Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization


  • Quentin Cappart Polytechnique Montréal
  • Thierry Moisan Element AI
  • Louis-Martin Rousseau Polytechnique Montréal
  • Isabeau Prémont-Schwarz Element AI
  • Andre A. Cire University of Toronto



Constraint Programming, Reinforcement Learning


Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have an important shortcoming: they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve three challenging problems: the traveling salesman problem with time windows, the 4-moments portfolio optimization problem, and the 0-1 knapsack problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.




How to Cite

Cappart, Q., Moisan, T., Rousseau, L.-M., Prémont-Schwarz, I., & Cire, A. A. (2021). Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization. Proceedings of the AAAI Conference on Artificial Intelligence, 35(5), 3677-3687.



AAAI Technical Track on Constraint Satisfaction and Optimization