Speeding Up Logic-Based Benders Decomposition by Strengthening Cuts with Graph Neural Networks

Abstract

Logic-based Benders decomposition is a technique to solve optimization problems to optimality. It works by splitting the problem into a master problem, which neglects some aspects of the problem, and a subproblem, which is used to iteratively produce cuts for the master problem to account for those aspects. It is critical for the computational performance that these cuts are strengthened, but the strengthening of cuts comes at the cost of solving additional subproblems. In this work we apply a graph neural network in an autoregressive fashion to approximate the compilation of an irreducible cut, which then only requires few postprocessing steps to ensure its validity. We test the approach on a job scheduling problem with a single machine and multiple time windows per job and compare to approaches from the literature. Results show that our approach is capable of considerably reducing the number of subproblems that need to be solved and hence the total computational effort.