(282b) A Modified Trust Region Filter Framework Designed for Computationally Expensive Black-Box Optimization

Glass box/black box optimization represents systems which include both equation-oriented process models and black-box models. There is no direct available derivative information for black-box functions, which offers great challenges to conventional derivative-based NLP solvers. In addition, black-box systems may be potentially computationally expensive. For example, when solving computational fluid dynamics problems, each simulation can be relatively time-consuming so that the number of calls to black-box functions becomes the bottleneck of the overall optimization speed. To address the issues efficiently and accelerate optimization, derivative-free optimization methods are preferred to search for the optimum while avoiding construction of derivative information, and the calls to black-box functions should be minimized as well.

In this study, we attempt to modify the trust region filter (TRF) method, which was first proposed by Eason and Biegler in 2016^[1], to formulate a general optimization framework for chemical systems involving computationally expensive black-box functions. The TRF method can deal with hybrid glass box/black box optimization by using a reduced model with κ-fully linear properties for prediction, and a filter to balance the trade-off between feasibility and the objective function. However, iteratively updating reduced models means plenty of calls to black-box functions per iteration. To improve the sampling efficiency, two main contributions can be summarized in this work: By employing the Gaussian process as the reduced model, we can utilize the known data beyond the trust region to assist modelling; by using information entropy, how to sample within the trust region can be guided automatically. Through comparison and validation of benchmark tests and case study, it demonstrates that using Gaussian process as the reduced model can reduce the number of calls to black-box functions by approximately half compared to linear and quadratic models, and the guidance of information entropy enables variable number of samplings depending on the current existing information within the trust region. With this high efficiency modelling method and sampling strategy, significant improvements and quantitative speed-ups can be achieved and convergence to first-order critical points can still be guaranteed.

References

[1] Eason, J. P., & Biegler, L. T. (2016). A trust region filter method for glass box/black box optimization. AIChE Journal, 62(9), 3124-3136.