Learning a Generic Value-Selection Heuristic Inside a Constraint Programming Solver

Constraint programming is known for being an efficient approach to solving combinatorial problems. Important design choices in a solver are the branching heuristics, designed to lead the search to the best solutions in a minimum amount of time. However, developing these heuristics is a time-consuming process that requires problem-specific expertise. This observation has motivated many efforts to use machine learning to automatically learn efficient heuristics without expert intervention. Although several generic variable-selection heuristics are available in the literature, the options for value-selection heuristics are more scarce. We propose to tackle this issue by introducing a generic learning procedure that can be used to obtain a value-selection heuristic inside a constraint programming solver. This has been achieved thanks to the combination of a deep Q-learning algorithm, a tailored reward signal, and a heterogeneous graph neural network. Experiments on graph coloring, maximum independent set, and maximum cut problems show that this framework competes with the well-known impact-based and activity-based search heuristics and can find solutions close to optimality without requiring a large number of backtracks.