlying functions. In particular, these characteristics dramatically impact the performance of Bayesian optimization methods, that otherwise have become the de-facto standard for sample-efficient optimization in unconstrained settings. Due to the lack of sample-efficient methods, practitioners usually fall back to evolutionary strategies or heuristics. We propose the scalable constrained Bayesian optimization (SCBO) algorithm that addresses the above challenges by data-independent transformations of the functions and follows the recent theme of local Bayesian optimization. A comprehensive experimental evaluation demonstrates that SCBO achieves excellent results and outperforms the state-of-the-art methods.