[2406.03099] Supplementary Materials to Graph Convolutional Branch and Bound Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2406.03099 (cs) [Submitted on 5 Jun 2024 ( v1 ), last revised 3 Apr 2026 (this version, v4)] Title: Supplementary Materials to Graph Convolutional Branch and Bound Authors: Lorenzo Sciandra , Roberto Esposito , Andrea Cesare Grosso , Laura Sacerdote , Cristina Zucca View a PDF of the paper titled Supplementary Materials to Graph Convolutional Branch and Bound, by Lorenzo Sciandra and 3 other authors View PDF Abstract: This article explores the integration of deep learning models into combinatorial optimization pipelines, specifically targeting NP-hard problems. Traditional exact algorithms for such problems often rely on heuristic criteria to guide the exploration of feasible solutions. In this work, we propose using neural networks to learn informative heuristics, most notably, an optimality score that estimates a solution's proximity to the optimum. This score is used to evaluate nodes within a branch-and-bound framework, enabling a more efficient traversal of the solution space. Focusing on the Traveling Salesman Problem, we introduce Concorde, a state-of-the-art solver, and present a hybrid approach called Graph Convolutional Branch and Bound, which augments it with a graph convolutional neural network trained with a novel unsupervised training strategy that facilitates generalization to graphs of varying sizes without requiring labeled data. Empirical results demonstrate the effectiveness of the proposed method, showing a significant reduction in the number of explored branch-and-bound nodes and overall computational time. Some of the results concerning the use of the 1-tree relaxation are in the supplementary materials. Comments: Supplementary materials of the Graph Convolutional Branch and Bound paper Subjects: Machine Learning (cs.LG) ; Optimization and Control (math.OC) MSC classes: 68T07, 90C27 Cite as: arXiv:2406.03099 [cs.LG] (or arXiv:2406.03099v4 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2406.03099 Focus to learn more arXiv-issued DOI via DataCite Journal reference: European Journal of Operational Research (2026) Related DOI : https://doi.org/10.1016/j.ejor.2026.03.036 Focus to learn more DOI(s) linking to related resources Submission history From: Lorenzo Sciandra [ view email ] [v1] Wed, 5 Jun 2024 09:42:43 UTC (509 KB) [v2] Thu, 6 Jun 2024 07:46:26 UTC (508 KB) [v3] Thu, 10 Jul 2025 19:29:49 UTC (198 KB) [v4] Fri, 3 Apr 2026 14:38:42 UTC (168 KB) Full-text links: Access Paper: View a PDF of the paper titled Supplementary Materials to Graph Convolutional Branch and Bound, by Lorenzo Sciandra and 3 other authors View PDF TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-06 Change to browse by: cs math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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