Exact solving scheduling problems accelerated by graph neural networks

Scheduling is a family of combinatorial problems where we need to find optimal time arrangements for activities. Scheduling problems in applications are usually notoriously hard to solve exactly. Existing exact solving procedures, based on mathematical programming and constraint programming, usually make manually-tuned heuristic choices. These heuristics can be improved by machine learning. In this paper, we apply the graph convolutional neural network from the literature on speeding up general branch&bound solver by learning its branching decisions. We test the augmented solver on job-shop scheduling problems and specific delivery scheduling problems in the supply chain of a local retailer. We get promising results and point to possible improvements. We discuss the interesting question of how much we can accelerate solving NP-hard problems in the light of the known limits and impossibility results in AI.