Comparison of derivative-free and gradient-based minimization for multi-objective compositional design of shape memory alloys

The study aims to design shape memory alloys (SMAs) whose martensitic start temperature (Ms) matches a target while also minimizing cost. To do this with limited data, the authors train machine learning surrogate models using experimentally characterized alloys plus physics-informed features. They then use numerical optimization to search for alloy compositions that satisfy the objectives. Two optimization pairings are compared: a tree-based model with a derivative-free optimizer (COBYLA), and a neural network that provides gradient information with a gradient-based optimizer (TRUST-CONSTR). The results indicate both models predict Ms with similar accuracy, but TRUST-CONSTR finds better solutions more consistently and behaves more stably, especially when starting guesses are not close to the target. The authors conclude that combining experimental-data ML surrogates with appropriate optimization algorithms is a practical way to explore new SMA compositions, and that the approach could be extended to other materials with design trade-offs under limited data.