  In model-based evolutionary algorithms (EAs), the underlying search
distribution is adapted to the problem at hand, for example based on
dependencies between decision variables. Hill-valley clustering is an adaptive
niching method in which a set of solutions is clustered such that each cluster
corresponds to a single mode in the fitness landscape. This can be used to
adapt the search distribution of an EA to the number of modes, exploring each
mode separately. Especially in a black-box setting, where the number of modes
is a priori unknown, an adaptive approach is essential for good performance. In
this work, we introduce multi-objective hill-valley clustering and combine it
with MAMaLGaM, a multi-objective EA, into the multi-objective hill-valley EA
(MO-HillVallEA). We empirically show that MO-HillVallEA outperforms MAMaLGaM
and other well-known multi-objective optimization algorithms on a set of
benchmark functions. Furthermore, and perhaps most important, we show that
MO-HillVallEA is capable of obtaining and maintaining multiple approximation
sets simultaneously over time.
