Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions

Abstract

Multi-objective optimization of complex engineering systems is a challenging problem. The design goals can exhibit dynamic and nonlinear behaviour with respect to the system's parameters. Additionally, modern engineering is driven by simulationbased design which can be computationally expensive due to the complexity of the system under study. Bayesian optimization (BO) is a popular technique to tackle this kind of problem. In multi-objective BO, a data-driven surrogate model is created for each design objective. However, not all of the objectives may be expensive to compute. We develop an approach that can deal with a mix of expensive and cheap-to-evaluate objective functions. As a result, the proposed technique offers lower complexity than standard multi-objective BO methods and performs significantly better when the cheap objective function is difficult to approximate. In particular, we extend the popular hypervolume-based Expected Improvement (EI) and Probability of Improvement (POI) in bi-objective settings. The proposed methods are validated on multiple benchmark functions and two real-world engineering design optimization problems, showing that it performs better than its non-cheap counterparts. Furthermore, it performs competitively or better compared to other optimization methods.

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