What Makes an Effective Scalarising Function for Multi-Objective Bayesian Optimisation?

Performing multi-objective Bayesian optimisation by scalarising the objectives avoids computation of expensive multi-dimensional integral-based acquisition functions, instead allowing one-dimensional standard acquisition functions—such as Expected Improvement—to be applied. Here, two infill criteria based on hypervolume improvement—one recently-introduced and one novel—are compared with the multi-surrogate Expected Hypervolume Improvement. The reasons for the disparities in these methods’ effectiveness in maximising the hypervolume of the acquired Pareto Front are investigated. In addition, the effect of the surrogate model mean function on exploration and exploitation is examined: careful choice of data normalisation is shown to be preferable to the exploration parameter commonly used with the Expected Improvement acquisition function. Finally, the effectiveness of all the methodological improvements defined here are demonstrated on a real-world problem: the optimisation of a wind turbine blade aerofoil for both aerodynamic performance and structural stiffness. With effective scalarisation, Bayesian optimisation finds a large number of new aerofoil shapes which strongly dominate standard designs.