A Comprehensive Study of Gaussian Process-Based Multi-Objective Multi-Fidelity Modeling Techniques and its Applications to Shell and Tube Heat Exchanger Design

In numerous automotive and industrial applications, efficient heat extraction is crucial to prevent system inefficiencies or catastrophic failures. The design of heat exchangers is inherently complex, involving multiple stages defined by the depth of analysis, number of design variables, and the accuracy of physical models. Designers must navigate the trade-offs between highly accurate yet computationally expensive models and less accurate but computationally cheaper alternatives. Multi-fidelity modeling offers a solution by integrating different fidelity models to deliver precise results at a reduced computational cost. In addition to managing these trade-offs, designers often face multi-objective challenges, where optimizing one aspect may lead to compromises in others. Multi-objective optimization, therefore, becomes essential in balancing these competing objectives to achieve the best overall design. In this context, Gaussian Process-based methods have gained prominence as effective tools for integrating information from models of varying fidelities while simultaneously addressing multiple objectives. A key component of multi-fidelity modeling is understanding the relationships between these fidelity models. This paper explores various Gaussian Process-based multi-fidelity and multi-objective optimization techniques, focusing on the different types of relationships between fidelity models, such as linearity, non-linearity, and variable correlation. Each technique is discussed within a unified design automation framework, with an emphasis on the connections between different methodologies. These approaches are evaluated through plate fin heat exchanger-related engineering problems to determine their respective advantages and limitations relative to specific problem characteristics.