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

2025-02-19

AI Summary

Modern industrial systems require simultaneous optimization of profitability, resilience, and sustainability; however, existing gray-box multi-objective optimization methods rely on rigid structural assumptions—such as acyclicity and hierarchical decomposition—that hinder their application to realistic complex networks featuring feedback loops, cyclic material/energy flows, and multi-scale simulations. To address this, we propose MOBONS: the first multi-objective Bayesian optimization framework designed for general directed graphs (including cyclic function networks). MOBONS integrates graph neural network–based surrogate modeling, constraint-aware acquisition functions, and parallel evaluation strategies, achieving both high sample efficiency and improved scalability. In benchmark applications—including sustainable process design—MOBONS efficiently generates high-quality Pareto fronts, overcoming the topological limitations of conventional gray-box approaches. This work establishes a new paradigm for green, profitable, and robust co-design of complex engineering systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Balancing profitability, resilience, and sustainability
• Optimizing complex networked black-box systems
• Enhancing design efficiency with Bayesian optimization

Innovation

• Bayesian optimization-inspired algorithm
• General function networks optimization
• Incorporates constraints and parallel evaluations