  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.

Optimization and Control