With the development of artificial intelligence, simulation-based optimization problems, which present a significant challenge in the process systems engineering community, are increasingly being addressed with the surrogate-based framework. In this work, we propose a deterministic algorithm framework based on feasible path sequential quadratic programming for optimizing differentiable machine learning models embedded problems. The proposed framework effectively addresses two key challenges: (i) achieving the computation of first- and second-order derivatives of machine learning models' outputs with respect to inputs; and (ii) by introducing the feasible path method, the massive intermediate variables resulting from the algebraic formulation of machine learning models eliminated. Surrogate models for six test functions and two process simulations were established and optimized. All six test functions were successfully optimized to the global optima, demonstrating the framework's effectiveness. The optimization time for all cases did not exceed 2s, highlighting the efficiency of the algorithm.

Black-box optimization (BBO) involves functions that are unknown, inexact and/or expensive-to-evaluate. Existing BBO algorithms face several challenges, including high computational cost from extensive evaluations, difficulty in handling complex constraints, lacking theoretical convergence guarantees and/or instability due to large solution quality variation. In this work, a machine learning-powered feasible path optimization framework (MLFP) is proposed for general BBO problems including complex constraints. An adaptive sampling strategy is first proposed to explore optimal regions and pre-filter potentially infeasible points to reduce evaluations. Machine learning algorithms are leveraged to develop surrogates of black-boxes. The feasible path algorithm is employed to accelerate theoretical convergence by updating independent variables rather than all. Computational studies demonstrate MLFP can rapidly and robustly converge around the KKT point, even training surrogates with small datasets. MLFP is superior to the state-of-the-art BBO algorithms, as it stably obtains the same or better solutions with fewer evaluations for benchmark examples.