# Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs

arXiv: https://arxiv.org/abs/2502.14121 · HTML: https://mlsanity.com/paper/2502.14121/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Digital Twins: State of the Art Theory and Practice, Challenges, and Open Research Questions](https://mlsanity.com/paper/2011.02833/) (2020)
- [COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information](https://mlsanity.com/paper/2105.04114/) (2021)
- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [Global Optimization of Gaussian processes](https://mlsanity.com/paper/2005.10902/) (2020)
- [Bayesian optimization with known experimental and design constraints for chemistry applications](https://mlsanity.com/paper/2203.17241/) (2022)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations](https://mlsanity.com/paper/2305.03824/) (2023)
- [On the Implementation of a Bayesian Optimization Framework for Interconnected Systems](https://mlsanity.com/paper/2501.00967/) (2025)
- [BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification](https://mlsanity.com/paper/2405.17875/) (2024)

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

- [NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information](https://mlsanity.com/paper/2510.05516/) (2025)
- [Rethinking Trust Region Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2604.22967/) (2026)
- [RAG-Stack: Co-Optimizing RAG Serving Performance and Quality](https://mlsanity.com/paper/2608.03487/) (2026)

## Abstract (arXiv)

Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they typically impose rigid assumptions on system structure, requiring models to conform to the underlying structural assumptions of the solver rather than the solver adapting to the natural representation of the system of interest. In this chapter, we introduce a unifying approach to grey-box MOO by leveraging network representations, which provide a general and flexible framework for modeling interconnected systems as a series of function nodes that share various inputs and outputs. Specifically, we propose MOBONS, a novel Bayesian optimization-inspired algorithm that can efficiently optimize general function networks, including those with cyclic dependencies, enabling the modeling of feedback loops, recycle streams, and multi-scale simulations - features that existing methods fail to capture. Furthermore, MOBONS incorporates constraints, supports parallel evaluations, and preserves the sample efficiency of Bayesian optimization while leveraging network structure for improved scalability. We demonstrate the effectiveness of MOBONS through two case studies, including one related to sustainable process design. By enabling efficient MOO under general graph representations, MOBONS has the potential to significantly enhance the design of more profitable, resilient, and sustainable engineering systems.