Learning-Augmented Decomposition Algorithms for Large-Scale Mixed-Integer Optimization

The primary objective of this presentation is to share our experiences and illustrate how two distinct classes of machine learning algorithms can be seamlessly integrated into decomposition frameworks to expedite the solution process's convergence. We exemplify this through the truck dock assignment and scheduling problem, an operational issue that requires frequent resolution throughout the day whenever the existing plan is disrupted by unforeseen events. The operational nature of this problem is crucial as the data distribution remains relatively stable over a considerable period, facilitating the accumulation of ample training data without issues caused by distribution shifts. Our focus is predominantly on two exact methods: Cut-and-Benders and Dantzig-Wolfe. However, given enough time, we also demonstrate that the same trained deep learning model can assist in constructing feasible solutions and can be incorporated into a reinforcement learning model to function as a very efficient heuristic.