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Constraint-Aware Self-Supervised Learning for Edge Selection

Authors Xinda Zheng , Frits de Nijs , Edward Lam

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LIPIcs.CP.2026.61.pdf
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Subject Classification

ACM Subject Classification
  • Computing methodologies → Machine learning approaches
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Combinatorial Optimization
  • Learning to optimize
  • Graph neural networks

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Abstract

Many edge-selection problems, such as the Traveling Salesman Problem and Orienteering Problem, are NP-hard, making them expensive to solve with exact methods and challenging to address with hand-crafted heuristics. Learning-based approaches provide an efficient alternative, while self-supervised methods avoid costly solution labels. However, existing approaches often still rely on heavy post-processing or narrow problem-specific designs. We propose a reusable self-supervised framework for edge-selection optimization that learns directly from unlabeled instances. The framework uses differentiable surrogate objectives and feasibility-driven penalties to encourage the model to learn feasibility-aware solution structure during training. To support efficient inference, we introduce a lightweight graph architecture centered on a cost-attention convolution, where edge costs and feasibility information directly shape message passing. Experiments on three problem families demonstrate strong solution quality and efficient inference across diverse edge-selection settings.

Cite As Get BibTex

Xinda Zheng, Frits de Nijs, and Edward Lam. Constraint-Aware Self-Supervised Learning for Edge Selection. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.61

Author Details

Xinda Zheng
  • Department of Data Science and AI, Faculty of IT, Monash University, Clayton, Australia
  • OPTIMA ARC Training Centre, Melbourne, Australia
Frits de Nijs
  • Department of Data Science and AI, Faculty of IT, Monash University, Clayton, Australia
  • OPTIMA ARC Training Centre, Melbourne, Australia
Edward Lam
  • Department of Data Science and AI, Faculty of IT, Monash University, Clayton, Australia
  • OPTIMA ARC Training Centre, Melbourne, Australia

Funding

This work was supported by the Australian Research Council under grant DE240100042 and the China Scholarship Council under grant 202508240018.

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