A Neural Benders Decomposition for the Hub Location Routing Problem

TL;DR

This paper introduces a neural imitation learning framework to improve Benders decomposition for the Hub Location Routing Problem, effectively addressing degeneracy issues and accelerating convergence.

Contribution

It develops two novel policies that replicate and optimize the Magnanti-Wong technique, significantly enhancing the efficiency of Benders decomposition in network design problems.

Findings

Learned policies improve decomposition efficiency

Significant reduction in computational time

Effective handling of degeneracy in subproblems

Abstract

In this study, we propose an imitation learning framework designed to enhance the Benders decomposition method. Our primary focus is addressing degeneracy in subproblems with multiple dual optima, among which Magnanti-Wong technique identifies the non-dominant solution. We develop two policies. In the first policy, we replicate the Magnanti-Wong method and learn from each iteration. In the second policy, our objective is to determine a trajectory that expedites the attainment of the final subproblem dual solution. We train and assess these two policies through extensive computational experiments on a network design problem with flow subproblem, confirming that the presence of such learned policies significantly enhances the efficiency of the decomposition process.