  Multi-objective combinatorial optimization (MOCO) problems are prevalent in
various real-world applications. Most existing neural MOCO methods rely on
problem decomposition to transform an MOCO problem into a series of
singe-objective combinatorial optimization (SOCO) problems. However, these
methods often approximate partial regions of the Pareto front and spend
excessive time on diversity enhancement because of ambiguous decomposition and
time-consuming precise hypervolume calculation. To address these limitations,
we design a Geometry-Aware Pareto set Learning algorithm named GAPL, which
provides a novel geometric perspective for neural MOCO via a Pareto attention
model based on hypervolume expectation maximization. In addition, we propose a
hypervolume residual update strategy to enable the Pareto attention model to
capture both local and non-local information of the Pareto set/front. We also
design a novel inference approach to further improve quality of the solution
set and speed up hypervolume calculation. Experimental results on three classic
MOCO problems demonstrate that our GAPL outperforms several state-of-the-art
baselines via superior decomposition and efficient diversity enhancement.
