  Combinatorial optimization (CO) on graphs is a classic topic that has been
extensively studied across many scientific and industrial fields. Recently,
solving CO problems on graphs through learning methods has attracted great
attention. Advanced deep learning methods, e.g., graph neural networks (GNNs),
have been used to effectively assist the process of solving COs. However,
current frameworks based on GNNs are mainly designed for certain CO problems,
thereby failing to consider their transferable and generalizable abilities
among different COs on graphs. Moreover, simply using original graphs to model
COs only captures the direct correlations among objects, which does not
consider the mathematical logicality and properties of COs. In this paper, we
propose a unified pre-training and adaptation framework for COs on graphs with
the help of the maximum satisfiability (Max-SAT) problem. We first use Max-SAT
to bridge different COs on graphs since they can be converted to Max-SAT
problems represented by standard formulas and clauses with logical information.
Then, we further design a pre-training and domain adaptation framework to
extract the transferable and generalizable features so that different COs can
benefit from them. In the pre-training stage, Max-SAT instances are generated
to initialize the parameters of the model. In the fine-tuning stage, instances
from CO and Max-SAT problems are used for adaptation so that the transferable
ability can be further improved. Numerical experiments on several datasets show
that features extracted by our framework exhibit superior transferability and
Max-SAT can boost the ability to solve COs on graphs.
