Abstract
Rather than optimizing expensive objective functions such as complex engineering simulations directly, Bayesian optimization methodologies fit a surrogate model (typically Kriging or a Gaussian Process) on evaluations of the objective function(s). To determine the next evaluation, an acquisition function is optimized (also referred to as infill criterion or sampling policy) which incorporates the model prediction and uncertainty and balances exploration and exploitation. Therefore, Bayesian optimization methodologies replace a single optimization of the objective function by a sequence of optimization problems: this makes sense as the acquisition function is cheap-to-evaluate whereas the objective is not. Depending on the goal different acquisition functions are available: multi-objective acquisition functions are relatively new and this chapter gives a state-of-the-art overview and illustrates some approaches based on hypervolume improvement. It is shown that the quality of the model is crucial for the performance of Bayesian optimization and illustrate this by using the more flexible Student-t processes as surrogate models.
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Notes
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Marginal likelihood as in: marginalized over \(\mathbf {f}\).
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Acknowledgements
Ivo Couckuyt is a post-doctoral research fellow of FWO-Vlaanderen.
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van der Herten, J., Knudde, N., Couckuyt, I., Dhaene, T. (2020). Multi-objective Bayesian Optimization for Engineering Simulation. In: Bartz-Beielstein, T., Filipič, B., Korošec, P., Talbi, EG. (eds) High-Performance Simulation-Based Optimization. Studies in Computational Intelligence, vol 833. Springer, Cham. https://doi.org/10.1007/978-3-030-18764-4_3
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