2025/09/01 by Hameed, Gul, Chen, Tao, Chanona, Antonio del Rio +2 · 1 citation
#90C56 (Primary) 65K10 (Secondary) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2509.01651
Optimising industrial processes often involves grey-box models that couple algebraic glass-box equations with black-box components lacking analytic derivatives. Such hybrid systems challenge derivative-based solvers. The classical trust-region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous black-box evaluations. This work introduces four Hessian-informed TRF variants (A1-A4) that use projected positive definite Hessians for automatic step scaling and minimal tuning, combined with both low-fidelity (linear, quadratic) and high-fidelity (Taylor series, Gaussian process) surrogates for local black-box approximation. Tested on 25 grey-box benchmarks and five engineering case studies (Himmelblau, liquid-liquid extraction, pressure vessel design, alkylation, and spring design), the new variants achieved up to an order-of-magnitude reduction in iterations and black-box evaluations, with reduced sensitivity to tuning parameters relative to the classical TRF algorithm. High-fidelity surrogates solved 92-100 % problems, compared to 72-84 % for the low-fidelity surrogates. Developed TRF methods also outperformed classical derivative-free optimisation solvers. The results show that new variants offer robust and scalable alternatives for grey-box process systems optimisation.