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In this study, we propose an imitation learning framework designed to enhancethe Benders decomposition method. Our primary focus is addressing degeneracy insubproblems with multiple dual optima, among which Magnanti-Wong techniqueidentifies the non-dominant solution. We develop two policies. In the firstpolicy, we replicate the Magnanti-Wong method and learn from each iteration. Inthe second policy, our objective is to determine a trajectory that expeditesthe attainment of the final subproblem dual solution. We train and assess thesetwo policies through extensive computational experiments on a network designproblem with flow subproblem, confirming that the presence of such learnedpolicies significantly enhances the efficiency of the decomposition process.

A Neural Benders Decomposition for the Hub Location Routing Problem