Feasible Path SQP Algorithm for Simulation-based Optimization Surrogated with Differentiable Machine Learning Models

TL;DR

This paper introduces a feasible path SQP algorithm for efficiently optimizing differentiable machine learning surrogates in simulation-based problems, achieving global optima with high speed and accuracy.

Contribution

It presents a novel deterministic framework that computes derivatives and eliminates intermediate variables, enhancing optimization of machine learning surrogates.

Findings

Successfully optimized six test functions to global optima

Achieved optimization times under 2 seconds for all cases

Demonstrated effectiveness and efficiency of the proposed method

Abstract

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.