  Many real-world multi-objective optimisation problems rely on computationally
expensive function evaluations. Multi-objective Bayesian optimisation (BO) can
be used to alleviate the computation time to find an approximated set of Pareto
optimal solutions. In many real-world problems, a decision-maker has some
preferences on the objective functions. One approach to incorporate the
preferences in multi-objective BO is to use a scalarising function and build a
single surrogate model (mono-surrogate approach) on it. This approach has two
major limitations. Firstly, the fitness landscape of the scalarising function
and the objective functions may not be similar. Secondly, the approach assumes
that the scalarising function distribution is Gaussian, and thus a closed-form
expression of an acquisition function e.g., expected improvement can be used.
We overcome these limitations by building independent surrogate models
(multi-surrogate approach) on each objective function and show that the
distribution of the scalarising function is not Gaussian. We approximate the
distribution using Generalised value distribution. We present an a-priori
multi-surrogate approach to incorporate the desirable objective function values
(or reference point) as the preferences of a decision-maker in multi-objective
BO. The results and comparison with the existing mono-surrogate approach on
benchmark and real-world optimisation problems show the potential of the
proposed approach.
