Learning heuristics for arc routing problems

Solid waste collection and street sweeping can each be formulated as a capacitated arc routing problem (CARP) in which the streets of a city require service by a fleet of vehicles at minimum total cost. Heuristic and meta-heuristic methods have been used to solve CARP because the problem is known to be NP-Hard. In this paper we introduce SPLICE, a novel machine learning framework that learns heuristics to solve routing problems, such as CARP, defined on the edges (rather than vertices) of a non-euclidean graph representation of the problem. SPLICE uses a message passing graph neural network to generate a graph embedding, and deep Q-learning feed-forward layers to learn heuristics to construct a giant tour that results in minimum total cost after applying the splitting procedure, iterating until all tasks are serviced. Compared to the two AI-driven approaches to CARP, SPLICE has a simpler network architecture and does not require a supervised learning method for training. The total costs of the solutions found by SPLICE are from 11-30% lower than those found by a path scanning heuristic and a memetic meta-heuristic algorithm. When trained on small instances, the heuristics learned by SPLICE generalize well, i.e., can be used to solve larger instances without retraining. Due to the route-first split-second form of heuristic learned, the SPLICE framework may be applied to solve other variants of routing problems by adapting the splitting procedure.