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.

翻译：设计现代工业系统需要在技术、经济和环境因素复杂交互作用下，平衡盈利能力、韧性与可持续性等多个相互冲突的目标。多目标优化方法常被用于权衡这些目标，但针对此类问题如何选择合适的算法往往并不明确，尤其是在系统表征方式从完全基于方程的白箱模型到完全数据驱动的黑箱模型连续变化的情况下。虽然灰箱多目标优化方法试图弥合这一鸿沟，但它们通常对系统结构施加刚性假设，要求模型必须符合求解器的底层结构假设，而非让求解器适应目标系统的自然表征方式。本章通过引入网络表征提出了一种统一的灰箱多目标优化方法，该框架将互联系统建模为共享多种输入输出的函数节点序列，提供了通用且灵活的建模范式。具体而言，我们提出了MOBONS——一种受贝叶斯优化启发的新型算法，能够高效优化包含循环依赖关系的通用函数网络，从而实现对反馈回路、循环流和多尺度模拟等现有方法无法捕捉特征的建模。此外，MOBONS能够处理约束条件、支持并行评估，在利用网络结构提升可扩展性的同时保持了贝叶斯优化的样本效率。我们通过两个案例研究（包括可持续过程设计案例）验证了MOBONS的有效性。通过在通用图表示下实现高效多目标优化，MOBONS有望显著提升工程系统在盈利性、韧性与可持续性方面的设计水平。