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DOI: 10.4230/LIPIcs.CP.2026.35

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

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

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

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.

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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)

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@InProceedings{knutarlewander_et_al:LIPIcs.CP.2026.35,
  author =	{Knutar Lewander, Frej and Flener, Pierre and Pearson, Justin and Stuckey, Peter J.},
  title =	{{Automatic Relaxation and Multi-Armed Bandit Learning for Large Neighbourhood Search}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.35},
  URN =		{urn:nbn:de:0030-drops-266675},
  doi =		{10.4230/LIPIcs.CP.2026.35},
  annote =	{Keywords: Combinatorial Optimisation, Large Neighbourhood Search (LNS), Constraint-Based Local Search (CBLS)}
}

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DOI: 10.4230/LIPIcs.CP.2025.20

Dependency-Curated Large Neighbourhood Search

Authors: Frej Knutar Lewander, Pierre Flener, and Justin Pearson

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract

In large neighbourhood search (LNS), an incumbent initial solution is incrementally improved by selecting a subset of the variables, called the freeze set, and fixing them to their values in the incumbent solution, while a value for each remaining variable is found and assigned via solving (such as constraint programming-style propagation and search). Much research has been performed on finding generic and problem-specific LNS selection heuristics that select freeze sets that lead to high-quality solutions. In constraint-based local search (CBLS), the relations between the variables via the constraints are fundamental and well-studied, as they capture dependencies of the variables. In this paper, we apply these ideas from CBLS to the LNS context, presenting the novel dependency curation scheme, which exploits them to find a low-cardinality set of variables that the freeze set of any selection heuristic should be a subset of. The scheme often improves the overall performance of generic selection heuristics. Even when the scheme is used with a naïve generic selection heuristic that selects random freeze sets, the performance is competitive with more elaborate generic selection heuristics.

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Frej Knutar Lewander, Pierre Flener, and Justin Pearson. Dependency-Curated Large Neighbourhood Search. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{knutarlewander_et_al:LIPIcs.CP.2025.20,
  author =	{Knutar Lewander, Frej and Flener, Pierre and Pearson, Justin},
  title =	{{Dependency-Curated Large Neighbourhood Search}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.20},
  URN =		{urn:nbn:de:0030-drops-238810},
  doi =		{10.4230/LIPIcs.CP.2025.20},
  annote =	{Keywords: Combinatorial Optimisation, Large Neighbourhood Search (LNS), Constraint-Based Local Search (CBLS)}
}

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

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Dependency-Curated Large Neighbourhood Search

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