System Architecture Optimization Strategies: Dealing with Expensive Hierarchical Problems

TL;DR

This paper tackles System Architecture Optimization (SAO) by addressing mixed-discrete, hierarchical, constrained, multi-objective, and expensive-evaluation challenges. It advances both MOEA and Bayesian Optimization approaches, introducing hierarchy-aware metrics ($IR$, $CR$, $CRF$, $MRD$) and a Gaussian process kernel for hierarchical categorical variables, plus hierarchical sampling and correction methods. It demonstrates that incorporating hierarchy information into BO substantially reduces function evaluations while maintaining or improving optimization quality, as shown in jet-engine experiments where BO achieved near-optimal results with orders of magnitude fewer evaluations than NSGA-II. The work is implemented in the open-source SBArchOpt library and offers practical tools for practitioners to model, sample, correct, and optimize hierarchical SAO problems, with a path toward larger, multi-fidelity, and graph-based design spaces.

Abstract

Choosing the right system architecture for the problem at hand is challenging due to the large design space and high uncertainty in the early stage of the design process. Formulating the architecting process as an optimization problem may mitigate some of these challenges. This work investigates strategies for solving System Architecture Optimization (SAO) problems: expensive, black-box, hierarchical, mixed-discrete, constrained, multi-objective problems that may be subject to hidden constraints. Imputation ratio, correction ratio, correction fraction, and max rate diversity metrics are defined for characterizing hierar chical design spaces. This work considers two classes of optimization algorithms for SAO: Multi-Objective Evolutionary Algorithms (MOEA) such as NSGA-II, and Bayesian Optimization (BO) algorithms. A new Gaussian process kernel is presented that enables modeling hierarchical categorical variables, extending previous work on modeling continuous and integer hierarchical variables. Next, a hierarchical sampling algorithm that uses design space hierarchy to group design vectors by active design variables is developed. Then, it is demonstrated that integrating more hierarchy information in the optimization algorithms yields better optimization results for BO algorithms. Several realistic single-objective and multi-objective test problems are used for investigations. Finally, the BO algorithm is applied to a jet engine architecture optimization problem. This work shows that the developed BO algorithm can effectively solve the problem with one order of magnitude less function evaluations than NSGA-II. The algorithms and problems used in this work are implemented in the open-source Python library SBArchOpt.

Figures (7)

• Figure 1: Illustration of correction and imputation in hierarchical design spaces, showing how the Cartesian product of all discrete values relates to the set of correct, imputed, and valid design vectors. Correction (step 2) modifies design variables such that value constraints are satisfied. Imputation (step 3) assigns canonical values to inactive design variables. $\delta_i$ represents the activeness function of design variable $x_i$.
• Figure 2: Principle of Surrogate-Based Optimization (SBO), adopted from Bussemaker2021
• Figure 3: A visualization of different eager correction strategies
• Figure 4: High-level strategies for dealing with hierarchical optimization
• Figure 5: Overview of the jet engine optimization testing framework. The user provides the problem definition (in terms of design variables and metrics selected from a database) and the flight conditions and power offtakes to size the engine for. Engine schematic adapted from original by K. Aainsqatsi, available at https://commons.wikimedia.org/wiki/File:Turbofan_operation.svg.