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Automatic Relaxation and Multi-Armed Bandit Learning for Large Neighbourhood Search

Authors Frej Knutar Lewander , Pierre Flener , Justin Pearson , Peter J. Stuckey

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Subject Classification

ACM Subject Classification
  • Computing methodologies → Heuristic function construction
Keywords
  • Combinatorial Optimisation
  • Large Neighbourhood Search (LNS)
  • Constraint-Based Local Search (CBLS)

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Abstract

Inspired by concepts of constraint-based local search, we present a novel scheme for automatically relaxing a given high-level model into an optimisation model that is better suited for large neighbourhood search (LNS). By exploiting the variable sharing and semantics of the constraints in a model, our scheme (1) identifies constraints that can easily be satisfied simultaneously and can thus constrain the neighbourhood, and (2) relaxes the remaining constraints. As a side effect, our scheme enables the LNS solving of a constraint satisfaction problem, by transforming it into an optimisation problem, and the faster solving of a difficult-to-satisfy constrained optimisation problem, by finding the initial incumbent faster. This scheme can be used with any CP-based LNS solver. We tested a portfolio of CP-based LNS variants running in parallel, with a multi-armed bandit to select which LNS variant to run. Our results show that this approach is very competitive.

Cite As Get BibTex

Frej Knutar Lewander, Pierre Flener, Justin Pearson, and Peter J. Stuckey. Automatic Relaxation and Multi-Armed Bandit Learning for Large Neighbourhood Search. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.35

Author Details

Frej Knutar Lewander
  • Uppsala University, Department of Information Technology, Uppsala, Sweden
Pierre Flener
  • Uppsala University, Department of Information Technology, Uppsala, Sweden
Justin Pearson
  • Uppsala University, Department of Information Technology, Uppsala, Sweden
Peter J. Stuckey
  • Monash University, Melbourne, Australia
  • OPTIMA ARC Industrial Training and Transformation Centre, Melbourne, Australia

Funding

Supported by grants 2018-04813 and 2025-039039 of the Swedish Research Council (VR), and the Australian Research Council OPTIMA ITTC, Project ID IC200100009. The first author visited the fourth author on stipends by Anna Maria Lundin’s Scholarship Committee (Smålands Nation) and by the Swedish Operations Research Association (SOAF).

Acknowledgements

We thank Guido Tack for his help with the Gecode implementation.

Supplementary Materials

References

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