  Recently, machine learning of the branch and bound algorithm has shown
promise in approximating competent solutions to NP-hard problems. In this
paper, we utilize and comprehensively compare the outcomes of three neural
networks--graph convolutional neural network (GCNN), GraphSAGE, and graph
attention network (GAT)--to solve the capacitated vehicle routing problem. We
train these neural networks to emulate the decision-making process of the
computationally expensive Strong Branching strategy. The neural networks are
trained on six instances with distinct topologies from the CVRPLIB and
evaluated on eight additional instances. Moreover, we reduced the minimum
number of vehicles required to solve a CVRP instance to a bin-packing problem,
which was addressed in a similar manner. Through rigorous experimentation, we
found that this approach can match or improve upon the performance of the
branch and bound algorithm with the Strong Branching strategy while requiring
significantly less computational time. The source code that corresponds to our
research findings and methodology is readily accessible and available for
reference at the following web address: https://isotlaboratory.github.io/ml4vrp
