  We consider a multi-objective optimization problem with objective functions
that are expensive to evaluate. The decision maker (DM) has unknown
preferences, and so the standard approach is to generate an approximation of
the Pareto front and let the DM choose from the generated non-dominated
designs. However, especially for expensive to evaluate problems where the
number of designs that can be evaluated is very limited, the true best solution
according to the DM's unknown preferences is unlikely to be among the small set
of non-dominated solutions found, even if these solutions are truly Pareto
optimal. We address this issue by using a multi-objective Bayesian optimization
algorithm and allowing the DM to select a preferred solution from a predicted
continuous Pareto front just once before the end of the algorithm rather than
selecting a solution after the end. This allows the algorithm to understand the
DM's preferences and make a final attempt to identify a more preferred
solution. We demonstrate the idea using ParEGO, and show empirically that the
found solutions are significantly better in terms of true DM preferences than
if the DM would simply pick a solution at the end.
