SOLO: Search Online, Learn Offline for Combinatorial Optimization Problems

Abstract: We study combinatorial problems with real world applications such as machine scheduling, routing, and assignment. We propose a method that combines Reinforcement Learning (RL) and planning. This method can equally be applied to both the offline, as well as online, variants of the combinatorial problem, in which the problem components (e.g., jobs in scheduling problems) are not known in advance, but rather arrive during the decision-making process. Our solution is quite generic, scalable, and leverages distributional knowledge of the problem parameters. We frame the solution process as an MDP, and take a Deep Q-Learning approach wherein states are represented as graphs, thereby allowing our trained policies to deal with arbitrary changes in a principled manner. Though learned policies work well in expectation, small deviations can have substantial negative effects in combinatorial settings. We mitigate these drawbacks by employing our graph-convolutional policies as non-optimal heuristics in a compatible search algorithm, Monte Carlo Tree Search, to significantly improve overall performance. We demonstrate our method on two problems: Machine Scheduling and Capacitated Vehicle Routing. We show that our method outperforms custom-tailored mathematical solvers, state of the art learning-based algorithms, and common heuristics, both in computation time and performance.