Neural benders decomposition for mixed-integer programming

Rahimeh Neamatian Monemi, Shahin Gelareh (), Nelson Maculan and Yu-Hong Dai
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Rahimeh Neamatian Monemi: Sharkey Predictim Globe
Shahin Gelareh: Université d’Artois
Nelson Maculan: Federal University of Rio de Janeiro, COPPE-PESC
Yu-Hong Dai: Chinese Academy of Sciencfes

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 33, issue 3, No 5, 548-579

Abstract: Abstract In this study, we propose an imitation learning framework to enhance the Benders decomposition method. This work aims to learn how to select dual values when there is a choice to be made among alternatives. To attain this objective, we mimic successful experts via two policies. In the first one, we replicate a technique for selecting non-dominated dual solutions and learn from each iteration of Benders. In the second policy, our objective is to determine a trajectory that expedites the attainment of the final subproblem’s dual solution. This approach is can be applied on a specific (or a specific class of) problem. From among different problems on which this technique has been examined, we report computational experiments on two successful cases of real-world problems. Our results confirm that incorporating these learned policies significantly enhances the efficiency of the solution process, although the first policy often outperforms the second one.

Keywords: Benders decomposition; Hub location problem; Deep learning; Graph neural network; 90C11; 90C90; 68T05; 90B06 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11750-024-00691-x

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