Surrogate-based optimization of system architectures subject to hidden constraints

TL;DR

This work tackles the optimization of system architectures under hidden constraints, where physics-based evaluations are expensive and can fail. It develops a Bayesian Optimization framework (ArchSBO) that combines hierarchical mixed-discrete Gaussian Processes, ensemble infill criteria, hierarchical sampling, and a correction/imputation repair operator to navigate complex SAO spaces. A key contribution is the explicit treatment of hidden constraints via Rejection, Replacement, and Prediction strategies using a Probability of Viability (PoV) predictor, with PoV-based constraints or penalties guiding infill selection; MD-GP and Random Forest predictors emerge as the most robust options, with PoV_min set around 25%. The Jet Engine Architecture Optimization example demonstrates substantial efficiency gains, solving problems with a 50% failure rate in a fraction of the evaluations required by prior methods, and the open-source SBArchOpt library provides practical tools for practitioners.

Abstract

The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and evaluations might fail. The former challenge is addressed by Surrogate-Based Optimization (SBO) algorithms, in particular Bayesian Optimization (BO) using Gaussian Process (GP) models. An overview is provided of how BO can deal with challenges specific to architecture optimization, such as design variable hierarchy and multiple objectives: specific measures include ensemble infills and a hierarchical sampling algorithm. Evaluations might fail due to non-convergence of underlying solvers or infeasible geometry in certain areas of the design space. Such failed evaluations, also known as hidden constraints, pose a particular challenge to SBO/BO, as the surrogate model cannot be trained on empty results. This work investigates various strategies for satisfying hidden constraints in BO algorithms. Three high-level strategies are identified: rejection of failed points from the training set, replacing failed points based on viable (non-failed) points, and predicting the failure region. Through investigations on a set of test problems including a jet engine architecture optimization problem, it is shown that best performance is achieved with a mixed-discrete GP to predict the Probability of Viability (PoV), and by ensuring selected infill points satisfy some minimum PoV threshold. This strategy is demonstrated by solving a jet engine architecture problem that features at 50% failure rate and could not previously be solved by a BO algorithm. The developed BO algorithm and used test problems are available in the open-source Python library SBArchOpt.

Figures (5)

• Figure 1: Principle of Surrogate-Based Optimization (SBO), reproduced from Bussemaker2024.
• Figure 2: Illustration of correction and imputation in hierarchical design spaces, showing how the different sets of design vectors relate to each other, reproduced from Bussemaker2024.
• Figure 3: Several optimization steps between iteration 1 and 20 of BO executed on a test problem with its optimum lying at the edge to the failed region, as shown in the bottom row by the magenta cross. The main GP is shown on the left (darker means a lower, more optimal value), and the RBF model for predicting PoV is shown on the right. The RBF model is used as an infill constraint with $\mathrm{PoV}_{\mathrm{min}} = 50\%$, showing green and red contours for satisfied and violated constraint values, respectively. Green, red, and magenta points represent viable, failed, and selected infill points, respectively.
• Figure 4: Comparison of hidden constraint strategy settings relative to the rejection strategy, averaged over all test problems at the end of the optimization runs. Abbreviations: HV = hypervolume, MD = mixed-discrete, GP = Gaussian Process, RFC = Random Forest Classifier.
• Figure 5: Optimization progression of the BO algorithm with the prediction hidden constraint strategy with two different predictors for the jet engine optimization problem. $\Delta \mathrm{HV}$ represents the distance to the known Pareto front. The bands around the lines represent the 50 percentile range around the median, obtained from 24 repeated runs. Abbreviations: MD = mixed-discrete, GP = Gaussian Process, RFC = Random Forest Classifier.