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

TL;DR

This paper introduces a machine learning approach using deep Q-learning and graph neural networks to develop a generic value-selection heuristic for constraint programming solvers, improving efficiency across multiple combinatorial problems.

Contribution

It presents the first generic learning procedure for value-selection heuristics in constraint programming, combining deep Q-learning with graph neural networks.

Findings

Achieves better solutions close to optimality

Reduces the number of backtracks needed

Demonstrates effectiveness across multiple problems

Abstract

Constraint programming is known for being an efficient approach for solving combinatorial problems. Important design choices in a solver are the branching heuristics, which are 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. To the best of our knowledge, it is still an open research question. Although several generic variable-selection heuristics are available in the literature, the options for a generic value-selection heuristic are more scarce. In this paper, 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 architecture. Experiments on graph coloring, maximum independent set, and maximum cut problems show that our framework is able to find better solutions close to optimality without requiring a large amounts of backtracks while being generic.