# Surrogate-based optimization of system architectures subject to hidden constraints

arXiv: https://arxiv.org/abs/2504.08721 · HTML: https://mlsanity.com/paper/2504.08721/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Bayesian optimization of variable-size design space problems](https://mlsanity.com/paper/2003.03300/) (2020)
- [A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables](https://mlsanity.com/paper/2204.00886/) (2022)
- [System Architecture Optimization Strategies: Dealing with Expensive Hierarchical Problems](https://mlsanity.com/paper/2502.00838/) (2025)
- [A First Analysis of Kernels for Kriging-based Optimization in Hierarchical Search Spaces](https://mlsanity.com/paper/1807.01011/) (2018)
- [Hidden-Variables Genetic Algorithm for Variable-Size Design Space Optimal Layout Problems with Application to Aerospace Vehicles](https://mlsanity.com/paper/2212.11011/) (2022)

## Built on by (most cited first, 3 of 3)

- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobility](https://mlsanity.com/paper/2507.08715/) (2025)
- [Efficient multidisciplinary design via Bayesian optimization](https://mlsanity.com/paper/2607.22560/) (2026)

## Abstract (arXiv)

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.