  We present a multi-objective Bayesian optimisation algorithm that allows the
user to express preference-order constraints on the objectives of the type
"objective A is more important than objective B". These preferences are defined
based on the stability of the obtained solutions with respect to preferred
objective functions. Rather than attempting to find a representative subset of
the complete Pareto front, our algorithm selects those Pareto-optimal points
that satisfy these constraints. We formulate a new acquisition function based
on expected improvement in dominated hypervolume (EHI) to ensure that the
subset of Pareto front satisfying the constraints is thoroughly explored. The
hypervolume calculation is weighted by the probability of a point satisfying
the constraints from a gradient Gaussian Process model. We demonstrate our
algorithm on both synthetic and real-world problems.
