  Domination-based multi-objective (MO) evolutionary algorithms (EAs) are today
arguably the most frequently used type of MOEA. These methods however stagnate
when the majority of the population becomes non-dominated, preventing
convergence to the Pareto set. Hypervolume-based MO optimization has shown
promising results to overcome this. Direct use of the hypervolume however
results in no selection pressure for dominated solutions. The recently
introduced Sofomore framework overcomes this by solving multiple interleaved
single-objective dynamic problems that iteratively improve a single
approximation set, based on the uncrowded hypervolume improvement (UHVI). It
thereby however loses many advantages of population-based MO optimization, such
as handling multimodality. Here, we reformulate the UHVI as a quality measure
for approximation sets, called the uncrowded hypervolume (UHV), which can be
used to directly solve MO optimization problems with a single-objective
optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary
algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically
available grey-box properties of this problem. The resulting algorithm,
UHV-GOMEA, is compared to Sofomore equipped with GOMEA, and the
domination-based MO-GOMEA. In doing so, we investigate in which scenarios
either domination-based or hypervolume-based methods are preferred. Finally, we
construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and
outperforms both.
