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Recently, machine learning of the branch and bound algorithm has shownpromise in approximating competent solutions to NP-hard problems. In thispaper, we utilize and comprehensively compare the outcomes of three neuralnetworks--graph convolutional neural network (GCNN), GraphSAGE, and graphattention network (GAT)--to solve the capacitated vehicle routing problem. Wetrain these neural networks to emulate the decision-making process of thecomputationally expensive Strong Branching strategy. The neural networks aretrained on six instances with distinct topologies from the CVRPLIB andevaluated on eight additional instances. Moreover, we reduced the minimumnumber of vehicles required to solve a CVRP instance to a bin-packing problem,which was addressed in a similar manner. Through rigorous experimentation, wefound that this approach can match or improve upon the performance of thebranch and bound algorithm with the Strong Branching strategy while requiringsignificantly less computational time. The source code that corresponds to ourresearch findings and methodology is readily accessible and available forreference at the following web address: https://isotlaboratory.github.io/ml4vrp

On Statistical Learning of Branch and Bound for Vehicle Routing Optimization