Using Multiple Models to Inform and Optimize Complex Systems

Abstract

Modeling is crucial for decision-making in complex systems, especially when simulations or black-box models are computationally intensive. Traditional multi-fidelity optimization relies on a single most accurate model, but such a model is often unavailable in real-world scenarios with multiple, similarly uncertain models. This necessitates methods that leverage multiple models without assuming a hierarchy of accuracy. This dissertation introduces a multi-model optimization approach that utilizes the collective insights from all models by focusing on regions of consistent performance rather than a single ``best" model. The goals are to address limitations of traditional approaches, develop a methodology for models without clear accuracy ranking, and demonstrate its application in a real-world biomanufacturing system. Two applications involving complex systems are examined. The first is a military maritime communication network and the second is a variable-yield biomanufacturing process. These applications reveal the risks of assuming one model is more accurate than another. In response, the dissertation presents Set-Based Optimization with Multiple Models (S-BOMM), a framework that identifies subregions of consistently good performance across multiple models, instead of relying on a presumed hierarchy of model accuracy. Theoretical properties and empirical results are provided to further provide insight and illustration. Applying S-BOMM to the biomanufacturing application demonstrates its practical benefits, uncovering performance regions consistent across models and providing insights beyond single-model analyses. Overall, this work advances decision-making in complex systems by leveraging multiple models collectively, moving beyond traditional multi-fidelity paradigms.